|
(finite_pointwise_orders
(IMP_infinite_pigeonhole_TCC1 0
(IMP_infinite_pigeonhole_TCC1-1 nil 3314641151
("" (forward-chain "nat_infinite") nil nil)
((nat_infinite formula-decl nil numbers_infinite nil)) nil))
(IMP_infinite_pigeonhole_TCC2 0
(IMP_infinite_pigeonhole_TCC2-1 nil 3314641151
("" (forward-chain "domain_finiteness") nil nil)
((domain_finiteness formula-decl nil finite_pointwise_orders nil))
nil))
(infinite_pigeonhole 0
(infinite_pigeonhole-1 nil 3314641222
("" (skolem!)
(("" (use "infinite_pigeonhole")
(("" (skolem!)
(("" (inst?)
(("" (use "enumerable")
(("1" (skolem-typepred)
(("1" (inst?)
(("1" (skolem!)
(("1" (decompose-equality)
(("1" (inst - "f!2(n!1)")
(("1"
(expand* "image" "inverse_image" "singleton"
"member")
(("1" (replace*)
(("1" (assert)
(("1" (inst?)
(("1"
(expand "fullset")
(("1" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand* "strictly_monotone?" "preserves" "preserves"
"restrict")
nil nil))
nil))
nil)
("2" (expand* "enumerable?" "bounded_below?")
(("2" (assert)
(("2" (inst + 0)
(("2" (expand* "lower_bound?" "restrict") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((infinite_pigeonhole formula-decl nil infinite_pigeonhole 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)
(D formal-type-decl nil finite_pointwise_orders nil)
(bounded_below? const-decl "bool" bounded_orders nil)
(lower_bound? const-decl "bool" bounded_orders nil)
(strictly_monotone? const-decl "bool" integer_enumerations nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(preserves const-decl "bool" functions nil)
(n!1 skolem-const-decl "nat" finite_pointwise_orders nil)
(member const-decl "bool" sets nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(image const-decl "set[R]" function_image nil)
(fullset const-decl "set" sets nil)
(f!2 skolem-const-decl "(strictly_monotone?)"
finite_pointwise_orders nil)
(< const-decl "bool" reals nil)
(restrict const-decl "R" restrict nil)
(preserves const-decl "bool" functions nil)
(PRED type-eq-decl nil defined_types nil)
(strict_total_order_restrict application-judgement
"(strict_total_order?[S])" restrict_order_props nil)
(trichotomous_restrict application-judgement "(trichotomous?[S])"
restrict_order_props nil)
(strict_order_restrict application-judgement "(strict_order?[S])"
restrict_order_props nil)
(transitive_restrict application-judgement "(transitive?[S])"
restrict_order_props nil)
(antisymmetric_restrict application-judgement "(antisymmetric?[S])"
restrict_order_props nil)
(irreflexive_restrict application-judgement "(irreflexive?[S])"
restrict_order_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" bounded_orders nil)
(r!1 skolem-const-decl "D" finite_pointwise_orders nil)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(f!1 skolem-const-decl "[nat -> D]" finite_pointwise_orders nil)
(inverse_image const-decl "set[D]" function_image nil)
(enumerable? const-decl "bool" integer_enumerations nil)
(set type-eq-decl nil sets nil)
(enumerable formula-decl nil integer_enumerations nil))
shostak))
(descending_exists 0
(descending_exists-1 nil 3314641512
("" (skosimp)
(("" (expand "descending?")
(("" (inst?)
((""
(expand* "strictly_pointwise" "irreflexive_kernel"
"difference" "member")
(("" (flatten)
(("" (decompose-equality)
((""
(expand* "pointwise" "reflexive_closure" "union"
"member")
(("" (inst?) (("" (inst?) (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((descending? const-decl "bool" monotone_sequences nil)
(irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil)
(member const-decl "bool" sets nil)
(difference const-decl "set" sets nil)
(strictly_pointwise const-decl "pred[[[D -> R], [D -> R]]]"
pointwise_orders nil)
(reflexive_closure_preserves_transitive application-judgement
"(preorder?)" well_foundedness nil)
(pointwise_preserves_preorder application-judgement
"(preorder?[[D -> R]])" finite_pointwise_orders nil)
(pointwise_preserves_transitive application-judgement
"(transitive?[[D -> R]])" finite_pointwise_orders nil)
(pointwise_preserves_reflexive application-judgement
"(reflexive?[[D -> R]])" finite_pointwise_orders nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(D formal-type-decl nil finite_pointwise_orders nil)
(R formal-type-decl nil finite_pointwise_orders nil)
(pointwise const-decl "bool" pointwise_orders nil)
(union const-decl "set" sets nil)
(reflexive_closure const-decl "(reflexive?)" closure_ops nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
shostak))
(descending_reflexive_closure 0
(descending_reflexive_closure-1 nil 3314641603
("" (expand "descending?")
(("" (skosimp*)
(("" (inst?)
((""
(expand* "strictly_pointwise" "irreflexive_kernel"
"difference" "member" "pointwise")
(("" (flatten) (("" (inst?) nil nil)) nil)) nil))
nil))
nil))
nil)
((irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil)
(member const-decl "bool" sets nil)
(pointwise const-decl "bool" pointwise_orders nil)
(difference const-decl "set" sets nil)
(strictly_pointwise const-decl "pred[[[D -> R], [D -> R]]]"
pointwise_orders nil)
(D formal-type-decl nil finite_pointwise_orders nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(descending? const-decl "bool" monotone_sequences nil))
shostak))
(pointwise_pigeonhole 0
(pointwise_pigeonhole-1 nil 3314641647
("" (skosimp)
(("" (use "infinite_pigeonhole")
((""
(inst -
"LAMBDA n: epsilon({d | rel!1(seq!1(n + 1)(d), seq!1(n)(d))})")
(("1" (skolem-typepred)
(("1" (inst? +)
(("1" (inst? +)
(("1" (expand "descending?" +)
(("1" (skolem!)
(("1" (inst - "n!1")
(("1" (use "epsilon_ax[D]")
(("1" (replace -3 :hide? t)
(("1" (split)
(("1" (lemma "descending_lem[R]")
(("1"
(inst - "reflexive_closure(rel!1)"
"LAMBDA n: seq!1(n)(d!1)")
(("1"
(expand*
"preserves"
"restrict"
"converse"
"reflexive_closure"
"union"
"member")
(("1"
(inst
-
"g!1(n!1) + 1"
"g!1(1 + n!1)")
(("1"
(assert)
(("1"
(split)
(("1"
(lemma "transitive[R]")
(("1"
(inst
-
"rel!1"
"seq!1(g!1(1 + n!1))(d!1)"
"seq!1(g!1(n!1) + 1)(d!1)"
"seq!1(g!1(n!1))(d!1)")
(("1" (assert) nil nil))
nil))
nil)
("2"
(expand*
"preserves"
"preserves"
"restrict")
(("2"
(inst - "n!1" "n!1 + 1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(rewrite
"descending_reflexive_closure")
nil
nil))
nil))
nil)
("2" (rewrite "descending_exists") nil nil))
nil))
nil)
("2" (inst + "d!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (use "descending_exists")
(("2" (assert) (("2" (skolem!) (("2" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((infinite_pigeonhole formula-decl nil finite_pointwise_orders nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(< const-decl "bool" reals nil)
(restrict const-decl "R" restrict nil)
(preserves const-decl "bool" functions nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(epsilon_ax formula-decl nil epsilons nil)
(reflexive_closure_preserves_transitive application-judgement
"(preorder?)" well_foundedness nil)
(sequence type-eq-decl nil sequences nil)
(reflexive? const-decl "bool" relations nil)
(reflexive_closure const-decl "(reflexive?)" closure_ops nil)
(rel!1 skolem-const-decl "(transitive?[R])" finite_pointwise_orders
nil)
(seq!1 skolem-const-decl "[nat -> [D -> R]]"
finite_pointwise_orders nil)
(d!1 skolem-const-decl "D" finite_pointwise_orders nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(transitive formula-decl nil relations_extra nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(preserves const-decl "bool" functions nil)
(converse const-decl "pred[[T2, T1]]" relation_defs nil)
(union const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(descending_reflexive_closure formula-decl nil
finite_pointwise_orders nil)
(descending_lem formula-decl nil monotone_sequences nil)
(descending_exists formula-decl nil finite_pointwise_orders nil)
(descending? const-decl "bool" monotone_sequences nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(transitive? const-decl "bool" relations nil)
(PRED type-eq-decl nil defined_types nil)
(R formal-type-decl nil finite_pointwise_orders nil)
(epsilon const-decl "T" epsilons nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(D formal-type-decl nil finite_pointwise_orders nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(TRUE const-decl "bool" booleans nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil))
shostak))
(strictly_pointwise_well_founded_order 0
(strictly_pointwise_well_founded_order-1 nil 3314641151
("" (skolem-typepred)
(("" (expand "well_founded_order?")
(("" (prop)
(("1" (rewrite "no_infinite_descending_sequence[R]")
(("1" (rewrite "no_infinite_descending_sequence[[D->R]]")
(("1" (expand* "empty?" "member")
(("1" (skolem!)
(("1" (forward-chain "pointwise_pigeonhole")
(("1" (skolem!) (("1" (inst?) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
("2" (expand "strictly_pointwise")
(("2" (invoke (typepred "%1") (! 1 1))
(("2" (expand "strict_order?") (("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((order_to_strict_order application-judgement "(strict_order?)"
well_foundedness nil)
(reflexive_closure const-decl "(reflexive?)" closure_ops nil)
(reflexive? const-decl "bool" relations nil)
(pointwise const-decl "bool" pointwise_orders nil)
(irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil)
(irreflexive? const-decl "bool" relations nil)
(strict_order? const-decl "bool" orders nil)
(pointwise_preserves_reflexive application-judgement
"(reflexive?[[D -> R]])" finite_pointwise_orders nil)
(order_to_partial_order application-judgement "(partial_order?)"
well_foundedness nil)
(no_infinite_descending_sequence formula-decl nil well_foundedness
nil)
(member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil)
(pointwise_pigeonhole formula-decl nil finite_pointwise_orders nil)
(PRED type-eq-decl nil defined_types nil)
(transitive? const-decl "bool" relations nil)
(number nonempty-type-decl nil numbers 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)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(sequence type-eq-decl nil sequences nil)
(preserves const-decl "bool" functions nil)
(restrict const-decl "R" restrict nil)
(< const-decl "bool" reals nil)
(D formal-type-decl nil finite_pointwise_orders nil)
(strictly_pointwise const-decl "pred[[[D -> R], [D -> R]]]"
pointwise_orders nil)
(well_founded_order? const-decl "bool" well_foundedness nil)
(pred type-eq-decl nil defined_types nil)
(R formal-type-decl nil finite_pointwise_orders nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil)))
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Lebenszyklus
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Ziele
Entwicklung einer Software für die statische Quellcodeanalyse
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