> S <> , <>
----------------
<

> S <>
Theorem (71) [serial 1181] used for:
add user-defined axioms to precondition:
<

> S <>
Theorem (73) [serial 1095]
P [271] <

> -> <**> and <****> -> < > then <> p! < >
and theorems 95 98:
Theorem (95) [serial 1116] used for:
applied port output <**

> -> <> [serial 1106] Theorem (98) [serial 1117] used for: applied port output < > -> <> [serial 1106] Theorem (100) [serial 1179] P [273] < > S [277] -> Q [278] < > by True Conclusion Schema (tc): P->true Theorem (101) [serial 1137] P [273] < > S [277] -> Q [278] < > by Equality Law (idistr): a=a <-> true Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 100: Theorem (100) [serial 1179] used for: Equality Law (idistr): a=a <-> true [serial 1137] Theorem (102) [serial 1118] P [273] < > S [277] -> Q [278] < > by Normalization and theorem 101: Theorem (101) [serial 1137] used for: normalize [serial 1118] Theorem (103) [serial 1107] P [273] < > S [277] last_vp_or_vs := now Q [278] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 102: Theorem (102) [serial 1118] used for: applied wp for assignment [serial 1107] Theorem (104) [serial 1096] P [273] <> S [276] < > vp! < > & last_vp_or_vs := now < > Q [276] <<(vp@now) and (last_vp_or_vs = now)>> by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < > -> <

> < > S1 < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 75 77 99 103: Theorem (75) [serial 1104] used for: P -> P1 in concurrent composition for [serial 1096] Theorem (77) [serial 1105] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1096] Theorem (99) [serial 1106] used for: < > S1 < > in concurrent composition for [serial 1096] Theorem (103) [serial 1107] used for: < > S2 <

> in concurrent composition for [serial 1096] Theorem (105) [serial 1255] P [276] < > S [272] -> Q [280] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (106) [serial 1251] P [276] < > S [272] -> Q [280] <<((vp@now)) or ((vs@now))>> by Normalization and theorem 105: Theorem (105) [serial 1255] used for: normalize [serial 1251] Theorem (107) [serial 1245] P [276] < > S [272] -> Q [280] <<(vp@now and true) or (vs@now and true)>> by Law of And-Simplification: P and true is P Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 106: Theorem (106) [serial 1251] used for: Law of And-Simplification: P and true is P [serial 1245] Theorem (108) [serial 1241] P [276] < > S [272] -> Q [280] <<(vp@now and not ((false))) or (vs@now and not ((false)))>> by Normalization and theorem 107: Theorem (107) [serial 1245] used for: normalize [serial 1241] Theorem (109) [serial 1240] P [276] < > S [272] -> Q [280] <<(vp@now and not ((false) or (false))) or (vs@now and not ((false) or (false)))>> by Law of Or-Simplification: P or P is P and theorem 108: Theorem (108) [serial 1241] used for: Law of Or-Simplification: P or P is P [serial 1240] Theorem (110) [serial 1237] P [276] < > S [272] -> Q [280] <<(vp@now and not ((exists t:BLESS_Types::Time in now,,now that vp@t ) or (exists t:BLESS_Types::Time in now,,now that vs@t ))) or (vs@now and not ((exists t:BLESS_Types::Time in now,,now that vp@t ) or (exists t:BLESS_Types::Time in now,,now that vs@t )))>> by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 109: Theorem (109) [serial 1240] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1237] Theorem (111) [serial 1229] P [276] < > S [272] -> Q [280] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Substitution in Postcondition of All Equivalents in Precondition Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 110: Theorem (110) [serial 1237] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1229] Theorem (112) [serial 1223] P [276] < > S [272] -> Q [280] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Normalization and theorem 111: Theorem (111) [serial 1229] used for: normalize [serial 1223] Theorem (113) [serial 1220] P [276] < > S [272] -> Q [280] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and and theorem 112: Theorem (112) [serial 1223] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1220] Theorem (114) [serial 1208] P [276] < > S [272] -> Q [280] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 113: Theorem (113) [serial 1220] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 1208] Theorem (115) [serial 1201] P [276] < > S [272] -> Q [280] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 114: Theorem (114) [serial 1208] used for: normalize [serial 1201] Theorem (116) [serial 1194] P [276] < > S [272] -> Q [280] < > by Substitution of Assertion Labels and theorem 115: Theorem (115) [serial 1201] used for: substituted Assertions' predicates for labels in postconditions [serial 1194] Theorem (117) [serial 1230] P [276] < > S [272] -> Q [280] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t ) or vp@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (118) [serial 1225] P [276] < > S [272] -> Q [280] <<(vp@now) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Normalization and theorem 117: Theorem (117) [serial 1230] used for: normalize [serial 1225] Theorem (119) [serial 1224] P [276] < > S [272] -> Q [280] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 118: Theorem (118) [serial 1225] used for: replace exists with upper or lower bound [serial 1224] Theorem (120) [serial 1221] P [276] < > S [272] -> Q [280] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and and theorem 119: Theorem (119) [serial 1224] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1221] Theorem (121) [serial 1209] P [276] < > S [272] -> Q [280] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 120: Theorem (120) [serial 1221] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 1209] Theorem (122) [serial 1202] P [276] < > S [272] -> Q [280] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 121: Theorem (121) [serial 1209] used for: normalize [serial 1202] Theorem (123) [serial 1195] P [276] < > S [272] -> Q [280] < > by Substitution of Assertion Labels and theorem 122: Theorem (122) [serial 1202] used for: substituted Assertions' predicates for labels in postconditions [serial 1195] Theorem (124) [serial 1138] P [276] < > S [272] -> Q [280] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 116 123: Theorem (116) [serial 1194] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1138] Theorem (123) [serial 1195] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1138] Theorem (125) [serial 1097] P [276] <<(vp@now) and (last_vp_or_vs = now)>> S [272] -> Q [280] < > by Normalization and theorem 124: Theorem (124) [serial 1138] used for: normalize [serial 1097] Theorem (126) [serial 1092] P [271] < > S [272] { < > vp! < > & last_vp_or_vs := now < > } Q [280] < > by Introduction of Existential Quantification (bl.elq) and theorems 73 104 125: Theorem (73) [serial 1095] used for: < > -> <> in existential lattice quantification for [serial 1092] Theorem (104) [serial 1096] used for: {A} T {B} in existential lattice quantification for [serial 1092] Theorem (125) [serial 1097] used for: <

> -> <> in existential lattice quantification for [serial 1092] Theorem (127) [serial 1098] P [282] <> S [284] -> Q [284] < > by Identity (id): P->P is tautology Theorem (128) [serial 1108] P [284] < > S [284] -> Q [284] < > by Identity (id): P->P is tautology Theorem (129) [serial 1141] P [287] < > S [286] -> Q [287] < > by Identity (id): P->P is tautology Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (130) [serial 1109] P [287] < > S [286] -> Q [287] <<(as@now) and (last_as = now)>> by Normalization and theorem 129: Theorem (129) [serial 1141] used for: normalize [serial 1109] Theorem (131) [serial 1119] P [284] < > S [285] -> Q [1] < > by Identity (id): P->P is tautology Theorem (132) [serial 1143] P [285] < > S [285] -> Q [286] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (133) [serial 1120] P [285] <<(AS(now)) and as@now>> S [285] -> Q [286] < > by Normalization and theorem 132: Theorem (132) [serial 1143] used for: normalize [serial 1120] Theorem (134) [serial 1110] P [284] < > S [285] as! Q [286] < > by Port Event Output: when < > -> <> and <> -> <> then < > p! <> and theorems 131 133: Theorem (131) [serial 1119] used for: applied port output <> -> <> [serial 1110] Theorem (133) [serial 1120] used for: applied port output < > -> <> [serial 1110] Theorem (135) [serial 1175] P [284] < > S [288] -> Q [289] < > by True Conclusion Schema (tc): P->true Theorem (136) [serial 1121] P [284] < > S [288] -> Q [289] < > by Equality Law (idistr): a=a <-> true and theorem 135: Theorem (135) [serial 1175] used for: Equality Law (idistr): a=a <-> true [serial 1121] Theorem (137) [serial 1111] P [284] < > S [288] last_as := now Q [289] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 136: Theorem (136) [serial 1121] used for: applied wp for assignment [serial 1111] Theorem (138) [serial 1099] P [284] <> S [287] < > as! < > & last_as := now < > Q [287] <<(as@now) and (last_as = now)>> by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < > -> <

> < > S1 < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 128 130 134 137: Theorem (128) [serial 1108] used for: P -> P1 in concurrent composition for [serial 1099] Theorem (130) [serial 1109] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1099] Theorem (134) [serial 1110] used for: < > S1 < > in concurrent composition for [serial 1099] Theorem (137) [serial 1111] used for: < > S2 <

> in concurrent composition for [serial 1099] Theorem (139) [serial 1253] P [287] < > S [283] -> Q [291] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (140) [serial 1249] P [287] < > S [283] -> Q [291] <<(as@now)>> by Normalization and theorem 139: Theorem (139) [serial 1253] used for: normalize [serial 1249] Theorem (141) [serial 1243] P [287] < > S [283] -> Q [291] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 140: Theorem (140) [serial 1249] used for: Law of And-Simplification: P and true is P [serial 1243] Theorem (142) [serial 1238] P [287] < > S [283] -> Q [291] < > by Normalization and theorem 141: Theorem (141) [serial 1243] used for: normalize [serial 1238] Theorem (143) [serial 1235] P [287] < > S [283] -> Q [291] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 142: Theorem (142) [serial 1238] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1235] Theorem (144) [serial 1226] P [287] < > S [283] -> Q [291] < > by Substitution in Postcondition of All Equivalents in Precondition Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 143: Theorem (143) [serial 1235] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1226] Theorem (145) [serial 1217] P [287] < > S [283] -> Q [291] < > by Normalization and theorem 144: Theorem (144) [serial 1226] used for: normalize [serial 1217] Theorem (146) [serial 1203] P [287] < > S [283] -> Q [291] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 145: Theorem (145) [serial 1217] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 1203] Theorem (147) [serial 1196] P [287] < > S [283] -> Q [291] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))>> by Normalization and theorem 146: Theorem (146) [serial 1203] used for: normalize [serial 1196] Theorem (148) [serial 1145] P [287] < > S [283] -> Q [291] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 147: Theorem (147) [serial 1196] used for: substituted Assertions' predicates for labels in postconditions [serial 1145] Theorem (149) [serial 1100] P [287] <<(as@now) and (last_as = now)>> S [283] -> Q [291] < > by Normalization and theorem 148: Theorem (148) [serial 1145] used for: normalize [serial 1100] Theorem (150) [serial 1093] P [282] < > S [283] { < > as! < > & last_as := now < > } Q [291] < > by Introduction of Existential Quantification (bl.elq) and theorems 127 138 149: Theorem (127) [serial 1098] used for: < > -> <> in existential lattice quantification for [serial 1093] Theorem (138) [serial 1099] used for: {A} T {B} in existential lattice quantification for [serial 1093] Theorem (149) [serial 1100] used for: <

> -> <> in existential lattice quantification for [serial 1093] Theorem (151) [serial 1101] P [293] <> S [295] -> Q [295] < > by Identity (id): P->P is tautology Theorem (152) [serial 1112] P [295] < > S [295] -> Q [295] < > by Identity (id): P->P is tautology Theorem (153) [serial 1148] P [298] < > S [297] -> Q [298] < > by Identity (id): P->P is tautology Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (154) [serial 1113] P [298] < > S [297] -> Q [298] <<(ap@now) and (last_ap = now)>> by Normalization and theorem 153: Theorem (153) [serial 1148] used for: normalize [serial 1113] Theorem (155) [serial 1122] P [295] < > S [296] -> Q [1] < > by Identity (id): P->P is tautology Theorem (156) [serial 1150] P [296] < > S [296] -> Q [297] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (157) [serial 1123] P [296] <<(AP(now)) and ap@now>> S [296] -> Q [297] < > by Normalization and theorem 156: Theorem (156) [serial 1150] used for: normalize [serial 1123] Theorem (158) [serial 1114] P [295] < > S [296] ap! Q [297] < > by Port Event Output: when < > -> <> and <> -> <> then < > p! <> and theorems 155 157: Theorem (155) [serial 1122] used for: applied port output <> -> <> [serial 1114] Theorem (157) [serial 1123] used for: applied port output < > -> <> [serial 1114] Theorem (159) [serial 1176] P [295] < > S [299] -> Q [300] < > by True Conclusion Schema (tc): P->true Theorem (160) [serial 1124] P [295] < > S [299] -> Q [300] < > by Equality Law (idistr): a=a <-> true and theorem 159: Theorem (159) [serial 1176] used for: Equality Law (idistr): a=a <-> true [serial 1124] Theorem (161) [serial 1115] P [295] < > S [299] last_ap := now Q [300] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 160: Theorem (160) [serial 1124] used for: applied wp for assignment [serial 1115] Theorem (162) [serial 1102] P [295] <> S [298] < > ap! < > & last_ap := now < > Q [298] <<(ap@now) and (last_ap = now)>> by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < > -> <

> < > S1 < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 152 154 158 161: Theorem (152) [serial 1112] used for: P -> P1 in concurrent composition for [serial 1102] Theorem (154) [serial 1113] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1102] Theorem (158) [serial 1114] used for: < > S1 < > in concurrent composition for [serial 1102] Theorem (161) [serial 1115] used for: < > S2 <

> in concurrent composition for [serial 1102] Theorem (163) [serial 1254] P [298] < > S [294] -> Q [302] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (164) [serial 1250] P [298] < > S [294] -> Q [302] <<(ap@now)>> by Normalization and theorem 163: Theorem (163) [serial 1254] used for: normalize [serial 1250] Theorem (165) [serial 1244] P [298] < > S [294] -> Q [302] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 164: Theorem (164) [serial 1250] used for: Law of And-Simplification: P and true is P [serial 1244] Theorem (166) [serial 1239] P [298] < > S [294] -> Q [302] < > by Normalization and theorem 165: Theorem (165) [serial 1244] used for: normalize [serial 1239] Theorem (167) [serial 1236] P [298] < > S [294] -> Q [302] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 166: Theorem (166) [serial 1239] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1236] Theorem (168) [serial 1227] P [298] < > S [294] -> Q [302] < > by Substitution in Postcondition of All Equivalents in Precondition Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 167: Theorem (167) [serial 1236] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1227] Theorem (169) [serial 1218] P [298] < > S [294] -> Q [302] < > by Normalization and theorem 168: Theorem (168) [serial 1227] used for: normalize [serial 1218] Theorem (170) [serial 1204] P [298] < > S [294] -> Q [302] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 169: Theorem (169) [serial 1218] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 1204] Theorem (171) [serial 1197] P [298] < > S [294] -> Q [302] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))>> by Normalization and theorem 170: Theorem (170) [serial 1204] used for: normalize [serial 1197] Theorem (172) [serial 1152] P [298] < > S [294] -> Q [302] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 171: Theorem (171) [serial 1197] used for: substituted Assertions' predicates for labels in postconditions [serial 1152] Theorem (173) [serial 1103] P [298] <<(ap@now) and (last_ap = now)>> S [294] -> Q [302] < > by Normalization and theorem 172: Theorem (172) [serial 1152] used for: normalize [serial 1103] Theorem (174) [serial 1094] P [293] < > S [294] { < > ap! < > & last_ap := now < > } Q [302] < > by Introduction of Existential Quantification (bl.elq) and theorems 151 162 173: Theorem (151) [serial 1101] used for: < > -> <> in existential lattice quantification for [serial 1094] Theorem (162) [serial 1102] used for: {A} T {B} in existential lattice quantification for [serial 1094] Theorem (173) [serial 1103] used for: <

> -> <> in existential lattice quantification for [serial 1094] Theorem (175) [serial 1086] P [281] <<((PACE_ON_LRL(now)) and (AS(now)) and (AP(now)))>> S [281] <> { < > vp! < > & last_vp_or_vs := now < > } < > & < > { < > as! < > & last_as := now < > } < > & < > { < > ap! < > & last_ap := now < > } < > Q [281] <<(LAST_VP_OR_VS(now) and LRL(now)) and (LAST_AS(now)) and (LAST_AP(now))>> by Concurrent Composition Rule: <

> -> <> in existential lattice quantification for [serial 1084] Theorem (175) [serial 1086] used for: {A} T {B} in existential lattice quantification for [serial 1084] Theorem (178) [serial 1087] used for: <> -> <> in existential lattice quantification for [serial 1084] Theorem (180) [serial 1011] P [239] <> S [270] < > { < > { < > vp! < > & last_vp_or_vs := now < > } < > & < > { < > as! < > & last_as := now < > } < > & < > { < > ap! < > & last_ap := now < > } < > } < > Q [260] < > by Introduction of Existential Quantification (bl.aab) and theorems 48 54 179: Theorem (48) [serial 1082] used for: as < > in <> { <

> S <> } < > for [serial 1011] Theorem (54) [serial 1083] used for: as <> -> < > in <> { <

> S <> } < > [serial 1011] Theorem (179) [serial 1084] used for: as <> S <> in < > { <

> S <> } < > [serial 1011] Theorem (181) [serial 1377] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] <> by And Introduction Schema (aisph): (X and Y)->X Theorem (182) [serial 1373] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Associativity: (b.c).a = a.b.c and theorem 181: Theorem (181) [serial 1377] used for: Associativity: (b.c).a = a.b.c [serial 1373] Theorem (183) [serial 1359] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 182: Theorem (182) [serial 1373] used for: Associativity: (b.c).a = a.b.c [serial 1359] Theorem (184) [serial 1352] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Normalization and theorem 183: Theorem (183) [serial 1359] used for: normalize [serial 1352] Theorem (185) [serial 1347] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Substitution of Assertion Labels and theorem 184: Theorem (184) [serial 1352] used for: substituted Assertions' predicates for labels in preconditions [serial 1347] Theorem (186) [serial 1329] P [308] < > S [308] -> Q [229] < > by Substitution of Assertion Labels and theorem 185: Theorem (185) [serial 1347] used for: substituted Assertions' predicates for labels in preconditions [serial 1329] Theorem (187) [serial 1378] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (188) [serial 1374] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Associativity: (b.c).a = a.b.c and theorem 187: Theorem (187) [serial 1378] used for: Associativity: (b.c).a = a.b.c [serial 1374] Theorem (189) [serial 1360] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 188: Theorem (188) [serial 1374] used for: Associativity: (b.c).a = a.b.c [serial 1360] Theorem (190) [serial 1353] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Normalization and theorem 189: Theorem (189) [serial 1360] used for: normalize [serial 1353] Theorem (191) [serial 1348] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Substitution of Assertion Labels and theorem 190: Theorem (190) [serial 1353] used for: substituted Assertions' predicates for labels in preconditions [serial 1348] Theorem (192) [serial 1330] P [308] < > S [308] -> Q [230] < > by Substitution of Assertion Labels and theorem 191: Theorem (191) [serial 1348] used for: substituted Assertions' predicates for labels in preconditions [serial 1330] Theorem (193) [serial 1318] P [308] < > S [308] -> Q [312] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 186 192: Theorem (186) [serial 1329] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1318] Theorem (192) [serial 1330] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1318] Theorem (194) [serial 1312] P [308] < > S [308] -> Q [312] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))>> by Normalization and theorem 193: Theorem (193) [serial 1318] used for: normalize [serial 1312] Theorem (195) [serial 1304] P [308] < > S [308] -> Q [312] < > by Substitution of Assertion Labels and theorem 194: Theorem (194) [serial 1312] used for: substituted Assertions' predicates for labels in postconditions [serial 1304] Theorem (196) [serial 1379] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (197) [serial 1375] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Associativity: (b.c).a = a.b.c and theorem 196: Theorem (196) [serial 1379] used for: Associativity: (b.c).a = a.b.c [serial 1375] Theorem (198) [serial 1361] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 197: Theorem (197) [serial 1375] used for: Associativity: (b.c).a = a.b.c [serial 1361] Theorem (199) [serial 1354] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Normalization and theorem 198: Theorem (198) [serial 1361] used for: normalize [serial 1354] Theorem (200) [serial 1349] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Substitution of Assertion Labels and theorem 199: Theorem (199) [serial 1354] used for: substituted Assertions' predicates for labels in preconditions [serial 1349] Theorem (201) [serial 1331] P [308] < > S [308] -> Q [224] < > by Substitution of Assertion Labels and theorem 200: Theorem (200) [serial 1349] used for: substituted Assertions' predicates for labels in preconditions [serial 1331] Theorem (202) [serial 1380] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (203) [serial 1376] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Associativity: (b.c).a = a.b.c and theorem 202: Theorem (202) [serial 1380] used for: Associativity: (b.c).a = a.b.c [serial 1376] Theorem (204) [serial 1362] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 203: Theorem (203) [serial 1376] used for: Associativity: (b.c).a = a.b.c [serial 1362] Theorem (205) [serial 1355] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Normalization and theorem 204: Theorem (204) [serial 1362] used for: normalize [serial 1355] Theorem (206) [serial 1350] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Substitution of Assertion Labels and theorem 205: Theorem (205) [serial 1355] used for: substituted Assertions' predicates for labels in preconditions [serial 1350] Theorem (207) [serial 1332] P [308] < > S [308] -> Q [225] < > by Substitution of Assertion Labels and theorem 206: Theorem (206) [serial 1350] used for: substituted Assertions' predicates for labels in preconditions [serial 1332] Theorem (208) [serial 1319] P [308] < > S [308] -> Q [313] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 201 207: Theorem (201) [serial 1331] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1319] Theorem (207) [serial 1332] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1319] Theorem (209) [serial 1313] P [308] < > S [308] -> Q [313] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))>> by Normalization and theorem 208: Theorem (208) [serial 1319] used for: normalize [serial 1313] Theorem (210) [serial 1305] P [308] < > S [308] -> Q [313] < > by Substitution of Assertion Labels and theorem 209: Theorem (209) [serial 1313] used for: substituted Assertions' predicates for labels in postconditions [serial 1305] Theorem (211) [serial 1306] P [308] < > S [308] -> Q [309] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval)>> by And Introduction Schema (aisph): (X and Y)->X Theorem (212) [serial 1307] P [308] < > S [308] -> Q [310] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (213) [serial 1298] P [308] < > S [308] -> Q [310] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) and theorems 195 210 211 212: Theorem (195) [serial 1304] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (210) [serial 1305] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (211) [serial 1306] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (212) [serial 1307] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (214) [serial 1294] P [308] < > S [308] -> Q [310] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 213: Theorem (213) [serial 1298] used for: Law of And-Simplification: P and true is P [serial 1294] Theorem (215) [serial 1290] P [308] < > S [308] -> Q [310] < > by Normalization and theorem 214: Theorem (214) [serial 1294] used for: normalize [serial 1290] Theorem (216) [serial 1377] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (217) [serial 1373] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Associativity: (b.c).a = a.b.c and theorem 216: Theorem (216) [serial 1377] used for: Associativity: (b.c).a = a.b.c [serial 1373] Theorem (218) [serial 1359] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 217: Theorem (217) [serial 1373] used for: Associativity: (b.c).a = a.b.c [serial 1359] Theorem (219) [serial 1352] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Normalization and theorem 218: Theorem (218) [serial 1359] used for: normalize [serial 1352] Theorem (220) [serial 1347] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [229] < > by Substitution of Assertion Labels and theorem 219: Theorem (219) [serial 1352] used for: substituted Assertions' predicates for labels in preconditions [serial 1347] Theorem (221) [serial 1329] P [308] < > S [308] -> Q [229] < > by Substitution of Assertion Labels and theorem 220: Theorem (220) [serial 1347] used for: substituted Assertions' predicates for labels in preconditions [serial 1329] Theorem (222) [serial 1378] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (223) [serial 1374] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Associativity: (b.c).a = a.b.c and theorem 222: Theorem (222) [serial 1378] used for: Associativity: (b.c).a = a.b.c [serial 1374] Theorem (224) [serial 1360] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 223: Theorem (223) [serial 1374] used for: Associativity: (b.c).a = a.b.c [serial 1360] Theorem (225) [serial 1353] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Normalization and theorem 224: Theorem (224) [serial 1360] used for: normalize [serial 1353] Theorem (226) [serial 1348] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [230] < > by Substitution of Assertion Labels and theorem 225: Theorem (225) [serial 1353] used for: substituted Assertions' predicates for labels in preconditions [serial 1348] Theorem (227) [serial 1330] P [308] < > S [308] -> Q [230] < > by Substitution of Assertion Labels and theorem 226: Theorem (226) [serial 1348] used for: substituted Assertions' predicates for labels in preconditions [serial 1330] Theorem (228) [serial 1318] P [308] < > S [308] -> Q [312] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 221 227: Theorem (221) [serial 1329] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1318] Theorem (227) [serial 1330] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1318] Theorem (229) [serial 1312] P [308] < > S [308] -> Q [312] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))>> by Normalization and theorem 228: Theorem (228) [serial 1318] used for: normalize [serial 1312] Theorem (230) [serial 1304] P [308] < > S [308] -> Q [312] < > by Substitution of Assertion Labels and theorem 229: Theorem (229) [serial 1312] used for: substituted Assertions' predicates for labels in postconditions [serial 1304] Theorem (231) [serial 1379] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (232) [serial 1375] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Associativity: (b.c).a = a.b.c and theorem 231: Theorem (231) [serial 1379] used for: Associativity: (b.c).a = a.b.c [serial 1375] Theorem (233) [serial 1361] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 232: Theorem (232) [serial 1375] used for: Associativity: (b.c).a = a.b.c [serial 1361] Theorem (234) [serial 1354] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Normalization and theorem 233: Theorem (233) [serial 1361] used for: normalize [serial 1354] Theorem (235) [serial 1349] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [224] < > by Substitution of Assertion Labels and theorem 234: Theorem (234) [serial 1354] used for: substituted Assertions' predicates for labels in preconditions [serial 1349] Theorem (236) [serial 1331] P [308] < > S [308] -> Q [224] < > by Substitution of Assertion Labels and theorem 235: Theorem (235) [serial 1349] used for: substituted Assertions' predicates for labels in preconditions [serial 1331] Theorem (237) [serial 1380] P [308] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (238) [serial 1376] P [308] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Associativity: (b.c).a = a.b.c and theorem 237: Theorem (237) [serial 1380] used for: Associativity: (b.c).a = a.b.c [serial 1376] Theorem (239) [serial 1362] P [308] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 238: Theorem (238) [serial 1376] used for: Associativity: (b.c).a = a.b.c [serial 1362] Theorem (240) [serial 1355] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Normalization and theorem 239: Theorem (239) [serial 1362] used for: normalize [serial 1355] Theorem (241) [serial 1350] P [308] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [225] < > by Substitution of Assertion Labels and theorem 240: Theorem (240) [serial 1355] used for: substituted Assertions' predicates for labels in preconditions [serial 1350] Theorem (242) [serial 1332] P [308] < > S [308] -> Q [225] < > by Substitution of Assertion Labels and theorem 241: Theorem (241) [serial 1350] used for: substituted Assertions' predicates for labels in preconditions [serial 1332] Theorem (243) [serial 1319] P [308] < > S [308] -> Q [313] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 236 242: Theorem (236) [serial 1331] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1319] Theorem (242) [serial 1332] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1319] Theorem (244) [serial 1313] P [308] < > S [308] -> Q [313] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))>> by Normalization and theorem 243: Theorem (243) [serial 1319] used for: normalize [serial 1313] Theorem (245) [serial 1305] P [308] < > S [308] -> Q [313] < > by Substitution of Assertion Labels and theorem 244: Theorem (244) [serial 1313] used for: substituted Assertions' predicates for labels in postconditions [serial 1305] Theorem (246) [serial 1306] P [308] < > S [308] -> Q [309] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval)>> by And Introduction Schema (aisph): (X and Y)->X Theorem (247) [serial 1307] P [308] < > S [308] -> Q [310] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (248) [serial 1298] P [308] < > S [308] -> Q [310] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) and theorems 230 245 246 247: Theorem (230) [serial 1304] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (245) [serial 1305] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (246) [serial 1306] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (247) [serial 1307] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1298] Theorem (249) [serial 1294] P [308] < > S [308] -> Q [310] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 248: Theorem (248) [serial 1298] used for: Law of And-Simplification: P and true is P [serial 1294] Theorem (250) [serial 1290] P [308] < > S [308] -> Q [310] < > by Normalization and theorem 249: Theorem (249) [serial 1294] used for: normalize [serial 1290] Theorem (251) [serial 1286] P [308] < > S [308] -> Q [310] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (250) [serial 1290] used for: add user-defined axioms to precondition: <> S <

> Theorem (252) [serial 1276] P [308] <<(LRL(now) and V(now)) and ((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [308] -> Q [310] <> -> <> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 251: Theorem (251) [serial 1286] used for: Associativity: (b.c).a = a.b.c [serial 1276] Theorem (253) [serial 1269] P [308] <<(LRL(now) and V(now)) and ((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [308] -> Q [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> by Normalization and theorem 252: Theorem (252) [serial 1276] used for: normalize [serial 1269] Theorem (254) [serial 1343] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t ) or vp@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (255) [serial 1335] P [322] < > S [260] -> Q [260] <<(vp@now) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Normalization and theorem 254: Theorem (254) [serial 1343] used for: normalize [serial 1335] Theorem (256) [serial 1333] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 255: Theorem (255) [serial 1335] used for: replace exists with upper or lower bound [serial 1333] Theorem (257) [serial 1314] P [322] < > S [260] -> Q [260] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 256: Theorem (256) [serial 1333] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1314] Theorem (258) [serial 1308] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 257: Theorem (257) [serial 1314] used for: normalize [serial 1308] Theorem (259) [serial 1300] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 258: Theorem (258) [serial 1308] used for: substituted Assertions' predicates for labels in postconditions [serial 1300] Theorem (260) [serial 1326] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (261) [serial 1327] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (262) [serial 1393] P [322] < > S [260] -> Q [219] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (263) [serial 1389] P [322] < > S [260] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Normalization and theorem 262: Theorem (262) [serial 1393] used for: normalize [serial 1389] Theorem (264) [serial 1399] P [322] < > S [260] -> Q [220] < > by True Conclusion Schema (tc): P->true Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (265) [serial 1397] P [322] < > S [260] -> Q [220] < > by Normalization and theorem 264: Theorem (264) [serial 1399] used for: normalize [serial 1397] Theorem (266) [serial 1396] P [322] < > S [260] -> Q [220] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 265: Theorem (265) [serial 1397] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1396] Theorem (267) [serial 1390] P [322] < > S [260] -> Q [220] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 266: Theorem (266) [serial 1396] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1390] Theorem (268) [serial 1385] P [322] < > S [260] -> Q [193] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 263 267: Theorem (263) [serial 1389] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1385] Theorem (267) [serial 1390] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1385] Theorem (269) [serial 1382] P [322] < > S [260] -> Q [193] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 268: Theorem (268) [serial 1385] used for: normalize [serial 1382] Theorem (270) [serial 1371] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 269: Theorem (269) [serial 1382] used for: substituted Assertions' predicates for labels in postconditions [serial 1371] Theorem (271) [serial 1357] P [322] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs and last_as <= tops>> S [260] -> Q [193] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 270: Theorem (270) [serial 1371] used for: Associativity: (b.c).a = a.b.c [serial 1357] Theorem (272) [serial 1346] P [322] <<(last_as <= tops) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs>> S [260] -> Q [193] < > by Normalization and theorem 271: Theorem (271) [serial 1357] used for: normalize [serial 1346] Theorem (273) [serial 1328] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 272: Theorem (272) [serial 1346] used for: substituted Assertions' predicates for labels in preconditions [serial 1328] Theorem (274) [serial 1315] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 260 261 273: Theorem (260) [serial 1326] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1315] Theorem (261) [serial 1327] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1315] Theorem (273) [serial 1328] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1315] Theorem (275) [serial 1309] P [322] < > S [260] -> Q [260] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now))>> by Normalization and theorem 274: Theorem (274) [serial 1315] used for: normalize [serial 1309] Theorem (276) [serial 1301] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 275: Theorem (275) [serial 1309] used for: substituted Assertions' predicates for labels in postconditions [serial 1301] Theorem (277) [serial 1277] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 259 276: Theorem (259) [serial 1300] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1277] Theorem (276) [serial 1301] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1277] Theorem (278) [serial 1270] P [322] < > S [260] -> Q [260] < > by Normalization and theorem 277: Theorem (277) [serial 1277] used for: normalize [serial 1270] Theorem (279) [serial 1406] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists #4#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@#4# ) or (exists #5#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@#5# )) and not (exists #6#:BLESS_Types::Time in last_ap,,now that ap@#6# ) and not (exists #7#:BLESS_Types::Time in last_as,,now that as@#7# ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (280) [serial 1405] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@t )) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 279: Theorem (279) [serial 1406] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 1405] Theorem (281) [serial 1403] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t or vs@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 280: Theorem (280) [serial 1405] used for: Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) [serial 1403] Theorem (282) [serial 1402] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp@t or vs@t) ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Normalization and theorem 281: Theorem (281) [serial 1403] used for: normalize [serial 1402] Theorem (283) [serial 1401] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) and theorem 282: Theorem (282) [serial 1402] used for: Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) [serial 1401] Theorem (284) [serial 1383] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Extend Existential Quantification Range: Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 283: Theorem (283) [serial 1401] used for: Extend Existential Quantification Range: [serial 1383] Theorem (285) [serial 1372] P [310] < > S [314] -> Q [1] < > by Normalization and theorem 284: Theorem (284) [serial 1383] used for: normalize [serial 1372] Theorem (286) [serial 1358] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 285: Theorem (285) [serial 1372] used for: Associativity: (b.c).a = a.b.c [serial 1358] Theorem (287) [serial 1351] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 286: Theorem (286) [serial 1358] used for: normalize [serial 1351] Theorem (288) [serial 1334] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 287: Theorem (287) [serial 1351] used for: substituted Assertions' predicates for labels in preconditions [serial 1334] Theorem (289) [serial 1316] P [310] < > S [314] -> Q [1] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 288: Theorem (288) [serial 1334] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1316] Theorem (290) [serial 1310] P [310] < > S [314] -> Q [1] <<(not (exists tu:BLESS_Types::Time in (now-PP::Upper_Rate_Limit_Interval),,now that (vs or vp)@tu ))>> by Normalization and theorem 289: Theorem (289) [serial 1316] used for: normalize [serial 1310] Theorem (291) [serial 1302] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 290: Theorem (290) [serial 1310] used for: substituted Assertions' predicates for labels in postconditions [serial 1302] Theorem (292) [serial 1384] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ))>> by Premise Has All Terms of Conjunction within Disjunction (animporan): |- ( /\( l1 l2 l3 ) -> \/( l4 /\( l2 ) l5 ) ) for proof obligations of the form < > -> < > find any bj=(c1 and ... and cj) such that forall c in {c1,...,cj} there exists a in {a1,...,an} Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Theorem (293) [serial 1381] P [310] < > S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vs or vp)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu ))>> by Normalization and theorem 292: Theorem (292) [serial 1384] used for: normalize [serial 1381] Theorem (294) [serial 1370] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 293: Theorem (293) [serial 1381] used for: substituted Assertions' predicates for labels in postconditions [serial 1370] Theorem (295) [serial 1356] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 294: Theorem (294) [serial 1370] used for: Associativity: (b.c).a = a.b.c [serial 1356] Theorem (296) [serial 1345] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 295: Theorem (295) [serial 1356] used for: normalize [serial 1345] Theorem (297) [serial 1317] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 296: Theorem (296) [serial 1345] used for: substituted Assertions' predicates for labels in preconditions [serial 1317] Theorem (298) [serial 1311] P [310] < > S [314] -> Q [1] <<(PACE_ON_LRL(now) or PACE_ON_SAV_DELAY(now))>> by Normalization and theorem 297: Theorem (297) [serial 1317] used for: normalize [serial 1311] Theorem (299) [serial 1303] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 298: Theorem (298) [serial 1311] used for: substituted Assertions' predicates for labels in postconditions [serial 1303] Theorem (300) [serial 1278] P [310] < > S [314] -> Q [1] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorems 291 299: Theorem (291) [serial 1302] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1278] Theorem (299) [serial 1303] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1278] Theorem (301) [serial 1273] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] -> Q [1] < > by Normalization and theorem 300: Theorem (300) [serial 1278] used for: normalize [serial 1273] Theorem (302) [serial 1287] P [314] < > S [314] -> Q [315] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (303) [serial 1279] P [314] <<(AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now) and LAST_AP(now) and LAST_AS(now) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and vp@now>> S [314] -> Q [315] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 302: Theorem (302) [serial 1287] used for: Associativity: (b.c).a = a.b.c [serial 1279] Theorem (304) [serial 1274] P [314] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)) and vp@now>> S [314] -> Q [315] < > by Normalization and theorem 303: Theorem (303) [serial 1279] used for: normalize [serial 1274] Theorem (305) [serial 1271] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] vp! Q [315] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 301 304: Theorem (301) [serial 1273] used for: applied port output <> -> <> [serial 1271] Theorem (304) [serial 1274] used for: applied port output < > -> <> [serial 1271] Theorem (306) [serial 1299] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (307) [serial 1295] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 306: Theorem (306) [serial 1299] used for: Law of And-Simplification: P and true is P [serial 1295] Theorem (308) [serial 1291] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 307: Theorem (307) [serial 1295] used for: normalize [serial 1291] Theorem (309) [serial 1299] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (310) [serial 1295] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 309: Theorem (309) [serial 1299] used for: Law of And-Simplification: P and true is P [serial 1295] Theorem (311) [serial 1291] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 310: Theorem (310) [serial 1295] used for: normalize [serial 1291] Theorem (312) [serial 1289] P [315] < > S [321] -> Q [322] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (311) [serial 1291] used for: add user-defined axioms to precondition: <> -> <

> which is < > --------------------------------------- <> S <

> , <> ---------------- <> S <

> Theorem (387) [serial 1428] used for: add user-defined axioms to precondition: <> S <

> Theorem (389) [serial 1414] P [308] <<(LRL(now) and SAV(now) and V(now)) and ((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that as@(u-PP::Sensed_AV_Delay) and not (exists t:BLESS_Types::Time in u-PP::Sensed_AV_Delay,,u that as@t ) )>> S [308] -> Q [310] <> -> <> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 388: Theorem (388) [serial 1424] used for: Associativity: (b.c).a = a.b.c [serial 1414] Theorem (390) [serial 1407] P [308] <<(SAV(now) and LRL(now) and V(now)) and ((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (as@(u-PP::Sensed_AV_Delay) and not (exists t:BLESS_Types::Time in u-PP::Sensed_AV_Delay,,u that as@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [308] -> Q [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> by Normalization and theorem 389: Theorem (389) [serial 1414] used for: normalize [serial 1407] Theorem (391) [serial 1481] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t ) or vp@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (392) [serial 1473] P [322] < > S [260] -> Q [260] <<(vp@now) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Normalization and theorem 391: Theorem (391) [serial 1481] used for: normalize [serial 1473] Theorem (393) [serial 1471] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 392: Theorem (392) [serial 1473] used for: replace exists with upper or lower bound [serial 1471] Theorem (394) [serial 1452] P [322] < > S [260] -> Q [260] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 393: Theorem (393) [serial 1471] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1452] Theorem (395) [serial 1446] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 394: Theorem (394) [serial 1452] used for: normalize [serial 1446] Theorem (396) [serial 1438] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 395: Theorem (395) [serial 1446] used for: substituted Assertions' predicates for labels in postconditions [serial 1438] Theorem (397) [serial 1464] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (398) [serial 1465] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (399) [serial 1533] P [322] < > S [260] -> Q [219] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (400) [serial 1529] P [322] < > S [260] -> Q [219] <<(vp@now or vs@now)>> by Normalization and theorem 399: Theorem (399) [serial 1533] used for: normalize [serial 1529] Theorem (401) [serial 1527] P [322] < > S [260] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Substitution in Postcondition of All Equivalents in Precondition and theorem 400: Theorem (400) [serial 1529] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1527] Theorem (402) [serial 1534] P [322] < > S [260] -> Q [220] < > by True Conclusion Schema (tc): P->true Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (403) [serial 1531] P [322] < > S [260] -> Q [220] < > by Normalization and theorem 402: Theorem (402) [serial 1534] used for: normalize [serial 1531] Theorem (404) [serial 1530] P [322] < > S [260] -> Q [220] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 403: Theorem (403) [serial 1531] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1530] Theorem (405) [serial 1528] P [322] < > S [260] -> Q [220] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 404: Theorem (404) [serial 1530] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1528] Theorem (406) [serial 1523] P [322] < > S [260] -> Q [193] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 401 405: Theorem (401) [serial 1527] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1523] Theorem (405) [serial 1528] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1523] Theorem (407) [serial 1520] P [322] < > S [260] -> Q [193] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 406: Theorem (406) [serial 1523] used for: normalize [serial 1520] Theorem (408) [serial 1509] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 407: Theorem (407) [serial 1520] used for: substituted Assertions' predicates for labels in postconditions [serial 1509] Theorem (409) [serial 1495] P [322] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs and last_as <= tops>> S [260] -> Q [193] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 408: Theorem (408) [serial 1509] used for: Associativity: (b.c).a = a.b.c [serial 1495] Theorem (410) [serial 1484] P [322] <<(last_as <= tops) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs>> S [260] -> Q [193] < > by Normalization and theorem 409: Theorem (409) [serial 1495] used for: normalize [serial 1484] Theorem (411) [serial 1466] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 410: Theorem (410) [serial 1484] used for: substituted Assertions' predicates for labels in preconditions [serial 1466] Theorem (412) [serial 1453] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 397 398 411: Theorem (397) [serial 1464] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1453] Theorem (398) [serial 1465] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1453] Theorem (411) [serial 1466] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1453] Theorem (413) [serial 1447] P [322] < > S [260] -> Q [260] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now))>> by Normalization and theorem 412: Theorem (412) [serial 1453] used for: normalize [serial 1447] Theorem (414) [serial 1439] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 413: Theorem (413) [serial 1447] used for: substituted Assertions' predicates for labels in postconditions [serial 1439] Theorem (415) [serial 1415] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 396 414: Theorem (396) [serial 1438] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1415] Theorem (414) [serial 1439] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1415] Theorem (416) [serial 1408] P [322] < > S [260] -> Q [260] < > by Normalization and theorem 415: Theorem (415) [serial 1415] used for: normalize [serial 1408] Theorem (417) [serial 1542] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists #10#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@#10# ) or (exists #11#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@#11# )) and not (exists #12#:BLESS_Types::Time in last_ap,,now that ap@#12# ) and not (exists #13#:BLESS_Types::Time in last_as,,now that as@#13# ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (418) [serial 1541] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists #10#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@#10# ) or (exists #11#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@#11# )) and not (exists #12#:BLESS_Types::Time in last_ap,,now that ap@#12# ) and not (exists #13#:BLESS_Types::Time in last_as,,now that as@#13# ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Extend Existential Quantification Range: and theorem 417: Theorem (417) [serial 1542] used for: Extend Existential Quantification Range: [serial 1541] Theorem (419) [serial 1540] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@t )) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 418: Theorem (418) [serial 1541] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 1540] Theorem (420) [serial 1538] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t or vs@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 419: Theorem (419) [serial 1540] used for: Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) [serial 1538] Theorem (421) [serial 1537] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp@t or vs@t) ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Normalization and theorem 420: Theorem (420) [serial 1538] used for: normalize [serial 1537] Theorem (422) [serial 1521] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 421: Theorem (421) [serial 1537] used for: Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) [serial 1521] Theorem (423) [serial 1510] P [310] < > S [314] -> Q [1] < > by Normalization and theorem 422: Theorem (422) [serial 1521] used for: normalize [serial 1510] Theorem (424) [serial 1496] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 423: Theorem (423) [serial 1510] used for: Associativity: (b.c).a = a.b.c [serial 1496] Theorem (425) [serial 1489] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 424: Theorem (424) [serial 1496] used for: normalize [serial 1489] Theorem (426) [serial 1472] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 425: Theorem (425) [serial 1489] used for: substituted Assertions' predicates for labels in preconditions [serial 1472] Theorem (427) [serial 1454] P [310] < > S [314] -> Q [1] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 426: Theorem (426) [serial 1472] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1454] Theorem (428) [serial 1448] P [310] < > S [314] -> Q [1] <<(not (exists tu:BLESS_Types::Time in (now-PP::Upper_Rate_Limit_Interval),,now that (vs or vp)@tu ))>> by Normalization and theorem 427: Theorem (427) [serial 1454] used for: normalize [serial 1448] Theorem (429) [serial 1440] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 428: Theorem (428) [serial 1448] used for: substituted Assertions' predicates for labels in postconditions [serial 1440] Theorem (430) [serial 1522] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ))>> by Premise Has All Terms of Conjunction within Disjunction (animporan): |- ( /\( l1 l2 l3 ) -> \/( l4 /\( l2 ) l5 ) ) for proof obligations of the form < > -> < > find any bj=(c1 and ... and cj) such that forall c in {c1,...,cj} there exists a in {a1,...,an} Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Theorem (431) [serial 1519] P [310] < > S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vs or vp)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu ))>> by Normalization and theorem 430: Theorem (430) [serial 1522] used for: normalize [serial 1519] Theorem (432) [serial 1508] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 431: Theorem (431) [serial 1519] used for: substituted Assertions' predicates for labels in postconditions [serial 1508] Theorem (433) [serial 1494] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 432: Theorem (432) [serial 1508] used for: Associativity: (b.c).a = a.b.c [serial 1494] Theorem (434) [serial 1483] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 433: Theorem (433) [serial 1494] used for: normalize [serial 1483] Theorem (435) [serial 1455] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 434: Theorem (434) [serial 1483] used for: substituted Assertions' predicates for labels in preconditions [serial 1455] Theorem (436) [serial 1449] P [310] < > S [314] -> Q [1] <<(PACE_ON_LRL(now) or PACE_ON_SAV_DELAY(now))>> by Normalization and theorem 435: Theorem (435) [serial 1455] used for: normalize [serial 1449] Theorem (437) [serial 1441] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 436: Theorem (436) [serial 1449] used for: substituted Assertions' predicates for labels in postconditions [serial 1441] Theorem (438) [serial 1416] P [310] < > S [314] -> Q [1] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorems 429 437: Theorem (429) [serial 1440] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1416] Theorem (437) [serial 1441] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1416] Theorem (439) [serial 1411] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] -> Q [1] < > by Normalization and theorem 438: Theorem (438) [serial 1416] used for: normalize [serial 1411] Theorem (440) [serial 1425] P [314] < > S [314] -> Q [315] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (441) [serial 1417] P [314] <<(AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now) and LAST_AP(now) and LAST_AS(now) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and vp@now>> S [314] -> Q [315] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 440: Theorem (440) [serial 1425] used for: Associativity: (b.c).a = a.b.c [serial 1417] Theorem (442) [serial 1412] P [314] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)) and vp@now>> S [314] -> Q [315] < > by Normalization and theorem 441: Theorem (441) [serial 1417] used for: normalize [serial 1412] Theorem (443) [serial 1409] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] vp! Q [315] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 439 442: Theorem (439) [serial 1411] used for: applied port output <> -> <> [serial 1409] Theorem (442) [serial 1412] used for: applied port output < > -> <> [serial 1409] Theorem (444) [serial 1437] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (445) [serial 1433] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 444: Theorem (444) [serial 1437] used for: Law of And-Simplification: P and true is P [serial 1433] Theorem (446) [serial 1429] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 445: Theorem (445) [serial 1433] used for: normalize [serial 1429] Theorem (447) [serial 1437] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (448) [serial 1433] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 447: Theorem (447) [serial 1437] used for: Law of And-Simplification: P and true is P [serial 1433] Theorem (449) [serial 1429] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 448: Theorem (448) [serial 1433] used for: normalize [serial 1429] Theorem (450) [serial 1427] P [315] < > S [321] -> Q [322] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (449) [serial 1429] used for: add user-defined axioms to precondition: <> -> <

> which is < > --------------------------------------- <> S <

> , <> ---------------- <> S <

> Theorem (525) [serial 1554] used for: add user-defined axioms to precondition: <> S <

> Theorem (527) [serial 1543] P [308] <<(PAV(now) and LRL(now) and V(now)) and ((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [308] -> Q [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> by Associativity: (b.c).a = a.b.c and theorem 526: Theorem (526) [serial 1550] used for: Associativity: (b.c).a = a.b.c [serial 1543] Theorem (528) [serial 1609] P [322] <> -> <> S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t ) or vp@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (529) [serial 1601] P [322] < > S [260] -> Q [260] <<(vp@now) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Normalization and theorem 528: Theorem (528) [serial 1609] used for: normalize [serial 1601] Theorem (530) [serial 1599] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 529: Theorem (529) [serial 1601] used for: replace exists with upper or lower bound [serial 1599] Theorem (531) [serial 1580] P [322] < > S [260] -> Q [260] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 530: Theorem (530) [serial 1599] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1580] Theorem (532) [serial 1574] P [322] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 531: Theorem (531) [serial 1580] used for: normalize [serial 1574] Theorem (533) [serial 1566] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 532: Theorem (532) [serial 1574] used for: substituted Assertions' predicates for labels in postconditions [serial 1566] Theorem (534) [serial 1592] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (535) [serial 1593] P [322] < > S [260] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (536) [serial 1659] P [322] < > S [260] -> Q [219] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (537) [serial 1655] P [322] < > S [260] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Normalization and theorem 536: Theorem (536) [serial 1659] used for: normalize [serial 1655] Theorem (538) [serial 1665] P [322] < > S [260] -> Q [220] < > by True Conclusion Schema (tc): P->true Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (539) [serial 1663] P [322] < > S [260] -> Q [220] < > by Normalization and theorem 538: Theorem (538) [serial 1665] used for: normalize [serial 1663] Theorem (540) [serial 1662] P [322] < > S [260] -> Q [220] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 539: Theorem (539) [serial 1663] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 1662] Theorem (541) [serial 1656] P [322] < > S [260] -> Q [220] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 540: Theorem (540) [serial 1662] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 1656] Theorem (542) [serial 1651] P [322] < > S [260] -> Q [193] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 537 541: Theorem (537) [serial 1655] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1651] Theorem (541) [serial 1656] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1651] Theorem (543) [serial 1648] P [322] < > S [260] -> Q [193] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 542: Theorem (542) [serial 1651] used for: normalize [serial 1648] Theorem (544) [serial 1637] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 543: Theorem (543) [serial 1648] used for: substituted Assertions' predicates for labels in postconditions [serial 1637] Theorem (545) [serial 1623] P [322] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs and last_as <= tops>> S [260] -> Q [193] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 544: Theorem (544) [serial 1637] used for: Associativity: (b.c).a = a.b.c [serial 1623] Theorem (546) [serial 1612] P [322] <<(last_as <= tops) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and vp@last_vp_or_vs and now = last_vp_or_vs>> S [260] -> Q [193] < > by Normalization and theorem 545: Theorem (545) [serial 1623] used for: normalize [serial 1612] Theorem (547) [serial 1594] P [322] < > S [260] -> Q [193] < > by Substitution of Assertion Labels and theorem 546: Theorem (546) [serial 1612] used for: substituted Assertions' predicates for labels in preconditions [serial 1594] Theorem (548) [serial 1581] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 534 535 547: Theorem (534) [serial 1592] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1581] Theorem (535) [serial 1593] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1581] Theorem (547) [serial 1594] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1581] Theorem (549) [serial 1575] P [322] < > S [260] -> Q [260] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now))>> by Normalization and theorem 548: Theorem (548) [serial 1581] used for: normalize [serial 1575] Theorem (550) [serial 1567] P [322] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 549: Theorem (549) [serial 1575] used for: substituted Assertions' predicates for labels in postconditions [serial 1567] Theorem (551) [serial 1556] P [322] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 533 550: Theorem (533) [serial 1566] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1556] Theorem (550) [serial 1567] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1556] Theorem (552) [serial 1544] P [322] < > S [260] -> Q [260] < > by Normalization and theorem 551: Theorem (551) [serial 1556] used for: normalize [serial 1544] Theorem (553) [serial 1672] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists #16#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@#16# ) or (exists #17#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@#17# )) and not (exists #18#:BLESS_Types::Time in last_ap,,now that ap@#18# ) and not (exists #19#:BLESS_Types::Time in last_as,,now that as@#19# ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (554) [serial 1671] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists #16#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@#16# ) or (exists #17#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@#17# )) and not (exists #18#:BLESS_Types::Time in last_ap,,now that ap@#18# ) and not (exists #19#:BLESS_Types::Time in last_as,,now that as@#19# ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Extend Existential Quantification Range: and theorem 553: Theorem (553) [serial 1672] used for: Extend Existential Quantification Range: [serial 1671] Theorem (555) [serial 1670] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not ((exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vs@t )) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 554: Theorem (554) [serial 1671] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 1670] Theorem (556) [serial 1668] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that vp@t or vs@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 555: Theorem (555) [serial 1670] used for: Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) [serial 1668] Theorem (557) [serial 1667] P [310] <<(vp@(now-PP::Lower_Rate_Limit_Interval) or vs@(now-PP::Lower_Rate_Limit_Interval)) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp@t or vs@t) ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Normalization and theorem 556: Theorem (556) [serial 1668] used for: normalize [serial 1667] Theorem (558) [serial 1649] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 557: Theorem (557) [serial 1667] used for: Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) [serial 1649] Theorem (559) [serial 1638] P [310] < > S [314] -> Q [1] < > by Normalization and theorem 558: Theorem (558) [serial 1649] used for: normalize [serial 1638] Theorem (560) [serial 1624] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 559: Theorem (559) [serial 1638] used for: Associativity: (b.c).a = a.b.c [serial 1624] Theorem (561) [serial 1617] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 560: Theorem (560) [serial 1624] used for: normalize [serial 1617] Theorem (562) [serial 1600] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 561: Theorem (561) [serial 1617] used for: substituted Assertions' predicates for labels in preconditions [serial 1600] Theorem (563) [serial 1582] P [310] < > S [314] -> Q [1] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 562: Theorem (562) [serial 1600] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1582] Theorem (564) [serial 1576] P [310] < > S [314] -> Q [1] <<(not (exists tu:BLESS_Types::Time in (now-PP::Upper_Rate_Limit_Interval),,now that (vs or vp)@tu ))>> by Normalization and theorem 563: Theorem (563) [serial 1582] used for: normalize [serial 1576] Theorem (565) [serial 1568] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 564: Theorem (564) [serial 1576] used for: substituted Assertions' predicates for labels in postconditions [serial 1568] Theorem (566) [serial 1650] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ))>> by Premise Has All Terms of Conjunction within Disjunction (animporan): |- ( /\( l1 l2 l3 ) -> \/( l4 /\( l2 ) l5 ) ) for proof obligations of the form < > -> < > find any bj=(c1 and ... and cj) such that forall c in {c1,...,cj} there exists a in {a1,...,an} Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Theorem (567) [serial 1647] P [310] < > S [314] -> Q [1] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vs or vp)@t )) or (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu ))>> by Normalization and theorem 566: Theorem (566) [serial 1650] used for: normalize [serial 1647] Theorem (568) [serial 1636] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 567: Theorem (567) [serial 1647] used for: substituted Assertions' predicates for labels in postconditions [serial 1636] Theorem (569) [serial 1622] P [310] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and last_as <= tops>> S [314] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 568: Theorem (568) [serial 1636] used for: Associativity: (b.c).a = a.b.c [serial 1622] Theorem (570) [serial 1611] P [310] <<(last_as <= tops) and ((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval,,now that (vp or vs)@t )>> S [314] -> Q [1] < > by Normalization and theorem 569: Theorem (569) [serial 1622] used for: normalize [serial 1611] Theorem (571) [serial 1583] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 570: Theorem (570) [serial 1611] used for: substituted Assertions' predicates for labels in preconditions [serial 1583] Theorem (572) [serial 1577] P [310] < > S [314] -> Q [1] <<(PACE_ON_LRL(now) or PACE_ON_SAV_DELAY(now))>> by Normalization and theorem 571: Theorem (571) [serial 1583] used for: normalize [serial 1577] Theorem (573) [serial 1569] P [310] < > S [314] -> Q [1] < > by Substitution of Assertion Labels and theorem 572: Theorem (572) [serial 1577] used for: substituted Assertions' predicates for labels in postconditions [serial 1569] Theorem (574) [serial 1557] P [310] < > S [314] -> Q [1] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorems 565 573: Theorem (565) [serial 1568] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1557] Theorem (573) [serial 1569] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1557] Theorem (575) [serial 1547] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] -> Q [1] < > by Normalization and theorem 574: Theorem (574) [serial 1557] used for: normalize [serial 1547] Theorem (576) [serial 1551] P [314] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now) and vp@now>> S [314] -> Q [315] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (577) [serial 1548] P [314] <<((vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)) and vp@now>> S [314] -> Q [315] < > by Associativity: (b.c).a = a.b.c and theorem 576: Theorem (576) [serial 1551] used for: Associativity: (b.c).a = a.b.c [serial 1548] Theorem (578) [serial 1545] P [310] <<(vp or vs)@(now-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval),,now that (vp or vs)@t ) and LAST_AP(now) and LAST_AS(now) and AXIOM_LAST_AS_LE_TOPS() and AXIOM_LRLi_gt_URLi_LIMIT(now)>> S [314] vp! Q [315] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 575 577: Theorem (575) [serial 1547] used for: applied port output <> -> <> [serial 1545] Theorem (577) [serial 1548] used for: applied port output < > -> <> [serial 1545] Theorem (579) [serial 1565] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (580) [serial 1559] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 579: Theorem (579) [serial 1565] used for: Law of And-Simplification: P and true is P [serial 1559] Theorem (581) [serial 1555] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 580: Theorem (580) [serial 1559] used for: normalize [serial 1555] Theorem (582) [serial 1565] P [315] < > S [321] -> Q [322] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (583) [serial 1559] P [315] < > S [321] -> Q [322] < > by Law of And-Simplification: P and true is P Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 582: Theorem (582) [serial 1565] used for: Law of And-Simplification: P and true is P [serial 1559] Theorem (584) [serial 1555] P [315] < > S [321] -> Q [322] < > by Normalization and theorem 583: Theorem (583) [serial 1559] used for: normalize [serial 1555] Theorem (585) [serial 1553] P [315] < > S [321] -> Q [322] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (584) [serial 1555] used for: add user-defined axioms to precondition: <> -> <

> which is < > --------------------------------------- <> S <

> , <> ---------------- <> S <

> Theorem (686) [serial 1695] used for: add user-defined axioms to precondition: <> S <

> Theorem (688) [serial 1686] P [334] <<(LAST_AP(now) and LAST_AS(now) and VS(now)) and vs@now>> S [334] -> Q [335] <> -> <> by Associativity: (b.c).a = a.b.c Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 687: Theorem (687) [serial 1693] used for: Associativity: (b.c).a = a.b.c [serial 1686] Theorem (689) [serial 1681] P [334] <<(VS(now) and LAST_AS(now) and LAST_AP(now)) and vs@now>> S [334] -> Q [335] < > by Normalization and theorem 688: Theorem (688) [serial 1686] used for: normalize [serial 1681] Theorem (690) [serial 1678] P [333] < > S [334] vs! Q [335] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 682 689: Theorem (682) [serial 1680] used for: applied port output <> -> <> [serial 1678] Theorem (689) [serial 1681] used for: applied port output < > -> <> [serial 1678] Theorem (691) [serial 1694] P [252] < > S [337] -> Q [337] < > by True Conclusion Schema (tc): P->true Theorem (692) [serial 1687] P [252] < > S [337] -> Q [337] < > by Equality Law (idistr): a=a <-> true Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 691: Theorem (691) [serial 1694] used for: Equality Law (idistr): a=a <-> true [serial 1687] Theorem (693) [serial 1682] P [252] < > S [337] -> Q [337] < > by Normalization and theorem 692: Theorem (692) [serial 1687] used for: normalize [serial 1682] Theorem (694) [serial 1679] P [252] < > S [337] last_vp_or_vs := now Q [337] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 693: Theorem (693) [serial 1682] used for: applied wp for assignment [serial 1679] Theorem (695) [serial 1017] P [252] <> S [336] < > vs! < > & last_vp_or_vs := now < > Q [260] < > by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 658 680 690 694: Theorem (658) [serial 1676] used for: P -> P1 in concurrent composition for [serial 1017] Theorem (680) [serial 1677] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1017] Theorem (690) [serial 1678] used for: < > S1 < > in concurrent composition for [serial 1017] Theorem (694) [serial 1679] used for: < > S2 <

> in concurrent composition for [serial 1017] Theorem (696) [serial 1828] P [340] < > S [340] -> Q [254] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (697) [serial 1829] P [340] < > S [340] -> Q [254] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (698) [serial 1830] P [340] < > S [340] -> Q [254] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (699) [serial 1831] P [340] < > S [340] -> Q [254] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (700) [serial 1826] P [340] < > S [340] -> Q [254] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 696 697 698 699: Theorem (696) [serial 1828] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1826] Theorem (697) [serial 1829] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1826] Theorem (698) [serial 1830] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1826] Theorem (699) [serial 1831] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1826] Theorem (701) [serial 1825] P [340] < > S [340] -> Q [254] < > by Normalization and theorem 700: Theorem (700) [serial 1826] used for: normalize [serial 1825] Theorem (702) [serial 1018] P [340] <<(SAV(now) and LRL(now) and V(now)) and (as@(now-PP::Sensed_AV_Delay) and not (exists t:BLESS_Types::Time in now-PP::Sensed_AV_Delay,,now that as@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (as@(u-PP::Sensed_AV_Delay) and not (exists t:BLESS_Types::Time in u-PP::Sensed_AV_Delay,,u that as@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [340] -> Q [254] < > by Associativity: (b.c).a = a.b.c and theorem 701: Theorem (701) [serial 1825] used for: Associativity: (b.c).a = a.b.c [serial 1018] Theorem (703) [serial 1019] P [254] < (now-PP::Upper_Rate_Limit_Interval))>> S [343] -> Q [260] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (704) [serial 1877] P [254] < > S [348] -> Q [168] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (705) [serial 1914] P [254] <<((exists #55#:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@#55# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vp@#56# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vs@#56# )) and ((exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@#57# ) or (exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@#57# )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not ((exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vp@#60# ) or (exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vs@#60# )) and not (exists #58#:BLESS_Types::Time in last_ap,,now that ap@#58# ) and not (exists #59#:BLESS_Types::Time in last_as,,now that as@#59# ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Theorem (706) [serial 1913] P [254] <<((exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vp@#56# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vs@#56# ) or (exists #55#:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@#55# )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and ((exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@#57# ) or (exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@#57# )) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists #58#:BLESS_Types::Time in last_ap,,now that ap@#58# ) and not (exists #59#:BLESS_Types::Time in last_as,,now that as@#59# ) and not ((exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vp@#60# ) or (exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vs@#60# )) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Normalization and theorem 705: Theorem (705) [serial 1914] used for: normalize [serial 1913] Theorem (707) [serial 1912] P [254] <<((exists #55#:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@#55# ) or ((exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vp@#56# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that vs@#56# ))) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and ((exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@#57# ) or (exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@#57# )) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists #58#:BLESS_Types::Time in last_ap,,now that ap@#58# ) and not (exists #59#:BLESS_Types::Time in last_as,,now that as@#59# ) and not ((exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vp@#60# ) or (exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that vs@#60# )) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Associativity: (b.c).a = a.b.c and theorem 706: Theorem (706) [serial 1913] used for: Associativity: (b.c).a = a.b.c [serial 1912] Theorem (708) [serial 1911] P [254] <<((exists #55#:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@#55# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that (vp@#56# or vs@#56#) )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp@#57# or vs@#57#) ) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists #58#:BLESS_Types::Time in last_ap,,now that ap@#58# ) and not (exists #59#:BLESS_Types::Time in last_as,,now that as@#59# ) and not (exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that (vp@#60# or vs@#60#) ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) and theorem 707: Theorem (707) [serial 1912] used for: Combine Existential Quantifications: exists x:t in R that (A or B) = (exists x:t in R that A) or (exists x:t in R that B) [serial 1911] Theorem (709) [serial 1910] P [254] <<((exists #55#:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@#55# ) or (exists #56#:BLESS_Types::Time in last_vp_or_vs..now that (vp or vs)@#56# )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #57#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#57# ) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists #58#:BLESS_Types::Time in last_ap,,now that ap@#58# ) and not (exists #59#:BLESS_Types::Time in last_as,,now that as@#59# ) and not (exists #60#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#60# ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) and theorem 708: Theorem (708) [serial 1911] used for: Combine Timed Atoms: (a or b)@t = (a@t or b@t) (a and b)@t = (a@t and b@t) [serial 1910] Theorem (710) [serial 1909] P [254] <<((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in last_vp_or_vs..now that (vp or vs)@tu )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 709: Theorem (709) [serial 1910] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 1909] Theorem (711) [serial 1904] P [254] <<((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vp or vs)@tu )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Extend Existential Quantification Range: and theorem 710: Theorem (710) [serial 1909] used for: Extend Existential Quantification Range: [serial 1904] Theorem (712) [serial 1899] P [254] <<((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vp or vs)@tu )) and (vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 711: Theorem (711) [serial 1904] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1899] Theorem (713) [serial 1896] P [254] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and ((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vp or vs)@tu )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and as@(now-PP::Sensed_AV_Delay) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Normalization and theorem 712: Theorem (712) [serial 1899] used for: normalize [serial 1896] Theorem (714) [serial 1893] P [254] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vp or vs)@tu )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and as@(now-PP::Sensed_AV_Delay) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Associativity: (b.c).a = a.b.c and theorem 713: Theorem (713) [serial 1896] used for: Associativity: (b.c).a = a.b.c [serial 1893] Theorem (715) [serial 1887] P [254] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and ((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vp or vs)@tu )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and as@(now-PP::Sensed_AV_Delay) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 714: Theorem (714) [serial 1893] used for: Associativity: (b.c).a = a.b.c [serial 1887] Theorem (716) [serial 1884] P [254] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and ((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vs or vp)@tu )) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and as@(now-PP::Sensed_AV_Delay) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Normalization and theorem 715: Theorem (715) [serial 1887] used for: normalize [serial 1884] Theorem (717) [serial 1881] P [254] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and ((exists ta:BLESS_Types::Time in now-PP::Sensed_AV_Delay..now that as@ta ) or (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval..now that (vs or vp)@tu )) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and as@(now-PP::Sensed_AV_Delay) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [348] -> Q [170] < > by Substitution of Assertion Labels and theorem 716: Theorem (716) [serial 1884] used for: substituted Assertions' predicates for labels [serial 1881] Theorem (718) [serial 1878] P [254] < > S [348] -> Q [170] < > by Substitution of Assertion Labels and theorem 717: Theorem (717) [serial 1881] used for: substituted Assertions' predicates for labels [serial 1878] Theorem (719) [serial 1869] P [254] < > S [348] -> Q [348] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 704 718: Theorem (704) [serial 1877] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1869] Theorem (718) [serial 1878] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1869] Theorem (720) [serial 1865] P [254] < > S [348] -> Q [348] <<(as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu ))>> by Normalization and theorem 719: Theorem (719) [serial 1869] used for: normalize [serial 1865] Theorem (721) [serial 1858] P [254] < > S [348] -> Q [348] < > by Substitution of Assertion Labels and theorem 720: Theorem (720) [serial 1865] used for: substituted Assertions' predicates for labels in postconditions [serial 1858] Theorem (722) [serial 1859] P [254] < > S [348] -> Q [348] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (723) [serial 1860] P [254] < > S [348] -> Q [349] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (724) [serial 1839] P [254] < > S [348] -> Q [348] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 721 722 723: Theorem (721) [serial 1858] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1839] Theorem (722) [serial 1859] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1839] Theorem (723) [serial 1860] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1839] Theorem (725) [serial 1832] P [254] < > S [348] -> Q [348] < > by Normalization and theorem 724: Theorem (724) [serial 1839] used for: normalize [serial 1832] Theorem (726) [serial 1907] P [352] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and vp@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t ) or vp@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (727) [serial 1905] P [352] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and vp@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] <<(vp@now) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Normalization and theorem 726: Theorem (726) [serial 1907] used for: normalize [serial 1905] Theorem (728) [serial 1903] P [352] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and vp@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 727: Theorem (727) [serial 1905] used for: replace exists with upper or lower bound [serial 1903] Theorem (729) [serial 1897] P [352] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and vp@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 728: Theorem (728) [serial 1903] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1897] Theorem (730) [serial 1894] P [352] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and vp@now and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] < > by Normalization and theorem 729: Theorem (729) [serial 1897] used for: normalize [serial 1894] Theorem (731) [serial 1891] P [352] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vp@now and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] < > by Associativity: (b.c).a = a.b.c and theorem 730: Theorem (730) [serial 1894] used for: Associativity: (b.c).a = a.b.c [serial 1891] Theorem (732) [serial 1885] P [352] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and vp@now and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [351] -> Q [260] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 731: Theorem (731) [serial 1891] used for: Associativity: (b.c).a = a.b.c [serial 1885] Theorem (733) [serial 1882] P [352] <<((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and vp@now and now = last_vp_or_vs>> S [351] -> Q [260] < > by Normalization and theorem 732: Theorem (732) [serial 1885] used for: normalize [serial 1882] Theorem (734) [serial 1879] P [352] <<((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and vp@now and now = last_vp_or_vs>> S [351] -> Q [260] < > by Substitution of Assertion Labels and theorem 733: Theorem (733) [serial 1882] used for: substituted Assertions' predicates for labels [serial 1879] Theorem (735) [serial 1870] P [352] < > S [351] -> Q [260] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 734: Theorem (734) [serial 1879] used for: substituted Assertions' predicates for labels [serial 1870] Theorem (736) [serial 1866] P [352] < > S [351] -> Q [260] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 735: Theorem (735) [serial 1870] used for: normalize [serial 1866] Theorem (737) [serial 1861] P [352] < > S [351] -> Q [260] < > by Substitution of Assertion Labels and theorem 736: Theorem (736) [serial 1866] used for: substituted Assertions' predicates for labels in postconditions [serial 1861] Theorem (738) [serial 1862] P [352] < > S [351] -> Q [260] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (739) [serial 1840] P [352] < > S [351] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 737 738: Theorem (737) [serial 1861] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1840] Theorem (738) [serial 1862] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1840] Theorem (740) [serial 1833] P [352] < > S [351] -> Q [260] < > by Normalization and theorem 739: Theorem (739) [serial 1840] used for: normalize [serial 1833] Theorem (741) [serial 1898] P [348] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@(now-PP::Sensed_AV_Delay) and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (742) [serial 1895] P [348] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by Normalization and theorem 741: Theorem (741) [serial 1898] used for: normalize [serial 1895] Theorem (743) [serial 1892] P [348] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu ) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by Associativity: (b.c).a = a.b.c and theorem 742: Theorem (742) [serial 1895] used for: Associativity: (b.c).a = a.b.c [serial 1892] Theorem (744) [serial 1886] P [348] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vp or vs)@tu )) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 743: Theorem (743) [serial 1892] used for: Associativity: (b.c).a = a.b.c [serial 1886] Theorem (745) [serial 1883] P [348] <<(as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu )) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by Normalization and theorem 744: Theorem (744) [serial 1886] used for: normalize [serial 1883] Theorem (746) [serial 1880] P [348] <<(as@(now-PP::Sensed_AV_Delay) and not (exists tu:BLESS_Types::Time in now-PP::Upper_Rate_Limit_Interval,,now that (vs or vp)@tu )) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)>> S [350] -> Q [1] < > by Substitution of Assertion Labels and theorem 745: Theorem (745) [serial 1883] used for: substituted Assertions' predicates for labels [serial 1880] Theorem (747) [serial 1871] P [348] < > S [350] -> Q [1] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 746: Theorem (746) [serial 1880] used for: substituted Assertions' predicates for labels [serial 1871] Theorem (748) [serial 1867] P [348] < > S [350] -> Q [1] <<(not (exists tu:BLESS_Types::Time in (now-PP::Upper_Rate_Limit_Interval),,now that (vs or vp)@tu ))>> by Normalization and theorem 747: Theorem (747) [serial 1871] used for: normalize [serial 1867] Theorem (749) [serial 1863] P [348] < > S [350] -> Q [1] < > by Substitution of Assertion Labels and theorem 748: Theorem (748) [serial 1867] used for: substituted Assertions' predicates for labels in postconditions [serial 1863] Theorem (750) [serial 1872] P [348] < > S [350] -> Q [1] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (751) [serial 1868] P [348] < > S [350] -> Q [1] <<(PACE_ON_LRL(now) or PACE_ON_SAV_DELAY(now))>> by Normalization and theorem 750: Theorem (750) [serial 1872] used for: normalize [serial 1868] Theorem (752) [serial 1864] P [348] < > S [350] -> Q [1] < > by Substitution of Assertion Labels and theorem 751: Theorem (751) [serial 1868] used for: substituted Assertions' predicates for labels in postconditions [serial 1864] Theorem (753) [serial 1841] P [348] < > S [350] -> Q [1] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 749 752: Theorem (749) [serial 1863] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1841] Theorem (752) [serial 1864] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1841] Theorem (754) [serial 1836] P [348] < > S [350] -> Q [1] < > by Normalization and theorem 753: Theorem (753) [serial 1841] used for: normalize [serial 1836] Theorem (755) [serial 1857] P [350] < > S [350] -> Q [351] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (756) [serial 1855] P [350] < > S [350] -> Q [351] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 755: Theorem (755) [serial 1857] used for: Law of And-Simplification: P and true is P [serial 1855] Theorem (757) [serial 1851] P [350] < > S [350] -> Q [351] < > by Normalization and theorem 756: Theorem (756) [serial 1855] used for: normalize [serial 1851] Theorem (758) [serial 1857] P [350] < > S [350] -> Q [351] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (759) [serial 1855] P [350] < > S [350] -> Q [351] < > by Law of And-Simplification: P and true is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 758: Theorem (758) [serial 1857] used for: Law of And-Simplification: P and true is P [serial 1855] Theorem (760) [serial 1851] P [350] < > S [350] -> Q [351] < > by Normalization and theorem 759: Theorem (759) [serial 1855] used for: normalize [serial 1851] Theorem (761) [serial 1849] P [350] < > S [350] -> Q [351] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (760) [serial 1851] used for: add user-defined axioms to precondition: <> S <

> Theorem (762) [serial 1842] P [350] <<(PACE_ON_SAV_DELAY(now) and V(now) and last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval)) and vp@now>> S [350] -> Q [351] <> -> <> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 761: Theorem (761) [serial 1849] used for: Associativity: (b.c).a = a.b.c [serial 1842] Theorem (763) [serial 1837] P [350] <<(PACE_ON_SAV_DELAY(now) and V(now) and (last_vp_or_vs <= (now-PP::Upper_Rate_Limit_Interval))) and vp@now>> S [350] -> Q [351] < > by Normalization and theorem 762: Theorem (762) [serial 1842] used for: normalize [serial 1837] Theorem (764) [serial 1834] P [348] < > S [350] vp! Q [351] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 754 763: Theorem (754) [serial 1836] used for: applied port output <> -> <> [serial 1834] Theorem (763) [serial 1837] used for: applied port output < > -> <> [serial 1834] Theorem (765) [serial 1850] P [254] < > S [353] -> Q [353] < > by True Conclusion Schema (tc): P->true Theorem (766) [serial 1843] P [254] < > S [353] -> Q [353] < > by Equality Law (idistr): a=a <-> true Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 765: Theorem (765) [serial 1850] used for: Equality Law (idistr): a=a <-> true [serial 1843] Theorem (767) [serial 1838] P [254] < > S [353] -> Q [353] < > by Normalization and theorem 766: Theorem (766) [serial 1843] used for: normalize [serial 1838] Theorem (768) [serial 1835] P [254] < > S [353] last_vp_or_vs := now Q [353] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 767: Theorem (767) [serial 1838] used for: applied wp for assignment [serial 1835] Theorem (769) [serial 1020] P [254] <> S [352] < > vp! < > & last_vp_or_vs := now < > Q [260] < > by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 725 740 764 768: Theorem (725) [serial 1832] used for: P -> P1 in concurrent composition for [serial 1020] Theorem (740) [serial 1833] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1020] Theorem (764) [serial 1834] used for: < > S1 < > in concurrent composition for [serial 1020] Theorem (768) [serial 1835] used for: < > S2 <

> in concurrent composition for [serial 1020] Theorem (770) [serial 1928] P [357] < > S [357] -> Q [258] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (771) [serial 1920] P [357] <<(LRL(now) and PAV(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) )>> S [357] -> Q [258] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 770: Theorem (770) [serial 1928] used for: Associativity: (b.c).a = a.b.c [serial 1920] Theorem (772) [serial 1916] P [357] <<(PAV(now) and LRL(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [357] -> Q [258] < > by Normalization and theorem 771: Theorem (771) [serial 1920] used for: normalize [serial 1916] Theorem (773) [serial 1929] P [357] < > S [357] -> Q [258] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (774) [serial 1921] P [357] <<(LRL(now) and PAV(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) )>> S [357] -> Q [258] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 773: Theorem (773) [serial 1929] used for: Associativity: (b.c).a = a.b.c [serial 1921] Theorem (775) [serial 1917] P [357] <<(PAV(now) and LRL(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [357] -> Q [258] < > by Normalization and theorem 774: Theorem (774) [serial 1921] used for: normalize [serial 1917] Theorem (776) [serial 1930] P [357] < > S [357] -> Q [258] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (777) [serial 1922] P [357] <<(LRL(now) and PAV(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) )>> S [357] -> Q [258] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 776: Theorem (776) [serial 1930] used for: Associativity: (b.c).a = a.b.c [serial 1922] Theorem (778) [serial 1918] P [357] <<(PAV(now) and LRL(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [357] -> Q [258] < > by Normalization and theorem 777: Theorem (777) [serial 1922] used for: normalize [serial 1918] Theorem (779) [serial 1931] P [357] < > S [357] -> Q [258] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (780) [serial 1923] P [357] <<(LRL(now) and PAV(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) )>> S [357] -> Q [258] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 779: Theorem (779) [serial 1931] used for: Associativity: (b.c).a = a.b.c [serial 1923] Theorem (781) [serial 1919] P [357] <<(PAV(now) and LRL(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [357] -> Q [258] < > by Normalization and theorem 780: Theorem (780) [serial 1923] used for: normalize [serial 1919] Theorem (782) [serial 1021] P [357] <<(PAV(now) and LRL(now) and V(now)) and v@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [357] -> Q [258] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) and theorems 772 775 778 781: Theorem (772) [serial 1916] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1021] Theorem (775) [serial 1917] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1021] Theorem (778) [serial 1918] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1021] Theorem (781) [serial 1919] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1021] Theorem (783) [serial 1932] P [258] < = (now-PP::Ventricular_Refractory_Period))>> S [360] -> Q [256] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (784) [serial 1933] P [258] < = (now-PP::Ventricular_Refractory_Period))>> S [360] -> Q [256] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (785) [serial 1934] P [258] < = (now-PP::Ventricular_Refractory_Period))>> S [360] -> Q [256] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (786) [serial 1022] P [258] < = (now-PP::Ventricular_Refractory_Period))>> S [360] -> Q [256] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) and theorems 783 784 785: Theorem (783) [serial 1932] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1022] Theorem (784) [serial 1933] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1022] Theorem (785) [serial 1934] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1022] Theorem (787) [serial 1972] P [258] < > S [258] -> Q [364] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (788) [serial 2012] P [258] < > S [258] -> Q [134] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (789) [serial 2066] P [258] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #69#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#69# ) and (exists #70#:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@#70# ) and ap@last_ap and as@last_as and v@now and not (exists #71#:BLESS_Types::Time in last_ap,,now that ap@#71# ) and not (exists #72#:BLESS_Types::Time in last_as,,now that as@#72# ) and not (exists #73#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#73# ) and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (790) [serial 2064] P [258] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 789: Theorem (789) [serial 2066] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2064] Theorem (791) [serial 2053] P [258] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Extend Existential Quantification Range: Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 790: Theorem (790) [serial 2064] used for: Extend Existential Quantification Range: [serial 2053] Theorem (792) [serial 2047] P [258] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and v@now and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Normalization and theorem 791: Theorem (791) [serial 2053] used for: normalize [serial 2047] Theorem (793) [serial 2042] P [258] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and v@now and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Associativity: (b.c).a = a.b.c and theorem 792: Theorem (792) [serial 2047] used for: Associativity: (b.c).a = a.b.c [serial 2042] Theorem (794) [serial 2030] P [258] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and v@now and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 793: Theorem (793) [serial 2042] used for: Associativity: (b.c).a = a.b.c [serial 2030] Theorem (795) [serial 2024] P [258] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and (((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and v@now and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Normalization and theorem 794: Theorem (794) [serial 2030] used for: normalize [serial 2024] Theorem (796) [serial 2019] P [258] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and v@now and last_vp_or_vs < (now-PP::Ventricular_Refractory_Period)>> S [258] -> Q [134] < > by Substitution of Assertion Labels and theorem 795: Theorem (795) [serial 2024] used for: substituted Assertions' predicates for labels [serial 2019] Theorem (797) [serial 2013] P [258] < > S [258] -> Q [134] < > by Substitution of Assertion Labels and theorem 796: Theorem (796) [serial 2019] used for: substituted Assertions' predicates for labels [serial 2013] Theorem (798) [serial 1990] P [258] < > S [258] -> Q [364] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 788 797: Theorem (788) [serial 2012] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1990] Theorem (797) [serial 2013] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1990] Theorem (799) [serial 1984] P [258] < > S [258] -> Q [364] <<(v@now and not VRP(now))>> by Normalization and theorem 798: Theorem (798) [serial 1990] used for: normalize [serial 1984] Theorem (800) [serial 1973] P [258] < > S [258] -> Q [364] < > by Substitution of Assertion Labels and theorem 799: Theorem (799) [serial 1984] used for: substituted Assertions' predicates for labels in postconditions [serial 1973] Theorem (801) [serial 1948] P [258] < > S [258] -> Q [364] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 787 800: Theorem (787) [serial 1972] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1948] Theorem (800) [serial 1973] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1948] Theorem (802) [serial 1935] P [258] < > S [258] -> Q [364] < > by Normalization and theorem 801: Theorem (801) [serial 1948] used for: normalize [serial 1935] Theorem (803) [serial 2010] P [373] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or vs@now>> by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (804) [serial 2004] P [373] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (vs@now)>> by Normalization and theorem 803: Theorem (803) [serial 2010] used for: normalize [serial 2004] Theorem (805) [serial 2002] P [373] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vp@t ) or (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that vs@t )>> by Introduction of Existential Quantification and theorem 804: Theorem (804) [serial 2004] used for: replace exists with upper or lower bound [serial 2002] Theorem (806) [serial 1991] P [373] < > S [260] -> Q [260] < > by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 805: Theorem (805) [serial 2002] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1991] Theorem (807) [serial 1985] P [373] < > S [260] -> Q [260] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t )>> by Normalization and theorem 806: Theorem (806) [serial 1991] used for: normalize [serial 1985] Theorem (808) [serial 1974] P [373] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 807: Theorem (807) [serial 1985] used for: substituted Assertions' predicates for labels in postconditions [serial 1974] Theorem (809) [serial 1992] P [373] < > S [260] -> Q [260] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (810) [serial 1986] P [373] < > S [260] -> Q [260] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now))>> by Normalization and theorem 809: Theorem (809) [serial 1992] used for: normalize [serial 1986] Theorem (811) [serial 1975] P [373] < > S [260] -> Q [260] < > by Substitution of Assertion Labels and theorem 810: Theorem (810) [serial 1986] used for: substituted Assertions' predicates for labels in postconditions [serial 1975] Theorem (812) [serial 1949] P [373] < > S [260] -> Q [260] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 808 811: Theorem (808) [serial 1974] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1949] Theorem (811) [serial 1975] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1949] Theorem (813) [serial 1936] P [373] < > S [260] -> Q [260] < > by Normalization and theorem 812: Theorem (812) [serial 1949] used for: normalize [serial 1936] Theorem (814) [serial 2054] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [229] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (815) [serial 2048] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [229] < > by Normalization and theorem 814: Theorem (814) [serial 2054] used for: normalize [serial 2048] Theorem (816) [serial 2043] P [364] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [229] < > by Associativity: (b.c).a = a.b.c and theorem 815: Theorem (815) [serial 2048] used for: Associativity: (b.c).a = a.b.c [serial 2043] Theorem (817) [serial 2031] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv ))>> S [366] -> Q [229] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 816: Theorem (816) [serial 2043] used for: Associativity: (b.c).a = a.b.c [serial 2031] Theorem (818) [serial 2025] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vs or vp)@tv ))>> S [366] -> Q [229] < > by Normalization and theorem 817: Theorem (817) [serial 2031] used for: normalize [serial 2025] Theorem (819) [serial 2020] P [364] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (v@now and not VRP(now))>> S [366] -> Q [229] < > by Substitution of Assertion Labels and theorem 818: Theorem (818) [serial 2025] used for: substituted Assertions' predicates for labels [serial 2020] Theorem (820) [serial 2014] P [364] < > S [366] -> Q [229] < > by Substitution of Assertion Labels and theorem 819: Theorem (819) [serial 2020] used for: substituted Assertions' predicates for labels [serial 2014] Theorem (821) [serial 2055] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [230] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (822) [serial 2049] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [230] < > by Normalization and theorem 821: Theorem (821) [serial 2055] used for: normalize [serial 2049] Theorem (823) [serial 2044] P [364] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [230] < > by Associativity: (b.c).a = a.b.c and theorem 822: Theorem (822) [serial 2049] used for: Associativity: (b.c).a = a.b.c [serial 2044] Theorem (824) [serial 2032] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv ))>> S [366] -> Q [230] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 823: Theorem (823) [serial 2044] used for: Associativity: (b.c).a = a.b.c [serial 2032] Theorem (825) [serial 2026] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vs or vp)@tv ))>> S [366] -> Q [230] < > by Normalization and theorem 824: Theorem (824) [serial 2032] used for: normalize [serial 2026] Theorem (826) [serial 2021] P [364] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (v@now and not VRP(now))>> S [366] -> Q [230] < > by Substitution of Assertion Labels and theorem 825: Theorem (825) [serial 2026] used for: substituted Assertions' predicates for labels [serial 2021] Theorem (827) [serial 2015] P [364] < > S [366] -> Q [230] < > by Substitution of Assertion Labels and theorem 826: Theorem (826) [serial 2021] used for: substituted Assertions' predicates for labels [serial 2015] Theorem (828) [serial 1993] P [364] < > S [366] -> Q [366] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 820 827: Theorem (820) [serial 2014] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1993] Theorem (827) [serial 2015] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1993] Theorem (829) [serial 1987] P [364] < > S [366] -> Q [366] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))>> by Normalization and theorem 828: Theorem (828) [serial 1993] used for: normalize [serial 1987] Theorem (830) [serial 1976] P [364] < > S [366] -> Q [366] < > by Substitution of Assertion Labels and theorem 829: Theorem (829) [serial 1987] used for: substituted Assertions' predicates for labels in postconditions [serial 1976] Theorem (831) [serial 2056] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [224] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (832) [serial 2050] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [224] < > by Normalization and theorem 831: Theorem (831) [serial 2056] used for: normalize [serial 2050] Theorem (833) [serial 2045] P [364] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [224] < > by Associativity: (b.c).a = a.b.c and theorem 832: Theorem (832) [serial 2050] used for: Associativity: (b.c).a = a.b.c [serial 2045] Theorem (834) [serial 2033] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv ))>> S [366] -> Q [224] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 833: Theorem (833) [serial 2045] used for: Associativity: (b.c).a = a.b.c [serial 2033] Theorem (835) [serial 2027] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vs or vp)@tv ))>> S [366] -> Q [224] < > by Normalization and theorem 834: Theorem (834) [serial 2033] used for: normalize [serial 2027] Theorem (836) [serial 2022] P [364] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (v@now and not VRP(now))>> S [366] -> Q [224] < > by Substitution of Assertion Labels and theorem 835: Theorem (835) [serial 2027] used for: substituted Assertions' predicates for labels [serial 2022] Theorem (837) [serial 2016] P [364] < > S [366] -> Q [224] < > by Substitution of Assertion Labels and theorem 836: Theorem (836) [serial 2022] used for: substituted Assertions' predicates for labels [serial 2016] Theorem (838) [serial 2057] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [225] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (839) [serial 2051] P [364] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [225] < > by Normalization and theorem 838: Theorem (838) [serial 2057] used for: normalize [serial 2051] Theorem (840) [serial 2046] P [364] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv )>> S [366] -> Q [225] < > by Associativity: (b.c).a = a.b.c and theorem 839: Theorem (839) [serial 2051] used for: Associativity: (b.c).a = a.b.c [serial 2046] Theorem (841) [serial 2034] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vp or vs)@tv ))>> S [366] -> Q [225] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 840: Theorem (840) [serial 2046] used for: Associativity: (b.c).a = a.b.c [serial 2034] Theorem (842) [serial 2028] P [364] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))) and (v@now and not (exists tv:BLESS_Types::Time in now-PP::Ventricular_Refractory_Period,,now that (vs or vp)@tv ))>> S [366] -> Q [225] < > by Normalization and theorem 841: Theorem (841) [serial 2034] used for: normalize [serial 2028] Theorem (843) [serial 2023] P [364] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (v@now and not VRP(now))>> S [366] -> Q [225] < > by Substitution of Assertion Labels and theorem 842: Theorem (842) [serial 2028] used for: substituted Assertions' predicates for labels [serial 2023] Theorem (844) [serial 2017] P [364] < > S [366] -> Q [225] < > by Substitution of Assertion Labels and theorem 843: Theorem (843) [serial 2023] used for: substituted Assertions' predicates for labels [serial 2017] Theorem (845) [serial 1994] P [364] < > S [366] -> Q [366] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 837 844: Theorem (837) [serial 2016] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1994] Theorem (844) [serial 2017] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1994] Theorem (846) [serial 1988] P [364] < > S [366] -> Q [366] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))>> by Normalization and theorem 845: Theorem (845) [serial 1994] used for: normalize [serial 1988] Theorem (847) [serial 1977] P [364] < > S [366] -> Q [366] < > by Substitution of Assertion Labels and theorem 846: Theorem (846) [serial 1988] used for: substituted Assertions' predicates for labels in postconditions [serial 1977] Theorem (848) [serial 1978] P [364] < > S [366] -> Q [366] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (849) [serial 1950] P [364] < > S [366] -> Q [366] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorems 830 847 848: Theorem (830) [serial 1976] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1950] Theorem (847) [serial 1977] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1950] Theorem (848) [serial 1978] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1950] Theorem (850) [serial 1938] P [364] < > S [366] -> Q [366] < > by Normalization and theorem 849: Theorem (849) [serial 1950] used for: normalize [serial 1938] Theorem (851) [serial 1951] P [366] < > S [366] -> Q [366] < > by Identity (id): P->P is tautology Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (852) [serial 1941] P [366] < > S [366] -> Q [366] < > by Normalization and theorem 851: Theorem (851) [serial 1951] used for: normalize [serial 1941] Theorem (853) [serial 1966] P [369] < > S [368] -> Q [369] < > by Identity (id): P->P is tautology Theorem (854) [serial 1952] P [369] < > S [368] -> Q [369] <<(AXIOM_LRLi_gt_URLi_LIMIT(now) and LAST_AP(now) and LAST_AS(now) and vs@now) and now = last_vp_or_vs>> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 853: Theorem (853) [serial 1966] used for: Associativity: (b.c).a = a.b.c [serial 1952] Theorem (855) [serial 1942] P [369] < > S [368] -> Q [369] <<(vs@now and LAST_AS(now) and LAST_AP(now) and AXIOM_LRLi_gt_URLi_LIMIT( now)) and (last_vp_or_vs = now)>> by Normalization and theorem 854: Theorem (854) [serial 1952] used for: normalize [serial 1942] Theorem (856) [serial 1953] P [366] < > S [367] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (857) [serial 1945] P [366] < > S [367] -> Q [1] < > by Normalization and theorem 856: Theorem (856) [serial 1953] used for: normalize [serial 1945] Theorem (858) [serial 1971] P [367] < > S [367] -> Q [368] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (859) [serial 1970] P [367] < > S [367] -> Q [368] < > by Law of And-Simplification: P and true is P and theorem 858: Theorem (858) [serial 1971] used for: Law of And-Simplification: P and true is P [serial 1970] Theorem (860) [serial 1971] P [367] < > S [367] -> Q [368] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (861) [serial 1970] P [367] < > S [367] -> Q [368] < > by Law of And-Simplification: P and true is P and theorem 860: Theorem (860) [serial 1971] used for: Law of And-Simplification: P and true is P [serial 1970] Theorem (862) [serial 1967] P [367] < > S [367] -> Q [368] < > by Introduction of an Axiom to Postcondition: < > S <

> , <> ---------------- <> S <

> Theorem (861) [serial 1970] used for: add user-defined axioms to precondition: <> S <

> Theorem (863) [serial 1954] P [367] <<(LAST_AP(now) and LAST_AS(now) and VS(now)) and vs@now>> S [367] -> Q [368] <> -> <> by Associativity: (b.c).a = a.b.c Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 862: Theorem (862) [serial 1967] used for: Associativity: (b.c).a = a.b.c [serial 1954] Theorem (864) [serial 1946] P [367] <<(VS(now) and LAST_AS(now) and LAST_AP(now)) and vs@now>> S [367] -> Q [368] < > by Normalization and theorem 863: Theorem (863) [serial 1954] used for: normalize [serial 1946] Theorem (865) [serial 1943] P [366] < > S [367] vs! Q [368] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 857 864: Theorem (857) [serial 1945] used for: applied port output <> -> <> [serial 1943] Theorem (864) [serial 1946] used for: applied port output < > -> <> [serial 1943] Theorem (866) [serial 1968] P [366] < > S [370] -> Q [371] < > by True Conclusion Schema (tc): P->true Theorem (867) [serial 1955] P [366] < > S [370] -> Q [371] < > by Equality Law (idistr): a=a <-> true Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 866: Theorem (866) [serial 1968] used for: Equality Law (idistr): a=a <-> true [serial 1955] Theorem (868) [serial 1947] P [366] < > S [370] -> Q [371] < > by Normalization and theorem 867: Theorem (867) [serial 1955] used for: normalize [serial 1947] Theorem (869) [serial 1944] P [366] < > S [370] last_vp_or_vs := now Q [371] < > by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 868: Theorem (868) [serial 1947] used for: applied wp for assignment [serial 1944] Theorem (870) [serial 1939] P [366] <> S [369] < > vs! < > & last_vp_or_vs := now < > Q [369] <<(vs@now and LAST_AS(now) and LAST_AP(now) and AXIOM_LRLi_gt_URLi_LIMIT( now)) and (last_vp_or_vs = now)>> by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 852 855 865 869: Theorem (852) [serial 1941] used for: P -> P1 in concurrent composition for [serial 1939] Theorem (855) [serial 1942] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1939] Theorem (865) [serial 1943] used for: < > S1 < > in concurrent composition for [serial 1939] Theorem (869) [serial 1944] used for: < > S2 <

> in concurrent composition for [serial 1939] Theorem (871) [serial 1979] P [369] < > S [365] -> Q [374] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (872) [serial 1980] P [369] < > S [365] -> Q [374] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (873) [serial 2073] P [369] < > S [365] -> Q [374] < > by And-Elimination/Or-Introduction Schema (ctao): (P and Q)->(P or R) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (874) [serial 2072] P [369] < > S [365] -> Q [374] <<((vp@now)) or ((vs@now))>> by Normalization and theorem 873: Theorem (873) [serial 2073] used for: normalize [serial 2072] Theorem (875) [serial 2070] P [369] < > S [365] -> Q [374] <<(vp@now and true) or (vs@now and true)>> by Law of And-Simplification: P and true is P Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 874: Theorem (874) [serial 2072] used for: Law of And-Simplification: P and true is P [serial 2070] Theorem (876) [serial 2069] P [369] < > S [365] -> Q [374] <<(vp@now and not ((false))) or (vs@now and not ((false)))>> by Normalization and theorem 875: Theorem (875) [serial 2070] used for: normalize [serial 2069] Theorem (877) [serial 2068] P [369] < > S [365] -> Q [374] <<(vp@now and not ((false) or (false))) or (vs@now and not ((false) or (false)))>> by Law of Or-Simplification: P or P is P and theorem 876: Theorem (876) [serial 2069] used for: Law of Or-Simplification: P or P is P [serial 2068] Theorem (878) [serial 2067] P [369] < > S [365] -> Q [374] <<(vp@now and not ((exists #65#:BLESS_Types::Time in now,,now that vp@#65# ) or (exists #66#:BLESS_Types::Time in now,,now that vs@#66# ))) or (vs@now and not ((exists #67#:BLESS_Types::Time in now,,now that vp@#67# ) or (exists #68#:BLESS_Types::Time in now,,now that vs@#68# )))>> by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 877: Theorem (877) [serial 2068] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2067] Theorem (879) [serial 2065] P [369] < > S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists #65#:BLESS_Types::Time in last_vp_or_vs,,now that vp@#65# ) or (exists #66#:BLESS_Types::Time in last_vp_or_vs,,now that vs@#66# ))) or (vs@last_vp_or_vs and not ((exists #67#:BLESS_Types::Time in last_vp_or_vs,,now that vp@#67# ) or (exists #68#:BLESS_Types::Time in last_vp_or_vs,,now that vs@#68# )))>> by Substitution in Postcondition of All Equivalents in Precondition and theorem 878: Theorem (878) [serial 2067] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 2065] Theorem (880) [serial 2052] P [369] < > S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 879: Theorem (879) [serial 2065] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2052] Theorem (881) [serial 2041] P [369] < > S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Normalization and theorem 880: Theorem (880) [serial 2052] used for: normalize [serial 2041] Theorem (882) [serial 2029] P [369] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vs@now and (now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval) and now = last_vp_or_vs>> S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 881: Theorem (881) [serial 2041] used for: Associativity: (b.c).a = a.b.c [serial 2029] Theorem (883) [serial 2018] P [369] <<((now-PP::Lower_Rate_Limit_Interval) < (now-PP::Upper_Rate_Limit_Interval)) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and vs@now and now = last_vp_or_vs>> S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Normalization and theorem 882: Theorem (882) [serial 2029] used for: normalize [serial 2018] Theorem (884) [serial 2003] P [369] < > S [365] -> Q [374] <<(vp@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t ))) or (vs@last_vp_or_vs and not ((exists t:BLESS_Types::Time in last_vp_or_vs,,now that vp@t ) or (exists t:BLESS_Types::Time in last_vp_or_vs,,now that vs@t )))>> by Substitution of Assertion Labels and theorem 883: Theorem (883) [serial 2018] used for: substituted Assertions' predicates for labels [serial 2003] Theorem (885) [serial 1995] P [369] < > S [365] -> Q [374] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Distribution of preconditions, and over or, and distribution of postcondtitions, or over and Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 884: Theorem (884) [serial 2003] used for: Distribution of preconditions, and over or, and distribution of postcondtitions, or over and [serial 1995] Theorem (886) [serial 1989] P [369] < > S [365] -> Q [374] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 885: Theorem (885) [serial 1995] used for: normalize [serial 1989] Theorem (887) [serial 1981] P [369] < > S [365] -> Q [374] < > by Substitution of Assertion Labels and theorem 886: Theorem (886) [serial 1989] used for: substituted Assertions' predicates for labels in postconditions [serial 1981] Theorem (888) [serial 1982] P [369] < > S [365] -> Q [373] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (889) [serial 1983] P [369] < > S [365] -> Q [373] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (890) [serial 1969] P [369] < > S [365] -> Q [373] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) and theorems 871 872 887 888 889: Theorem (871) [serial 1979] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1969] Theorem (872) [serial 1980] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1969] Theorem (887) [serial 1981] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1969] Theorem (888) [serial 1982] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1969] Theorem (889) [serial 1983] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 1969] Theorem (891) [serial 1956] P [369] <<(AXIOM_LRLi_gt_URLi_LIMIT(now) and LAST_AP(now) and LAST_AS(now) and vs@now) and now = last_vp_or_vs>> S [365] -> Q [373] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 890: Theorem (890) [serial 1969] used for: Associativity: (b.c).a = a.b.c [serial 1956] Theorem (892) [serial 1940] P [369] <<(vs@now and LAST_AS(now) and LAST_AP(now) and AXIOM_LRLi_gt_URLi_LIMIT( now)) and (last_vp_or_vs = now)>> S [365] -> Q [373] < > by Normalization and theorem 891: Theorem (891) [serial 1956] used for: normalize [serial 1940] Theorem (893) [serial 1937] P [364] < > S [365] { < > vs! < > & last_vp_or_vs := now < > } Q [373] < > by Introduction of Existential Quantification (bl.elq) and theorems 850 870 892: Theorem (850) [serial 1938] used for: < > -> <> in existential lattice quantification for [serial 1937] Theorem (870) [serial 1939] used for: {A} T {B} in existential lattice quantification for [serial 1937] Theorem (892) [serial 1940] used for: <

> -> <> in existential lattice quantification for [serial 1937] Theorem (894) [serial 1023] P [258] <> S [365] < > { < > vs! < > & last_vp_or_vs := now < > } < > Q [260] < > by Introduction of Existential Quantification (bl.aab) and theorems 802 813 893: Theorem (802) [serial 1935] used for: as < > in <> { <

> S <> } < > for [serial 1023] Theorem (813) [serial 1936] used for: as <> -> < > in <> { <

> S <> } < > [serial 1023] Theorem (893) [serial 1937] used for: as <> S <> in < > { <

> S <> } < > [serial 1023] Theorem (895) [serial 2076] P [377] <> S [377] -> Q [262] <> by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (896) [serial 2075] P [377] <<(LRL(now) and V(now)) and a@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [377] -> Q [262] <> by Law of And-Simplification: P and true is P and theorem 895: Theorem (895) [serial 2076] used for: Law of And-Simplification: P and true is P [serial 2075] Theorem (897) [serial 2076] P [377] < > S [377] -> Q [262] <> by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (898) [serial 2075] P [377] <<(LRL(now) and V(now)) and a@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [377] -> Q [262] <> by Law of And-Simplification: P and true is P and theorem 897: Theorem (897) [serial 2076] used for: Law of And-Simplification: P and true is P [serial 2075] Theorem (899) [serial 1024] P [377] <<(LRL(now) and V(now)) and a@now and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [377] -> Q [262] <> by Introduction of an Axiom to Postcondition: <

> S <> , <

>
----------------
<

> S <>
Theorem (898) [serial 2075] used for:
add user-defined axioms to precondition:
<

> S <>
Theorem (900) [serial 2169]
P [262] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)
and
(exists #84#:BLESS_Types::Time
in now-PP::Lower_Rate_Limit_Interval..now
that (vp or vs)@#84# )
and
a@now
and
ap@last_ap
and
as@last_as
and
not (exists #81#:BLESS_Types::Time
in last_vp_or_vs,,now
that (vp or vs)@#81# )
and
not (exists #82#:BLESS_Types::Time
in last_as,,now
that ap@#82# )
and
not (exists #83#:BLESS_Types::Time
in last_as,,now
that as@#83# )
and
last_ap < (now-PP::Atrial_Refractory_Period)
and
last_as < (now-PP::Atrial_Refractory_Period)
and
last_as < last_ap
and
last_vp_or_vs < (now-PP::PVARP)>>
S [383] ->
Q [142] <>
by And Introduction Schema (aisph): (X and Y)->X
Theorem (901) [serial 2184]
P [262] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)
and
(exists #84#:BLESS_Types::Time
in now-PP::Lower_Rate_Limit_Interval..now
that (vp or vs)@#84# )
and
(all #81#:BLESS_Types::Time
in last_vp_or_vs,,now
are not (vp or vs)@#81# )
and
(all #82#:BLESS_Types::Time
in last_as,,now
are not ap@#82# )
and
(all #83#:BLESS_Types::Time
in last_as,,now
are not as@#83# )
and
a@now
and
ap@last_ap
and
as@last_as
and
last_ap < (now-PP::Atrial_Refractory_Period)
and
last_as < (now-PP::Atrial_Refractory_Period)
and
last_as < last_ap
and
last_vp_or_vs < (now-PP::PVARP)>>
S [383] ->
Q [113] <

> S <> , <

>
----------------
<

> S <>
Theorem (970) [serial 2098] used for:
add user-defined axioms to precondition:
<

> S <>
Theorem (972) [serial 2085]
P [384] <

> -> <**> and <****> -> < > then <> p! < >
and theorems 966 973:
Theorem (966) [serial 2081] used for:
applied port output <**

> -> <> [serial 2079] Theorem (973) [serial 2082] used for: applied port output < > -> <> [serial 2079] Theorem (975) [serial 2160] P [262] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and a@now and last_ap < (now-PP::Atrial_Refractory_Period) and last_as < (now-PP::Atrial_Refractory_Period) and last_as < last_ap and last_vp_or_vs < (now-PP::PVARP)>> S [388] -> Q [389] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Theorem (976) [serial 2151] P [262] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and a@now and last_ap < (now-PP::Atrial_Refractory_Period) and last_as < (now-PP::Atrial_Refractory_Period) and last_as < last_ap and last_vp_or_vs < (now-PP::PVARP)>> S [388] -> Q [389] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 975: Theorem (975) [serial 2160] used for: Associativity: (b.c).a = a.b.c [serial 2151] Theorem (977) [serial 2146] P [262] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and a@now and last_ap < (now-PP::Atrial_Refractory_Period) and last_as < (now-PP::Atrial_Refractory_Period) and last_as < last_ap and last_vp_or_vs < (now-PP::PVARP)>> S [388] -> Q [389] < > by Normalization and theorem 976: Theorem (976) [serial 2151] used for: normalize [serial 2146] Theorem (978) [serial 2141] P [262] < > S [388] -> Q [389] < > by Substitution of Assertion Labels and theorem 977: Theorem (977) [serial 2146] used for: substituted Assertions' predicates for labels in preconditions [serial 2141] Theorem (979) [serial 2131] P [262] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and a@now and last_ap < (now-PP::Atrial_Refractory_Period) and last_as < (now-PP::Atrial_Refractory_Period) and last_as < last_ap and last_vp_or_vs < (now-PP::PVARP)>> S [388] -> Q [389] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 978: Theorem (978) [serial 2141] used for: Associativity: (b.c).a = a.b.c [serial 2131] Theorem (980) [serial 2126] P [262] <<(last_as < last_ap) and (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and a@now and last_ap < (now-PP::Atrial_Refractory_Period) and last_as < (now-PP::Atrial_Refractory_Period) and last_vp_or_vs < (now-PP::PVARP)>> S [388] -> Q [389] < > by Normalization and theorem 979: Theorem (979) [serial 2131] used for: normalize [serial 2126] Theorem (981) [serial 2114] P [262] < > S [388] -> Q [389] < > by Substitution of Assertion Labels Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 980: Theorem (980) [serial 2126] used for: substituted Assertions' predicates for labels in preconditions [serial 2114] Theorem (982) [serial 2108] P [262] < > S [388] -> Q [389] <<((as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )))>> by Normalization and theorem 981: Theorem (981) [serial 2114] used for: normalize [serial 2108] Theorem (983) [serial 2099] P [262] < > S [388] -> Q [389] <<(LAST_AS(now))>> by Substitution of Assertion Labels and theorem 982: Theorem (982) [serial 2108] used for: substituted Assertions' predicates for labels in postconditions [serial 2099] Theorem (984) [serial 2092] P [262] < > S [388] -> Q [389] < > by Law of And-Simplification: P and true is P Normalization Axioms: Irreflexivity of Greater Than: (a>b) = (b last_vp_or_vs) and ((now-PP::Atrial_Refractory_Period) > last_as) and ((now-PP::Atrial_Refractory_Period) > last_ap) and a@now and LRL(now) and V(now) and AXIOM_LAST_AS_LT_LAST_AP()>> S [388] -> Q [389] <<(true) and LAST_AS(now)>> by Normalization and theorem 984: Theorem (984) [serial 2092] used for: normalize [serial 2087] Theorem (986) [serial 2086] P [262] < last_vp_or_vs) and ((now-PP::Atrial_Refractory_Period) > last_as) and ((now-PP::Atrial_Refractory_Period) > last_ap))>> S [388] -> Q [389] <<(true) and LAST_AS(now)>> by Associativity: (b.c).a = a.b.c and theorem 985: Theorem (985) [serial 2087] used for: Associativity: (b.c).a = a.b.c [serial 2086] Theorem (987) [serial 2083] P [262] < last_vp_or_vs) and ((now-PP::Atrial_Refractory_Period) > last_as) and ((now-PP::Atrial_Refractory_Period) > last_ap))>> S [388] -> Q [389] <<(now = now) and LAST_AS(now)>> by Equality Law (idistr): a=a <-> true and theorem 986: Theorem (986) [serial 2086] used for: Equality Law (idistr): a=a <-> true [serial 2083] Theorem (988) [serial 2080] P [262] < last_vp_or_vs) and ((now-PP::Atrial_Refractory_Period) > last_as) and ((now-PP::Atrial_Refractory_Period) > last_ap))>> S [388] last_as := now Q [389] <<(last_as = now) and LAST_AS(now)>> by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 987: Theorem (987) [serial 2083] used for: applied wp for assignment [serial 2080] Theorem (989) [serial 1025] P [262] < last_vp_or_vs) and ((now-PP::Atrial_Refractory_Period) > last_as) and ((now-PP::Atrial_Refractory_Period) > last_ap))>> S [387] <> as! < > & last_as := now <<(last_as = now) and LAST_AS(now)>> Q [250] < > by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 949 964 974 988: Theorem (949) [serial 2077] used for: P -> P1 in concurrent composition for [serial 1025] Theorem (964) [serial 2078] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1025] Theorem (974) [serial 2079] used for: < > S1 < > in concurrent composition for [serial 1025] Theorem (988) [serial 2080] used for: <

> S2 <**> and <****> -> < > then <> p! < >
and theorems 1087 1090:
Theorem (1087) [serial 2195] used for:
applied port output <**

> -> <> [serial 2193] Theorem (1090) [serial 2196] used for: applied port output < > -> <> [serial 2193] Theorem (1092) [serial 2335] P [264] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1093) [serial 2325] P [264] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by Normalization and theorem 1092: Theorem (1092) [serial 2335] used for: normalize [serial 2325] Theorem (1094) [serial 2316] P [264] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by Associativity: (b.c).a = a.b.c and theorem 1093: Theorem (1093) [serial 2325] used for: Associativity: (b.c).a = a.b.c [serial 2316] Theorem (1095) [serial 2297] P [264] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1094: Theorem (1094) [serial 2316] used for: Associativity: (b.c).a = a.b.c [serial 2297] Theorem (1096) [serial 2287] P [264] <<((ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by Normalization and theorem 1095: Theorem (1095) [serial 2297] used for: normalize [serial 2287] Theorem (1097) [serial 2266] P [264] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1096: Theorem (1096) [serial 2287] used for: substituted Assertions' predicates for labels [serial 2266] Theorem (1098) [serial 2255] P [264] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Normalization and theorem 1097: Theorem (1097) [serial 2266] used for: normalize [serial 2255] Theorem (1099) [serial 2244] P [264] < > S [410] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Substitution of Assertion Labels and theorem 1098: Theorem (1098) [serial 2255] used for: substituted Assertions' predicates for labels [serial 2244] Theorem (1100) [serial 2336] P [264] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@last_as and v@now and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1101) [serial 2326] P [264] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Normalization and theorem 1100: Theorem (1100) [serial 2336] used for: normalize [serial 2326] Theorem (1102) [serial 2317] P [264] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Associativity: (b.c).a = a.b.c and theorem 1101: Theorem (1101) [serial 2326] used for: Associativity: (b.c).a = a.b.c [serial 2317] Theorem (1103) [serial 2298] P [264] <<(((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1102: Theorem (1102) [serial 2317] used for: Associativity: (b.c).a = a.b.c [serial 2298] Theorem (1104) [serial 2288] P [264] <<((ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Normalization and theorem 1103: Theorem (1103) [serial 2298] used for: normalize [serial 2288] Theorem (1105) [serial 2267] P [264] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Substitution of Assertion Labels Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1104: Theorem (1104) [serial 2288] used for: substituted Assertions' predicates for labels [serial 2267] Theorem (1106) [serial 2256] P [264] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and v@now and last_vp_or_vs <= (now-PP::Ventricular_Refractory_Period)>> S [410] -> Q [220] < > by Normalization and theorem 1105: Theorem (1105) [serial 2267] used for: normalize [serial 2256] Theorem (1107) [serial 2245] P [264] < > S [410] -> Q [220] < > by Substitution of Assertion Labels and theorem 1106: Theorem (1106) [serial 2256] used for: substituted Assertions' predicates for labels [serial 2245] Theorem (1108) [serial 2230] P [264] < > S [410] -> Q [411] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1099 1107: Theorem (1099) [serial 2244] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2230] Theorem (1107) [serial 2245] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2230] Theorem (1109) [serial 2223] P [264] < > S [410] -> Q [411] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t ))>> by Normalization and theorem 1108: Theorem (1108) [serial 2230] used for: normalize [serial 2223] Theorem (1110) [serial 2215] P [264] < > S [410] -> Q [411] < > by Substitution of Assertion Labels Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1109: Theorem (1109) [serial 2223] used for: substituted Assertions' predicates for labels in postconditions [serial 2215] Theorem (1111) [serial 2210] P [264] < > S [410] -> Q [411] <<(LAST_VP_OR_VS(now))>> by Normalization and theorem 1110: Theorem (1110) [serial 2215] used for: normalize [serial 2210] Theorem (1112) [serial 2209] P [264] < > S [410] -> Q [411] < > by Law of And-Simplification: P and true is P and theorem 1111: Theorem (1111) [serial 2210] used for: Law of And-Simplification: P and true is P [serial 2209] Theorem (1113) [serial 2202] P [264] < > S [410] -> Q [411] < > by Equality Law (idistr): a=a <-> true Normalization Axioms: Irreflexivity of At Least: (a>=b) = (b<=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1112: Theorem (1112) [serial 2209] used for: Equality Law (idistr): a=a <-> true [serial 2202] Theorem (1114) [serial 2197] P [264] < = last_vp_or_vs)>> S [410] -> Q [411] <<(now = now) and LAST_VP_OR_VS(now)>> by Normalization and theorem 1113: Theorem (1113) [serial 2202] used for: normalize [serial 2197] Theorem (1115) [serial 2194] P [264] < = last_vp_or_vs)>> S [410] last_vp_or_vs := now Q [411] <<(last_vp_or_vs = now) and LAST_VP_OR_VS(now)>> by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 1114: Theorem (1114) [serial 2197] used for: applied wp for assignment [serial 2194] Theorem (1116) [serial 1029] P [264] <= last_vp_or_vs)>> S [409] < > vs! < > & last_vp_or_vs := now <<(last_vp_or_vs = now) and LAST_VP_OR_VS(now)>> Q [260] < > by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 1069 1085 1091 1115: Theorem (1069) [serial 2191] used for: P -> P1 in concurrent composition for [serial 1029] Theorem (1085) [serial 2192] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 1029] Theorem (1091) [serial 2193] used for: < > S1 < > in concurrent composition for [serial 1029] Theorem (1115) [serial 2194] used for: < > S2 <

> in concurrent composition for [serial 1029] Theorem (1117) [serial 2416] P [428] < > -> <> S [256] -> Q [256] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1118) [serial 2558] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and (exists #111#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#111# ) and ap@now and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #113#:BLESS_Types::Time in last_as,,last_ap that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and not (exists #115#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1119) [serial 2554] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and (exists #111#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#111# ) and ap@now and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #113#:BLESS_Types::Time in last_as,,last_ap that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and not (exists #115#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] < > by Introduction of Existential Quantification and theorem 1118: Theorem (1118) [serial 2558] used for: replace exists with upper or lower bound [serial 2554] Theorem (1120) [serial 2544] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and (exists #111#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#111# ) and ap@now and ap@last_ap and as@last_as and true and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #113#:BLESS_Types::Time in last_as,,last_ap that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and not (exists #115#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1119: Theorem (1119) [serial 2554] used for: Law of And-Simplification: P and true is P [serial 2544] Theorem (1121) [serial 2536] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and now = last_ap and (exists #111#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#111# ) and ap@now and not (false) and not (exists #113#:BLESS_Types::Time in last_as,,last_ap that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#115# )>> S [256] -> Q [256] < > by Normalization and theorem 1120: Theorem (1120) [serial 2544] used for: normalize [serial 2536] Theorem (1122) [serial 2528] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and now = last_ap and (exists #111#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#111# ) and ap@now and not (exists #112#:BLESS_Types::Time in last_ap,,last_ap that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,last_ap that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#115# )>> S [256] -> Q [256] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 1121: Theorem (1121) [serial 2536] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2528] Theorem (1123) [serial 2501] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1122: Theorem (1122) [serial 2528] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2501] Theorem (1124) [serial 2494] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] <<(exists ts:BLESS_Types::Time in now-PP::Fixed_AV_Delay..now that ap@ts )>> by Normalization and theorem 1123: Theorem (1123) [serial 2501] used for: normalize [serial 2494] Theorem (1125) [serial 2487] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #111#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#111# ) and ap@last_ap and as@last_as and not (exists #112#:BLESS_Types::Time in last_ap,,now that ap@#112# ) and not (exists #113#:BLESS_Types::Time in last_as,,now that as@#113# ) and not (exists #114#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#114# ) and not (exists #115#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#115# ) and now = last_ap>> S [256] -> Q [256] < > by Substitution of Assertion Labels and theorem 1124: Theorem (1124) [serial 2494] used for: substituted Assertions' predicates for labels [serial 2487] Theorem (1126) [serial 2470] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1125: Theorem (1125) [serial 2487] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2470] Theorem (1127) [serial 2461] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Normalization and theorem 1126: Theorem (1126) [serial 2470] used for: normalize [serial 2461] Theorem (1128) [serial 2443] P [428] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1127: Theorem (1127) [serial 2461] used for: Associativity: (b.c).a = a.b.c [serial 2443] Theorem (1129) [serial 2434] P [428] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Normalization and theorem 1128: Theorem (1128) [serial 2443] used for: normalize [serial 2434] Theorem (1130) [serial 2417] P [428] < > S [256] -> Q [256] < > by Substitution of Assertion Labels and theorem 1129: Theorem (1129) [serial 2434] used for: substituted Assertions' predicates for labels in preconditions [serial 2417] Theorem (1131) [serial 2589] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (1132) [serial 2586] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] <<(ap@last_ap)>> by Normalization and theorem 1131: Theorem (1131) [serial 2589] used for: normalize [serial 2586] Theorem (1133) [serial 2584] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1132: Theorem (1132) [serial 2586] used for: Law of And-Simplification: P and true is P [serial 2584] Theorem (1134) [serial 2581] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Normalization and theorem 1133: Theorem (1133) [serial 2584] used for: normalize [serial 2581] Theorem (1135) [serial 2575] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Solitary Open Range Law: exists a:t in j,,j that V is false Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1134: Theorem (1134) [serial 2581] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2575] Theorem (1136) [serial 2572] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,last_ap that ap@t ))>> by Normalization and theorem 1135: Theorem (1135) [serial 2575] used for: normalize [serial 2572] Theorem (1137) [serial 2562] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution of Assertion Labels and theorem 1136: Theorem (1136) [serial 2572] used for: substituted Assertions' predicates for labels in postconditions [serial 2562] Theorem (1138) [serial 2555] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 1137: Theorem (1137) [serial 2562] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 2555] Theorem (1139) [serial 2545] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and true and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1138: Theorem (1138) [serial 2555] used for: Law of And-Simplification: P and true is P [serial 2545] Theorem (1140) [serial 2537] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (false) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Normalization and theorem 1139: Theorem (1139) [serial 2545] used for: normalize [serial 2537] Theorem (1141) [serial 2529] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (exists #117#:BLESS_Types::Time in last_ap,,last_ap that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 1140: Theorem (1140) [serial 2537] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2529] Theorem (1142) [serial 2520] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1141: Theorem (1141) [serial 2529] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2520] Theorem (1143) [serial 2591] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [224] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1144) [serial 2600] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [225] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1145) [serial 2592] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [225] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1144: Theorem (1144) [serial 2600] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2592] Theorem (1146) [serial 2576] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1143 1145: Theorem (1143) [serial 2591] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2576] Theorem (1145) [serial 2592] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2576] Theorem (1147) [serial 2573] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,last_ap that as@t ))>> by Normalization and theorem 1146: Theorem (1146) [serial 2576] used for: normalize [serial 2573] Theorem (1148) [serial 2563] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution of Assertion Labels and theorem 1147: Theorem (1147) [serial 2573] used for: substituted Assertions' predicates for labels in postconditions [serial 2563] Theorem (1149) [serial 2556] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 1148: Theorem (1148) [serial 2563] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 2556] Theorem (1150) [serial 2546] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and true and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1149: Theorem (1149) [serial 2556] used for: Law of And-Simplification: P and true is P [serial 2546] Theorem (1151) [serial 2538] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (false) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Normalization and theorem 1150: Theorem (1150) [serial 2546] used for: normalize [serial 2538] Theorem (1152) [serial 2530] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (exists #117#:BLESS_Types::Time in last_ap,,last_ap that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 1151: Theorem (1151) [serial 2538] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2530] Theorem (1153) [serial 2521] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1152: Theorem (1152) [serial 2530] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2521] Theorem (1154) [serial 2597] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [219] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (1155) [serial 2593] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [219] <<(vp@last_vp_or_vs or vs@last_vp_or_vs)>> by Normalization and theorem 1154: Theorem (1154) [serial 2597] used for: normalize [serial 2593] Theorem (1156) [serial 2601] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [220] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1157) [serial 2594] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [220] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1156: Theorem (1156) [serial 2601] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2594] Theorem (1158) [serial 2577] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@t )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1155 1157: Theorem (1155) [serial 2593] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2577] Theorem (1157) [serial 2594] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2577] Theorem (1159) [serial 2574] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vs or vp)@t ))>> by Normalization and theorem 1158: Theorem (1158) [serial 2577] used for: normalize [serial 2574] Theorem (1160) [serial 2564] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution of Assertion Labels and theorem 1159: Theorem (1159) [serial 2574] used for: substituted Assertions' predicates for labels in postconditions [serial 2564] Theorem (1161) [serial 2557] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 1160: Theorem (1160) [serial 2564] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 2557] Theorem (1162) [serial 2547] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and ap@last_ap and as@last_as and true and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Law of And-Simplification: P and true is P Normalization Axioms: Complement Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1161: Theorem (1161) [serial 2557] used for: Law of And-Simplification: P and true is P [serial 2547] Theorem (1163) [serial 2539] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (false) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Normalization and theorem 1162: Theorem (1162) [serial 2547] used for: normalize [serial 2539] Theorem (1164) [serial 2531] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap and (exists #116#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#116# ) and ap@now and not (exists #117#:BLESS_Types::Time in last_ap,,last_ap that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,last_ap that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#120# )>> S [256] -> Q [193] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 1163: Theorem (1163) [serial 2539] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2531] Theorem (1165) [serial 2522] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [193] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1164: Theorem (1164) [serial 2531] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2522] Theorem (1166) [serial 2502] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [256] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1142 1153 1165: Theorem (1142) [serial 2520] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2502] Theorem (1153) [serial 2521] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2502] Theorem (1165) [serial 2522] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2502] Theorem (1167) [serial 2495] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [256] <<(LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now))>> by Normalization and theorem 1166: Theorem (1166) [serial 2502] used for: normalize [serial 2495] Theorem (1168) [serial 2488] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #116#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#116# ) and ap@last_ap and as@last_as and not (exists #117#:BLESS_Types::Time in last_ap,,now that ap@#117# ) and not (exists #118#:BLESS_Types::Time in last_as,,now that as@#118# ) and not (exists #119#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#119# ) and not (exists #120#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#120# ) and now = last_ap>> S [256] -> Q [256] < > by Substitution of Assertion Labels and theorem 1167: Theorem (1167) [serial 2495] used for: substituted Assertions' predicates for labels [serial 2488] Theorem (1169) [serial 2471] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@last_ap and as@last_as and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1168: Theorem (1168) [serial 2488] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2471] Theorem (1170) [serial 2462] P [428] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Normalization and theorem 1169: Theorem (1169) [serial 2471] used for: normalize [serial 2462] Theorem (1171) [serial 2444] P [428] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1170: Theorem (1170) [serial 2462] used for: Associativity: (b.c).a = a.b.c [serial 2444] Theorem (1172) [serial 2435] P [428] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and now = last_ap>> S [256] -> Q [256] < > by Normalization and theorem 1171: Theorem (1171) [serial 2444] used for: normalize [serial 2435] Theorem (1173) [serial 2418] P [428] < > S [256] -> Q [256] < > by Substitution of Assertion Labels and theorem 1172: Theorem (1172) [serial 2435] used for: substituted Assertions' predicates for labels in preconditions [serial 2418] Theorem (1174) [serial 2374] P [428] < > S [256] -> Q [256] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1117 1130 1173: Theorem (1117) [serial 2416] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2374] Theorem (1130) [serial 2417] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2374] Theorem (1173) [serial 2418] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2374] Theorem (1175) [serial 2361] P [428] <<(last_ap = now) and LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and LRL(now)>> S [256] -> Q [256] < > by Normalization and theorem 1174: Theorem (1174) [serial 2374] used for: normalize [serial 2361] Theorem (1176) [serial 2525] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [181] <<(vp or vs)@(now-va_interval)>> by And Introduction Schema (aisph): (X and Y)->X Theorem (1177) [serial 2559] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #135#:BLESS_Types::Time in last_ap,,now that ap@#135# ) and not (exists #136#:BLESS_Types::Time in last_as,,now that as@#136# ) and not (exists #137#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#137# ) and not (exists #138#:BLESS_Types::Time in tops,,now that (vp or vs)@(#138#-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in #138#-PP::Lower_Rate_Limit_Interval,,#138# that (vp or vs)@#101# ) ) and not (exists #139#:BLESS_Types::Time in tops,,now that (vp or vs)@(#139#-va_interval) and not (exists #102#:BLESS_Types::Time in #139#-va_interval,,#139# that (vp or vs)@#102# ) ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# )>> S [424] -> Q [188] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1178) [serial 2534] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [188] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1177: Theorem (1177) [serial 2559] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2534] Theorem (1179) [serial 2526] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [188] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1178: Theorem (1178) [serial 2534] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2526] Theorem (1180) [serial 2560] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #141#:BLESS_Types::Time in last_ap,,now that ap@#141# ) and not (exists #142#:BLESS_Types::Time in last_as,,now that as@#142# ) and not (exists #143#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#143# ) and not (exists #144#:BLESS_Types::Time in tops,,now that (vp or vs)@(#144#-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in #144#-PP::Lower_Rate_Limit_Interval,,#144# that (vp or vs)@#101# ) ) and not (exists #145#:BLESS_Types::Time in tops,,now that (vp or vs)@(#145#-va_interval) and not (exists #102#:BLESS_Types::Time in #145#-va_interval,,#145# that (vp or vs)@#102# ) ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# )>> S [424] -> Q [183] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1181) [serial 2535] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [183] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1180: Theorem (1180) [serial 2560] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2535] Theorem (1182) [serial 2527] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [183] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1181: Theorem (1181) [serial 2535] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2527] Theorem (1183) [serial 2516] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [415] <<(vp or vs)@(now-va_interval) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorems 1176 1179 1182: Theorem (1176) [serial 2525] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2516] Theorem (1179) [serial 2526] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2516] Theorem (1182) [serial 2527] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2516] Theorem (1184) [serial 2509] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [415] <<(vp or vs)@(now-va_interval) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> by Normalization and theorem 1183: Theorem (1183) [serial 2516] used for: normalize [serial 2509] Theorem (1185) [serial 2499] P [414] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [415] <<(vp or vs)@(now-va_interval) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1184: Theorem (1184) [serial 2509] used for: Associativity: (b.c).a = a.b.c [serial 2499] Theorem (1186) [serial 2492] P [414] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists #96#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#96# ) and (vp or vs)@(now-va_interval) and not (exists #100#:BLESS_Types::Time in tops,,now that v@#100# ) and not (exists #97#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#97# ) and not (exists #98#:BLESS_Types::Time in tops,,now that stop@#98# ) and not (exists #99#:BLESS_Types::Time in tops,,now that a@#99# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #101#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#101# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #102#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#102# ) )>> S [424] -> Q [415] <<((vp or vs)@(now-va_interval) and not (exists tv:BLESS_Types::Time in (now-va_interval),,now that (vs or vp)@tv ) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ))>> by Normalization and theorem 1185: Theorem (1185) [serial 2499] used for: normalize [serial 2492] Theorem (1187) [serial 2485] P [414] < > S [424] -> Q [415] < > by Substitution of Assertion Labels and theorem 1186: Theorem (1186) [serial 2492] used for: substituted Assertions' predicates for labels [serial 2485] Theorem (1188) [serial 2463] P [414] < > S [424] -> Q [415] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1187: Theorem (1187) [serial 2485] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2463] Theorem (1189) [serial 2445] P [414] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1188: Theorem (1188) [serial 2463] used for: Associativity: (b.c).a = a.b.c [serial 2445] Theorem (1190) [serial 2436] P [414] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Normalization and theorem 1189: Theorem (1189) [serial 2445] used for: normalize [serial 2436] Theorem (1191) [serial 2419] P [414] < > S [424] -> Q [415] < > by Substitution of Assertion Labels and theorem 1190: Theorem (1190) [serial 2436] used for: substituted Assertions' predicates for labels in preconditions [serial 2419] Theorem (1192) [serial 2464] P [414] < > S [424] -> Q [415] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1193) [serial 2446] P [414] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1192: Theorem (1192) [serial 2464] used for: Associativity: (b.c).a = a.b.c [serial 2446] Theorem (1194) [serial 2437] P [414] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Normalization and theorem 1193: Theorem (1193) [serial 2446] used for: normalize [serial 2437] Theorem (1195) [serial 2420] P [414] < > S [424] -> Q [415] < > by Substitution of Assertion Labels and theorem 1194: Theorem (1194) [serial 2437] used for: substituted Assertions' predicates for labels in preconditions [serial 2420] Theorem (1196) [serial 2465] P [414] < > S [424] -> Q [415] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1197) [serial 2447] P [414] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1196: Theorem (1196) [serial 2465] used for: Associativity: (b.c).a = a.b.c [serial 2447] Theorem (1198) [serial 2438] P [414] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [415] < > by Normalization and theorem 1197: Theorem (1197) [serial 2447] used for: normalize [serial 2438] Theorem (1199) [serial 2421] P [414] < > S [424] -> Q [415] < > by Substitution of Assertion Labels and theorem 1198: Theorem (1198) [serial 2438] used for: substituted Assertions' predicates for labels in preconditions [serial 2421] Theorem (1200) [serial 2422] P [414] < > S [424] -> Q [425] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1201) [serial 2517] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #103#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#103# ) and (vp or vs)@(now-va_interval) and ap@last_ap and as@last_as and not (exists #104#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#104# ) and not (exists #105#:BLESS_Types::Time in tops,,now that stop@#105# ) and not (exists #106#:BLESS_Types::Time in tops,,now that a@#106# ) and not (exists #107#:BLESS_Types::Time in tops,,now that v@#107# ) and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #108#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#108# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #109#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#109# ) )>> S [424] -> Q [416] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1202) [serial 2510] P [414] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists #103#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#103# ) and (vp or vs)@(now-va_interval) and not (exists #104#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#104# ) and not (exists #105#:BLESS_Types::Time in tops,,now that stop@#105# ) and not (exists #106#:BLESS_Types::Time in tops,,now that a@#106# ) and not (exists #107#:BLESS_Types::Time in tops,,now that v@#107# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #108#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#108# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #109#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#109# ) )>> S [424] -> Q [416] < > by Normalization and theorem 1201: Theorem (1201) [serial 2517] used for: normalize [serial 2510] Theorem (1203) [serial 2500] P [414] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists #103#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#103# ) and (vp or vs)@(now-va_interval) and not (exists #104#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#104# ) and not (exists #105#:BLESS_Types::Time in tops,,now that stop@#105# ) and not (exists #106#:BLESS_Types::Time in tops,,now that a@#106# ) and not (exists #107#:BLESS_Types::Time in tops,,now that v@#107# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #108#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#108# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #109#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#109# ) )>> S [424] -> Q [416] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1202: Theorem (1202) [serial 2510] used for: Associativity: (b.c).a = a.b.c [serial 2500] Theorem (1204) [serial 2493] P [414] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists #103#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#103# ) and (vp or vs)@(now-va_interval) and not (exists #104#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#104# ) and not (exists #105#:BLESS_Types::Time in tops,,now that stop@#105# ) and not (exists #106#:BLESS_Types::Time in tops,,now that a@#106# ) and not (exists #107#:BLESS_Types::Time in tops,,now that v@#107# ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists #108#:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@#108# ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists #109#:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@#109# ) )>> S [424] -> Q [416] < > by Normalization and theorem 1203: Theorem (1203) [serial 2500] used for: normalize [serial 2493] Theorem (1205) [serial 2486] P [414] < > S [424] -> Q [416] < > by Substitution of Assertion Labels and theorem 1204: Theorem (1204) [serial 2493] used for: substituted Assertions' predicates for labels [serial 2486] Theorem (1206) [serial 2466] P [414] < > S [424] -> Q [416] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1205: Theorem (1205) [serial 2486] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2466] Theorem (1207) [serial 2448] P [414] <<(LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now)) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [416] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1206: Theorem (1206) [serial 2466] used for: Associativity: (b.c).a = a.b.c [serial 2448] Theorem (1208) [serial 2439] P [414] <<(exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and (LAST_VP_OR_VS(now) and LAST_AS(now) and LAST_AP(now)) and (vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [416] < > by Normalization and theorem 1207: Theorem (1207) [serial 2448] used for: normalize [serial 2439] Theorem (1209) [serial 2423] P [414] < > S [424] -> Q [416] < > by Substitution of Assertion Labels and theorem 1208: Theorem (1208) [serial 2439] used for: substituted Assertions' predicates for labels in preconditions [serial 2423] Theorem (1210) [serial 2402] P [414] < > S [424] -> Q [424] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorems 1191 1195 1199 1200 1209: Theorem (1191) [serial 2419] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2402] Theorem (1195) [serial 2420] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2402] Theorem (1199) [serial 2421] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2402] Theorem (1200) [serial 2422] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2402] Theorem (1209) [serial 2423] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2402] Theorem (1211) [serial 2392] P [414] < > S [424] -> Q [424] < > by Normalization and theorem 1210: Theorem (1210) [serial 2402] used for: normalize [serial 2392] Theorem (1212) [serial 2375] P [414] <<(LRL(now) and V(now)) and ((vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that stop@u ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t ) ) and not (exists u:BLESS_Types::Time in tops,,now that (vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t ) )>> S [424] -> Q [424] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1211: Theorem (1211) [serial 2392] used for: Associativity: (b.c).a = a.b.c [serial 2375] Theorem (1213) [serial 2363] P [414] <<(LRL(now) and V(now)) and ((vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [424] -> Q [424] <<((AP(now) and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and (LRL(now)))>> by Normalization and theorem 1212: Theorem (1212) [serial 2375] used for: normalize [serial 2363] Theorem (1214) [serial 2403] P [424] < > S [415] -> Q [415] < > by And Introduction Schema (aiswl): (X and Y and Z)->(X and Y) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1215) [serial 2393] P [424] < > S [415] -> Q [415] < > by Normalization and theorem 1214: Theorem (1214) [serial 2403] used for: normalize [serial 2393] Theorem (1216) [serial 2376] P [424] < > S [415] -> Q [415] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1215: Theorem (1215) [serial 2393] used for: Associativity: (b.c).a = a.b.c [serial 2376] Theorem (1217) [serial 2366] P [424] <<((AP(now) and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and (LRL(now)))>> S [415] -> Q [415] < > by Normalization and theorem 1216: Theorem (1216) [serial 2376] used for: normalize [serial 2366] Theorem (1218) [serial 2404] P [424] < > S [425] -> Q [425] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1219) [serial 2394] P [424] < > S [425] -> Q [425] < > by Normalization and theorem 1218: Theorem (1218) [serial 2404] used for: normalize [serial 2394] Theorem (1220) [serial 2377] P [424] < > S [425] -> Q [425] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1219: Theorem (1219) [serial 2394] used for: Associativity: (b.c).a = a.b.c [serial 2377] Theorem (1221) [serial 2367] P [424] <<((AP(now) and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and (LRL(now)))>> S [425] -> Q [425] < > by Normalization and theorem 1220: Theorem (1220) [serial 2377] used for: normalize [serial 2367] Theorem (1222) [serial 2405] P [424] < > S [420] -> Q [424] < > by Identity (id): P->P is tautology Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1223) [serial 2395] P [424] < > S [420] -> Q [424] < > by Normalization and theorem 1222: Theorem (1222) [serial 2405] used for: normalize [serial 2395] Theorem (1224) [serial 2378] P [424] < > S [420] -> Q [424] <<(LAST_AS(now) and LAST_VP_OR_VS(now) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap )) and (LRL(now) and now = last_ap)>> by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1223: Theorem (1223) [serial 2395] used for: Associativity: (b.c).a = a.b.c [serial 2378] Theorem (1225) [serial 2368] P [424] < > S [420] -> Q [424] <<(ap@now and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap )) and ((last_ap = now) and LRL(now))>> by Normalization and theorem 1224: Theorem (1224) [serial 2378] used for: normalize [serial 2368] Theorem (1226) [serial 2379] P [415] < > S [419] -> Q [1] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1227) [serial 2371] P [415] < > S [419] -> Q [1] < > by Normalization and theorem 1226: Theorem (1226) [serial 2379] used for: normalize [serial 2371] Theorem (1228) [serial 2424] P [419] < > S [419] -> Q [420] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1229) [serial 2425] P [419] < > S [419] -> Q [420] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1230) [serial 2426] P [419] < > S [419] -> Q [420] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1231) [serial 2491] P [419] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (vp or vs)@(now-va_interval) and ap@now and as@last_as and not (exists #130#:BLESS_Types::Time in last_as,,now that as@#130# ) and not (exists #131#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#131# ) and not (exists #132#:BLESS_Types::Time in tops,,now that a@#132# ) and not (exists #133#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#133# )>> S [419] -> Q [421] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1232) [serial 2484] P [419] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (vp or vs)@(now-va_interval) and ap@now and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> S [419] -> Q [421] < > by Replacement of Quantified Variables with #1, #2, etc. and theorem 1231: Theorem (1231) [serial 2491] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2484] Theorem (1233) [serial 2476] P [419] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (vp or vs)@(now-va_interval) and ap@now and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> S [419] -> Q [421] < > by Law of And-Simplification: P and P is P Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1232: Theorem (1232) [serial 2484] used for: Law of And-Simplification: P and P is P [serial 2476] Theorem (1234) [serial 2467] P [419] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and (vp or vs)@(now-va_interval) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and ap@now and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> S [419] -> Q [421] < > by Normalization and theorem 1233: Theorem (1233) [serial 2476] used for: normalize [serial 2467] Theorem (1235) [serial 2449] P [419] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and ((vp or vs)@(now-va_interval) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta ) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ap@now and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> S [419] -> Q [421] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1234: Theorem (1234) [serial 2467] used for: Associativity: (b.c).a = a.b.c [serial 2449] Theorem (1236) [serial 2440] P [419] <<((vp or vs)@(now-va_interval) and not (exists tv:BLESS_Types::Time in (now-va_interval),,now that (vs or vp)@tv ) and not (exists ta:BLESS_Types::Time in tops,,now that a@ta )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and ap@now and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )>> S [419] -> Q [421] < > by Normalization and theorem 1235: Theorem (1235) [serial 2449] used for: normalize [serial 2440] Theorem (1237) [serial 2427] P [419] < > S [419] -> Q [421] < > by Substitution of Assertion Labels and theorem 1236: Theorem (1236) [serial 2440] used for: substituted Assertions' predicates for labels in preconditions [serial 2427] Theorem (1238) [serial 2406] P [419] < > S [419] -> Q [420] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorems 1228 1229 1230 1237: Theorem (1228) [serial 2424] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2406] Theorem (1229) [serial 2425] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2406] Theorem (1230) [serial 2426] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2406] Theorem (1237) [serial 2427] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2406] Theorem (1239) [serial 2396] P [419] < > S [419] -> Q [420] < > by Normalization and theorem 1238: Theorem (1238) [serial 2406] used for: normalize [serial 2396] Theorem (1240) [serial 2380] P [419] <<(AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and ap@now>> S [419] -> Q [420] < > by Associativity: (b.c).a = a.b.c Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1239: Theorem (1239) [serial 2396] used for: Associativity: (b.c).a = a.b.c [serial 2380] Theorem (1241) [serial 2372] P [419] <<(AP(now) and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and ap@now>> S [419] -> Q [420] < > by Normalization and theorem 1240: Theorem (1240) [serial 2380] used for: normalize [serial 2372] Theorem (1242) [serial 2369] P [415] < > S [419] ap! Q [420] < > by Port Event Output: when < > and <> -> <> then < > p! <> and theorems 1227 1241: Theorem (1227) [serial 2371] used for: applied port output <> -> <> [serial 2369] Theorem (1241) [serial 2372] used for: applied port output < > -> <> [serial 2369] Theorem (1243) [serial 2408] P [425] < > S [426] -> Q [427] < > by Identity (id): P->P is tautology Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (1244) [serial 2399] P [425] < > S [426] -> Q [427] <<(LRL(now))>> by Normalization and theorem 1243: Theorem (1243) [serial 2408] used for: normalize [serial 2399] Theorem (1245) [serial 2397] P [425] < > S [426] -> Q [427] < > by Law of And-Simplification: P and true is P and theorem 1244: Theorem (1244) [serial 2399] used for: Law of And-Simplification: P and true is P [serial 2397] Theorem (1246) [serial 2381] P [425] < > S [426] -> Q [427] < > by Equality Law (idistr): a=a <-> true Normalization Axioms: Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1245: Theorem (1245) [serial 2397] used for: Equality Law (idistr): a=a <-> true [serial 2381] Theorem (1247) [serial 2373] P [425] < > S [426] -> Q [427] <<(now = now) and LRL(now)>> by Normalization and theorem 1246: Theorem (1246) [serial 2381] used for: normalize [serial 2373] Theorem (1248) [serial 2370] P [425] < > S [426] last_ap := now Q [427] <<(last_ap = now) and LRL(now)>> by Assignment Rule: < > -> <

> which is < > --------------------------------------- <> x:=e <

> (bl.a) and theorem 1247: Theorem (1247) [serial 2373] used for: applied wp for assignment [serial 2370] Theorem (1249) [serial 2364] P [424] <<((AP(now) and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv )) and (LRL(now)))>> S [424] <> ap! < > & < > last_ap := now <<(last_ap = now) and LRL(now)>> Q [424] <<(ap@now and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap )) and ((last_ap = now) and LRL(now))>> by Concurrent Composition Rule: < > -> <

>, < > -> <

>, . . . , < >, < > S2 < >, . . . , < > Sn < > < > -> < > ----------------------------------------------- <> S <

> where S is <> S1 < > & < > S2 < > & . . . & < > Sn < > (bl.cck) and theorems 1217 1221 1225 1242 1248: Theorem (1217) [serial 2366] used for: P -> P1 in concurrent composition for [serial 2364] Theorem (1221) [serial 2367] used for: P -> P2 in concurrent composition for [serial 2364] Theorem (1225) [serial 2368] used for: Q1 and Q2 and . . . and Qn -> Q in concurrent composition for [serial 2364] Theorem (1242) [serial 2369] used for: < > S1 < > in concurrent composition for [serial 2364] Theorem (1248) [serial 2370] used for: < > S2 < > in concurrent composition for [serial 2364] Theorem (1250) [serial 2540] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [229] < > by And Introduction Schema (aisph): (X and Y)->X Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) Theorem (1251) [serial 2532] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@last_ap and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# )>> S [415] -> Q [229] < > by Normalization and theorem 1250: Theorem (1250) [serial 2540] used for: normalize [serial 2532] Theorem (1252) [serial 2523] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [229] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1251: Theorem (1251) [serial 2532] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2523] Theorem (1253) [serial 2570] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by True Conclusion Schema (tc): P->true Normalization Axioms: Complement Add Unnecessary Parentheses For No Good Reason: a = (a) Theorem (1254) [serial 2566] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by Normalization and theorem 1253: Theorem (1253) [serial 2570] used for: normalize [serial 2566] Theorem (1255) [serial 2565] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by Solitary Open Range Law: exists a:t in j,,j that V is false and theorem 1254: Theorem (1254) [serial 2566] used for: Solitary Open Range Law: exists a:t in j,,j that V is false [serial 2565] Theorem (1256) [serial 2561] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by Substitution in Postcondition of All Equivalents in Precondition and theorem 1255: Theorem (1255) [serial 2565] used for: Substitution in Postcondition of All Equivalents in Precondition substituting in postcondition all equivalents in precondition [serial 2561] Theorem (1257) [serial 2541] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@now and ap@last_ap and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1256: Theorem (1256) [serial 2561] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2541] Theorem (1258) [serial 2533] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap and (exists #121#:BLESS_Types::Time in last_ap-PP::Lower_Rate_Limit_Interval..last_ap that (vp or vs)@#121# ) and ap@last_ap and not (exists #122#:BLESS_Types::Time in last_as,,last_ap that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,last_ap that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in last_ap-va_interval,,last_ap that (vp or vs)@#124# )>> S [415] -> Q [230] < > by Normalization and theorem 1257: Theorem (1257) [serial 2541] used for: normalize [serial 2533] Theorem (1259) [serial 2524] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [230] < > by Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b and theorem 1258: Theorem (1258) [serial 2533] used for: Remove Equivalent Term: P(a) and P(b) and a=b is P(a) and a=b [serial 2524] Theorem (1260) [serial 2503] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [428] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Add Unnecessary Parentheses For No Good Reason: a = (a) and theorems 1252 1259: Theorem (1252) [serial 2523] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2503] Theorem (1259) [serial 2524] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2503] Theorem (1261) [serial 2496] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [428] <<(ap@last_ap and not (exists t:BLESS_Types::Time in last_ap,,now that ap@t ))>> by Normalization and theorem 1260: Theorem (1260) [serial 2503] used for: normalize [serial 2496] Theorem (1262) [serial 2489] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #121#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#121# ) and ap@now and as@last_as and not (exists #122#:BLESS_Types::Time in last_as,,now that as@#122# ) and not (exists #123#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#123# ) and not (exists #124#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#124# ) and now = last_ap>> S [415] -> Q [428] < > by Substitution of Assertion Labels and theorem 1261: Theorem (1261) [serial 2496] used for: substituted Assertions' predicates for labels [serial 2489] Theorem (1263) [serial 2477] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [428] < > by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1262: Theorem (1262) [serial 2489] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2477] Theorem (1264) [serial 2468] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [428] < > by Normalization and theorem 1263: Theorem (1263) [serial 2477] used for: normalize [serial 2468] Theorem (1265) [serial 2450] P [424] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [428] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1264: Theorem (1264) [serial 2468] used for: Associativity: (b.c).a = a.b.c [serial 2450] Theorem (1266) [serial 2441] P [424] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [428] < > by Normalization and theorem 1265: Theorem (1265) [serial 2450] used for: normalize [serial 2441] Theorem (1267) [serial 2428] P [424] < > S [415] -> Q [428] < > by Substitution of Assertion Labels and theorem 1266: Theorem (1266) [serial 2441] used for: substituted Assertions' predicates for labels in preconditions [serial 2428] Theorem (1268) [serial 2429] P [424] < > S [415] -> Q [428] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1269) [serial 2430] P [424] < > S [415] -> Q [428] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1270) [serial 2431] P [424] < > S [415] -> Q [432] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1271) [serial 2490] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists #125#:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@#125# ) and ap@now and as@last_as and not (exists #126#:BLESS_Types::Time in last_as,,now that as@#126# ) and not (exists #127#:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@#127# ) and not (exists #128#:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@#128# ) and now = last_ap>> S [415] -> Q [429] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1272) [serial 2478] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [429] < > by Replacement of Quantified Variables with #1, #2, etc. Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorem 1271: Theorem (1271) [serial 2490] used for: Replacement of Quantified Variables with #1, #2, etc. [serial 2478] Theorem (1273) [serial 2469] P [424] <<(vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t ) and as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t ) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [429] < > by Normalization and theorem 1272: Theorem (1272) [serial 2478] used for: normalize [serial 2469] Theorem (1274) [serial 2451] P [424] <<((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vp or vs)@t )) and (as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and (exists t:BLESS_Types::Time in now-PP::Lower_Rate_Limit_Interval..now that (vp or vs)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [429] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Disjunction: (m or k) = (k or m) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses to Range Bound For No Good Reason: a..b = (a)..b and theorem 1273: Theorem (1273) [serial 2469] used for: Associativity: (b.c).a = a.b.c [serial 2451] Theorem (1275) [serial 2442] P [424] <<(as@last_as and not (exists t:BLESS_Types::Time in last_as,,now that as@t )) and ((vp@last_vp_or_vs or vs@last_vp_or_vs) and not (exists t:BLESS_Types::Time in last_vp_or_vs,,now that (vs or vp)@t )) and (exists t:BLESS_Types::Time in (now-PP::Lower_Rate_Limit_Interval)..now that (vs or vp)@t ) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap ) and now = last_ap>> S [415] -> Q [429] < > by Normalization and theorem 1274: Theorem (1274) [serial 2451] used for: normalize [serial 2442] Theorem (1276) [serial 2432] P [424] < > S [415] -> Q [429] < > by Substitution of Assertion Labels and theorem 1275: Theorem (1275) [serial 2442] used for: substituted Assertions' predicates for labels in preconditions [serial 2432] Theorem (1277) [serial 2433] P [424] < > S [415] -> Q [428] < > by And Introduction Schema (aisph): (X and Y)->X Theorem (1278) [serial 2407] P [424] < > S [415] -> Q [428] < > by Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) Normalization Axiom: Reflexivity of Conjunction: (m and k) = (k and m) and theorems 1267 1268 1269 1270 1276 1277: Theorem (1267) [serial 2428] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1268) [serial 2429] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1269) [serial 2430] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1270) [serial 2431] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1276) [serial 2432] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1277) [serial 2433] used for: Sequent Composition: if A->B and A->C and A->D then A->(B and C and D) [serial 2407] Theorem (1279) [serial 2398] P [424] < > S [415] -> Q [428] < > by Normalization and theorem 1278: Theorem (1278) [serial 2407] used for: normalize [serial 2398] Theorem (1280) [serial 2382] P [424] <<(LAST_AS(now) and LAST_VP_OR_VS(now) and ap@now and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap )) and (LRL(now) and now = last_ap)>> S [415] -> Q [428] < > by Associativity: (b.c).a = a.b.c Normalization Axioms: Reflexivity of Equality: (a=b) = (b=a) Reflexivity of Conjunction: (m and k) = (k and m) Add Unnecessary Parentheses For No Good Reason: a = (a) and theorem 1279: Theorem (1279) [serial 2398] used for: Associativity: (b.c).a = a.b.c [serial 2382] Theorem (1281) [serial 2365] P [424] <<(ap@now and LAST_VP_OR_VS(now) and LAST_AS(now) and not (exists tap:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tap )) and ((last_ap = now) and LRL(now))>> S [415] -> Q [428] <<(last_ap = now) and LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and LRL(now)>> by Normalization and theorem 1280: Theorem (1280) [serial 2382] used for: normalize [serial 2365] Theorem (1282) [serial 2362] P [414] <<(LRL(now) and V(now)) and ((vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [415] { < > ap! < > & < > last_ap := now <<(last_ap = now) and LRL(now)>> } Q [428] <<(last_ap = now) and LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and LRL(now)>> by Introduction of Existential Quantification (bl.elq) and theorems 1213 1249 1281: Theorem (1213) [serial 2363] used for: < > -> <> in existential lattice quantification for [serial 2362] Theorem (1249) [serial 2364] used for: {A} T {B} in existential lattice quantification for [serial 2362] Theorem (1281) [serial 2365] used for: <

> -> <> in existential lattice quantification for [serial 2362] Theorem (1283) [serial 1030] P [414] <<(LRL(now) and V(now)) and ((vp or vs)@(now-va_interval) and not (exists t:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@t )) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-PP::Lower_Rate_Limit_Interval) and not (exists t:BLESS_Types::Time in u-PP::Lower_Rate_Limit_Interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that a@u ) and not (exists u:BLESS_Types::Time in tops,,now that v@u ) and not (exists u:BLESS_Types::Time in tops,,now that ((vp or vs)@(u-va_interval) and not (exists t:BLESS_Types::Time in u-va_interval,,u that (vp or vs)@t )) ) and not (exists u:BLESS_Types::Time in tops,,now that stop@u )>> S [415] { <> ap! < > & < > last_ap := now <<(last_ap = now) and LRL(now)>> } <<(last_ap = now) and LAST_AP(now) and LAST_AS(now) and LAST_VP_OR_VS(now) and not (exists tv:BLESS_Types::Time in now-va_interval,,now that (vp or vs)@tv ) and LRL(now)>> Q [256] < > by Introduction of Existential Quantification (bl.aapost) and theorems 1175 1282: Theorem (1175) [serial 2361] used for: as < > -> < > in <

> { S <> } < > [serial 1030] Theorem (1282) [serial 2362] used for: as <