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("" (expand "is_finite") (("" (propax) nil nil)) nil)
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shostak))
(from_list_index 0
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("" (induct "l")
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(list type-decl nil list_adt nil))
shostak))
(from_list_nth_TCC1 0
(from_list_nth_TCC1-1 nil 3513689704
("" (skolem!) (("" (rewrite "from_list_index") nil nil)) nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(from_list_index formula-decl nil csequence_list nil)
(T formal-type-decl nil csequence_list nil)
(list type-decl nil list_adt nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
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(real nonempty-type-from-decl nil reals nil)
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(below type-eq-decl nil nat_types nil))
nil))
(from_list_nth 0
(from_list_nth-1 nil 3513689877
("" (induct "l")
(("1" (skolem-typepred)
(("1" (expand "length") (("1" (assert) nil nil)) nil)) nil)
("2" (skosimp* t)
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(("2" (expand "nth" +)
(("2" (expand "length")
(("2" (lift-if)
(("2" (ground) (("2" (inst - "n!1 - 1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("3" (lemma "from_list_nth_TCC1") (("3" (propax) nil nil)) nil))
nil)
((from_list_nth_TCC1 subtype-tcc nil csequence_list nil)
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(cons adt-constructor-decl "[[T, list] -> (cons?)]" list_adt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(posint_plus_nnint_is_posint application-judgement "posint"
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(int_minus_int_is_int application-judgement "int" integers nil)
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(real_lt_is_strict_total_order name-judgement
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(list_induction formula-decl nil list_adt nil)
(T formal-type-decl nil csequence_list nil)
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(indexes type-eq-decl nil csequence_nth nil)
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(list type-decl nil list_adt 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)
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(rational nonempty-type-from-decl nil rationals nil)
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(bool nonempty-type-eq-decl nil booleans nil)
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(below type-eq-decl nil nat_types nil)
(csequence type-decl nil csequence_codt nil)
(index? def-decl "bool" csequence_nth nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(from_list def-decl "finite_csequence" csequence_list nil))
shostak))
(to_list_TCC1 0
(to_list_TCC1-1 nil 3513689704 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T formal-type-decl nil csequence_list nil)
(csequence type-decl nil csequence_codt nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil))
nil))
(to_list_TCC2 0
(to_list_TCC2-1 nil 3513689704
("" (skosimp :preds? t)
(("" (expand "is_finite" -) (("" (assert) nil nil)) nil)) nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T formal-type-decl nil csequence_list nil)
(csequence type-decl nil csequence_codt nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil))
nil))
(to_list_TCC3 0
(to_list_TCC3-1 nil 3513689704 ("" (termination-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
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(T formal-type-decl nil csequence_list nil)
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(posint_plus_nnint_is_posint application-judgement "posint"
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(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
(to_list_length 0
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("" (induct "fseq" :name "is_finite_induction")
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(("2" (expand "length" +)
(("2" (lift-if) (("2" (ground) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
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integers nil)
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(T formal-type-decl nil csequence_list nil)
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(length def-decl "nat" list_props nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
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(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)
(list type-decl nil list_adt nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(number nonempty-type-decl nil numbers nil)
(is_finite inductive-decl "bool" csequence_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil))
shostak))
(to_list_index 0
(to_list_index-1 nil 3513690035
("" (induct "fseq" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (split)
(("1" (expand* "to_list" "length" "index?")
(("1" (assert) nil nil)) nil)
("2" (flatten)
(("2" (assert)
(("2" (expand "to_list" +)
(("2" (expand "length" +)
(("2" (expand "index?" +)
(("2" (lift-if)
(("2" (ground)
(("1" (inst - "n!1 - 1") (("1" (assert) nil nil))
nil)
("2" (inst - "n!1 - 1") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
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(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_list nil)
(index? def-decl "bool" csequence_nth nil)
(to_list def-decl "list" csequence_list nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(length def-decl "nat" list_props nil)
(list type-decl nil list_adt nil) (< const-decl "bool" reals nil)
(IFF const-decl "[bool, bool -> bool]" booleans 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)
(is_finite inductive-decl "bool" csequence_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil))
shostak))
(to_list_nth_TCC1 0
(to_list_nth_TCC1-1 nil 3513689704
("" (skolem!) (("" (rewrite "to_list_index") nil nil)) nil)
((to_list_index formula-decl nil csequence_list nil)
(T formal-type-decl nil csequence_list nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(to_list_nth 0
(to_list_nth-1 nil 3513690129
("" (induct "fseq" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp* t)
(("3" (expand "index?")
(("3" (expand "to_list" +)
(("3" (expand "nth" +) (("3" (reduce) nil nil)) nil)) nil))
nil))
nil)
("4" (skosimp*) (("4" (use "to_list_nth_TCC1") nil nil)) nil))
nil)
((to_list_nth_TCC1 subtype-tcc nil csequence_list nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(n!1 skolem-const-decl "indexes[T](cseq!1)" csequence_list nil)
(cseq!1 skolem-const-decl "csequence[T]" csequence_list nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_list nil)
(nth def-decl "T" csequence_nth nil)
(nth def-decl "T" list_props nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
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(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
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(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
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(int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil)
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(length def-decl "nat" list_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(to_list def-decl "list" csequence_list nil))
shostak))
(to_from_list 0
(to_from_list-1 nil 3513690168
("" (induct "l")
(("1" (expand* "from_list" "to_list") nil nil)
("2" (skosimp)
(("2" (expand "from_list" +)
(("2" (expand "to_list" +) (("2" (assert) nil nil)) nil)) nil))
nil))
nil)
((list_induction formula-decl nil list_adt nil)
(T formal-type-decl nil csequence_list nil)
(from_list def-decl "finite_csequence" csequence_list nil)
(to_list def-decl "list" csequence_list nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(bool nonempty-type-eq-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(boolean nonempty-type-decl nil booleans nil)
(list type-decl nil list_adt nil))
shostak))
(from_to_list 0
(from_to_list-1 nil 3513690211
("" (induct "fseq" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (expand "to_list" +)
(("3" (expand "from_list" +) (("3" (reduce-with-ext) nil nil))
nil))
nil))
nil))
nil)
((rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(csequence_add_extensionality formula-decl nil csequence_codt nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_list nil)
(to_list def-decl "list" csequence_list nil)
(from_list def-decl "finite_csequence" csequence_list nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(list type-decl nil list_adt nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(is_finite inductive-decl "bool" csequence_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil))
shostak)))
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Lebenszyklus
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Ziele
Entwicklung einer Software für die statische Quellcodeanalyse
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