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6691 lines (6690 loc) · 361 KB
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(Lemmata
(lemma_1 0
(lemma_1-1 nil 3834042957
("" (skos 1 s0 s1 p alpha j)
(("" (flatten 1)
(("" (label "tran" -1) (("" (for-alpha :lazy? nil) nil nil))
nil))
nil))
nil)
((Winner const-decl "bool" Lemmata nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(transition const-decl "bool" IOA nil)
(Effect const-decl "cState" FilterLock nil)
(PcEff const-decl "PCs" FilterLock nil)
(LogicEff const-decl "cState" FilterLock nil)
(Precondition const-decl "bool" FilterLock nil)
(PcPrec const-decl "PCs" FilterLock nil)
(LogicPrec const-decl "bool" FilterLock nil)
(co_ioa_inst const-decl "CO_IOA" FilterLock nil)
(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockInv_eta formula-decl nil actions nil)
(LockRet? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockRet_eta formula-decl nil actions nil)
(lock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock1_eta formula-decl nil actions nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(lock2T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2T_eta formula-decl nil actions nil)
(lock2F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2F_eta formula-decl nil actions nil)
(lock3? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock3_eta formula-decl nil actions nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(lock4? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock4_eta formula-decl nil actions nil)
(lock5? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock5_eta formula-decl nil actions nil)
(member const-decl "bool" sets nil)
(lock6T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6T_eta formula-decl nil actions nil)
(empty? const-decl "bool" sets nil)
(lock6F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6F_eta formula-decl nil actions nil)
(lock7T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7T_eta formula-decl nil actions nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(lock7F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7F_eta formula-decl nil actions nil)
(lock8T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8T_eta formula-decl nil actions nil)
(lock8F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8F_eta formula-decl nil actions nil)
(lock9T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9T_eta formula-decl nil actions nil)
(/= const-decl "boolean" notequal nil)
(lock9F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9F_eta formula-decl nil actions nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(lock10? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock10_eta formula-decl nil actions nil)
(unlock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_unlock1_eta formula-decl nil actions nil)
(action_inclusive formula-decl nil actions nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(action type-decl nil actions nil)
(external adt-def-decl "boolean" actions nil)
(internal adt-def-decl "boolean" actions nil)
(action? nonempty-type-eq-decl nil actions nil))
shostak))
(lemma_2 0
(lemma_2-1 nil 3834043013
("" (skos 1 s0 s1 proc alpha j)
(("" (flatten 1)
(("" (label "tran" -1) (("" (for-alpha :lazy? nil) nil nil))
nil))
nil))
nil)
((Competitor const-decl "bool" Lemmata nil)
(CheckVictim const-decl "bool" Lemmata nil)
(CheckFlag const-decl "bool" Lemmata nil)
(Winner const-decl "bool" Lemmata nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(transition const-decl "bool" IOA nil)
(Effect const-decl "cState" FilterLock nil)
(PcEff const-decl "PCs" FilterLock nil)
(LogicEff const-decl "cState" FilterLock nil)
(Precondition const-decl "bool" FilterLock nil)
(PcPrec const-decl "PCs" FilterLock nil)
(LogicPrec const-decl "bool" FilterLock nil)
(co_ioa_inst const-decl "CO_IOA" FilterLock nil)
(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockInv_eta formula-decl nil actions nil)
(LockRet? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockRet_eta formula-decl nil actions nil)
(lock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock1_eta formula-decl nil actions nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(lock2T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2T_eta formula-decl nil actions nil)
(lock2F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2F_eta formula-decl nil actions nil)
(lock3? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock3_eta formula-decl nil actions nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(lock4? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock4_eta formula-decl nil actions nil)
(lock5? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock5_eta formula-decl nil actions nil)
(member const-decl "bool" sets nil)
(lock6T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6T_eta formula-decl nil actions nil)
(empty? const-decl "bool" sets nil)
(lock6F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6F_eta formula-decl nil actions nil)
(lock7T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7T_eta formula-decl nil actions nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(lock7F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7F_eta formula-decl nil actions nil)
(lock8T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8T_eta formula-decl nil actions nil)
(lock8F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8F_eta formula-decl nil actions nil)
(lock9T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9T_eta formula-decl nil actions nil)
(/= const-decl "boolean" notequal nil)
(lock9F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9F_eta formula-decl nil actions nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(lock10? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock10_eta formula-decl nil actions nil)
(unlock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_unlock1_eta formula-decl nil actions nil)
(action_inclusive formula-decl nil actions nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(action type-decl nil actions nil)
(external adt-def-decl "boolean" actions nil)
(internal adt-def-decl "boolean" actions nil)
(action? nonempty-type-eq-decl nil actions nil))
shostak))
(lemma_3 0
(lemma_3-1 nil 3839771083
("" (skos 1 s0 s1 alpha p)
(("" (flatten) (("" (for-alpha :lazy? nil) nil nil)) nil)) nil)
((action? nonempty-type-eq-decl nil actions nil)
(internal adt-def-decl "boolean" actions nil)
(external adt-def-decl "boolean" actions nil)
(action type-decl nil actions nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(action_inclusive formula-decl nil actions nil)
(action_unlock1_eta formula-decl nil actions nil)
(unlock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock10_eta formula-decl nil actions nil)
(lock10? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9F_eta formula-decl nil actions nil)
(lock9F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9T_eta formula-decl nil actions nil)
(lock9T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8F_eta formula-decl nil actions nil)
(lock8F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8T_eta formula-decl nil actions nil)
(lock8T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7F_eta formula-decl nil actions nil)
(lock7F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7T_eta formula-decl nil actions nil)
(lock7T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6F_eta formula-decl nil actions nil)
(lock6F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6T_eta formula-decl nil actions nil)
(lock6T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock5_eta formula-decl nil actions nil)
(lock5? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock4_eta formula-decl nil actions nil)
(lock4? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock3_eta formula-decl nil actions nil)
(lock3? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2F_eta formula-decl nil actions nil)
(lock2F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2T_eta formula-decl nil actions nil)
(lock2T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock1_eta formula-decl nil actions nil)
(lock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockRet_eta formula-decl nil actions nil)
(LockRet? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockInv_eta formula-decl nil actions nil)
(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
(co_ioa_inst const-decl "CO_IOA" FilterLock nil)
(LogicPrec const-decl "bool" FilterLock nil)
(PcPrec const-decl "PCs" FilterLock nil)
(Precondition const-decl "bool" FilterLock nil)
(LogicEff const-decl "cState" FilterLock nil)
(PcEff const-decl "PCs" FilterLock nil)
(Effect const-decl "cState" FilterLock nil)
(transition const-decl "bool" IOA nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(/= const-decl "boolean" notequal nil)
(empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil))
shostak))
(lemma_4 0
(lemma_4-1 nil 3846230230
("" (skeep)
(("" (split)
(("1" (lemma card_1_has_1)
(("1" (inst -1 S)
(("1" (notice -1)
(("1" (skeep) (("1" (inst?) (("1" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2" (lemma card_bij)
(("2" (inst -1 1 S)
(("2" (replace -4)
(("2" (flatten)
(("2" (skeep)
(("2" (expand "bijective?")
(("2" (flatten)
(("2" (expand "injective?")
(("2"
(case "NOT (forall (P,Q:bool) : (P => Q) IFF (NOT Q => NOT P))")
(("1" (hide-all-but 1)
(("1" (grind) nil nil)) nil)
("2" (expand "member")
(("2" (inst -2 p q)
(("2"
(inst -1 "f(p)=f(q)" "p=q")
(("2"
(replace -2)
(("2"
(flatten)
(("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(member const-decl "bool" sets nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(card_1_has_1 formula-decl nil finite_sets nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil) (> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(THREADS const-decl "above(1)" PROC nil)
(PROC nonempty-type-eq-decl nil PROC nil)
(card_bij formula-decl nil finite_sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(below type-eq-decl nil nat_types nil)
(injective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil))
shostak))
(lemma_5 0
(lemma_5-1 nil 3846230762
("" (skeep)
(("" (split)
(("1" (lemma card_2_has_2)
(("1" (inst -1 S)
(("1" (notice -1)
(("1" (skeep)
(("1" (inst?)
(("1" (inst 2 y) (("1" (grind) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2" (expand "member")
(("2" (lemma card_bij)
(("2" (inst -1 2 S)
(("2" (replace -5)
(("2" (flatten)
(("2" (skeep)
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(copy -1)
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(inst -1 p q)
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(inst -2 q r)
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(inst -3 p r)
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(copy -1)
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"p=q")
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(inst
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(replace -5)
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(replace -6)
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(flatten)
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1)
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4)
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7)
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nil)
(number_field nonempty-type-from-decl nil number_fields nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(THREADS const-decl "above(1)" PROC nil)
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(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
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(below type-eq-decl nil nat_types nil)
(injective? const-decl "bool" functions nil)
(card_bij formula-decl nil finite_sets nil))
shostak))
(lemma_6_TCC1 0
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nil))
nil))
nil))
nil))
nil)
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nil)
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nil (lemma_6 subtype "sets[PROC].fullset" "finite_set[PROC]")))
(lemma_6 0
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nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
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(THREADS const-decl "above(1)" PROC nil)
(PROC nonempty-type-eq-decl nil PROC nil))
shostak))
(inv_14 0
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("2" (install-rewrites "Lemmata")
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(LockRet? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockInv_eta formula-decl nil actions nil)
(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
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(Precondition const-decl "bool" FilterLock nil)
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"(strict_total_order?[real])" real_props nil)
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(above nonempty-type-eq-decl nil integers nil)
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(PCs type-decl nil FilterLock nil)
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(action type-decl nil actions nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(external adt-def-decl "boolean" actions nil)
(internal adt-def-decl "boolean" actions nil)
(action? nonempty-type-eq-decl nil actions nil)
(invariant const-decl "bool" invariant nil))
shostak))
(inv_15 0
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("" (inv-setup)
(("1" (conc-rewrite)
(("1" (assert -1)
(("1" (expand CSI)
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nil))
nil)
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nil))
nil))
nil))
nil))
nil)
((transition const-decl "bool" IOA nil)
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(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
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"(strict_total_order?[real])" real_props nil)
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real_props nil)
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(/= const-decl "boolean" notequal nil)
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integers nil)
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nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(< const-decl "bool" reals nil) (> const-decl "bool" reals nil)
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shostak))
(inv_16 0
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nil))
nil))
nil))
nil))
nil)
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(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
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real_props nil)
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(/= const-decl "boolean" notequal nil)
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integers nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
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(number nonempty-type-decl nil numbers nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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(< const-decl "bool" reals nil) (> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(THREADS const-decl "above(1)" PROC nil)
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(invariant const-decl "bool" invariant nil))
shostak))
(inv_17 0
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("" (inv-setup)
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(("1" (assert -1)
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nil)
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(("2" (inst ind-hyp p)
(("2" (case "proc(alpha)=p")
(("1" (for-alpha :lazy? nil) nil nil)
("2" (for-alpha :lazy? nil) nil nil))
nil))
nil))
nil))
nil))
nil)
((transition const-decl "bool" IOA nil)
(Effect const-decl "cState" FilterLock nil)
(PcEff const-decl "PCs" FilterLock nil)
(LogicEff const-decl "cState" FilterLock nil)
(Precondition const-decl "bool" FilterLock nil)
(PcPrec const-decl "PCs" FilterLock nil)
(LogicPrec const-decl "bool" FilterLock nil)
(LockInv? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockInv_eta formula-decl nil actions nil)
(LockRet? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_LockRet_eta formula-decl nil actions nil)
(lock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock1_eta formula-decl nil actions nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(lock2T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2T_eta formula-decl nil actions nil)
(lock2F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock2F_eta formula-decl nil actions nil)
(lock3? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock3_eta formula-decl nil actions nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(lock4? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock4_eta formula-decl nil actions nil)
(lock5? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock5_eta formula-decl nil actions nil)
(member const-decl "bool" sets nil)
(lock6T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6T_eta formula-decl nil actions nil)
(empty? const-decl "bool" sets nil)
(lock6F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock6F_eta formula-decl nil actions nil)
(lock7T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7T_eta formula-decl nil actions nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(lock7F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock7F_eta formula-decl nil actions nil)
(lock8T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8T_eta formula-decl nil actions nil)
(lock8F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock8F_eta formula-decl nil actions nil)
(lock9T? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9T_eta formula-decl nil actions nil)
(/= const-decl "boolean" notequal nil)
(lock9F? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock9F_eta formula-decl nil actions nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(lock10? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_lock10_eta formula-decl nil actions nil)
(unlock1? adt-recognizer-decl "[action -> boolean]" actions nil)
(action_unlock1_eta formula-decl nil actions nil)
(action_inclusive formula-decl nil actions nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(proc shared-adt-accessor-decl "[action -> PROC]" actions nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(InitialStatePredicate const-decl "bool" FilterLock nil)
(reachable?_induction formula-decl nil IOA nil)
(IOA type-eq-decl nil IOA nil)
(CO_IOA type-eq-decl nil FilterLock nil)
(co_ioa_inst const-decl "CO_IOA" FilterLock nil)
(LevelValue const-decl "bool" Lemmata nil)
(PROC nonempty-type-eq-decl nil PROC nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)