|
(csequence_merge
(merge_struct_TCC1 0
(merge_struct_TCC1-1 nil 3513693179 ("" (subtype-tcc) nil nil) nil
nil))
(merge_struct_TCC2 0
(merge_struct_TCC2-1 nil 3513693179 ("" (subtype-tcc) nil nil) nil
nil))
(merge_empty 0
(merge_empty-1 nil 3513693197
("" (expand* "merge" "merge_struct" "coreduce")
(("" (reduce) nil nil)) nil)
((merge const-decl "csequence" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil))
shostak))
(merge_nonempty 0
(merge_nonempty-1 nil 3513693216
("" (expand* "merge" "merge_struct" "coreduce")
(("" (reduce) nil nil)) nil)
((merge const-decl "csequence" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil))
shostak))
(merge_empty_left 0
(merge_empty_left-1 nil 3513693224
("" (skolem!)
(("" (lemma "coinduction")
((""
(inst -
"LAMBDA cseq1, cseq2: cseq1 = merge(cseq2, eseq!1) OR cseq1 = merge(eseq!1, cseq2)"
"merge(eseq!1, cseq!1)" "cseq!1")
(("" (delete 2)
(("" (expand "bisimulation?")
(("" (skosimp)
(("" (smash)
(("1" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("2" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("3" (replace -1)
(("3" (hide -1)
(("3" (expand* "merge" "merge_struct")
(("3" (expand "coreduce" 1 1)
(("3" (expand "coreduce" 2 1)
(("3" (expand "coreduce" -)
(("3" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("4" (expand* "merge" "merge_struct" "coreduce")
(("4" (reduce) nil nil)) nil)
("5" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("6" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("7" (replace -1)
(("7" (hide -1)
(("7" (expand* "merge" "merge_struct")
(("7" (expand "coreduce" 1 1)
(("7" (expand "coreduce" 2 1)
(("7" (expand "coreduce" -)
(("7" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("8" (expand* "merge" "merge_struct" "coreduce")
(("8" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T formal-type-decl nil csequence_merge nil)
(coinduction formula-decl nil csequence_codt nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(eseq!1 skolem-const-decl "empty_csequence[T]" csequence_merge nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(merge const-decl "csequence" csequence_merge nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil))
shostak))
(merge_empty_right 0
(merge_empty_right-1 nil 3513693378
("" (skolem!)
(("" (lemma "coinduction")
((""
(inst -
"LAMBDA cseq1, cseq2: cseq1 = merge(cseq2, eseq!1) OR cseq1 = merge(eseq!1, cseq2)"
"merge(cseq!1, eseq!1)" "cseq!1")
(("" (delete 2)
(("" (expand "bisimulation?")
(("" (skosimp)
(("" (smash)
(("1" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("2" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("3" (replace -1)
(("3" (hide -1)
(("3" (expand* "merge" "merge_struct")
(("3" (expand "coreduce" 1 1)
(("3" (expand "coreduce" 2 1)
(("3" (expand "coreduce" -)
(("3" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("4" (expand* "merge" "merge_struct" "coreduce")
(("4" (reduce) nil nil)) nil)
("5" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("6" (expand* "merge" "merge_struct" "coreduce") nil
nil)
("7" (replace -1)
(("7" (hide -1)
(("7" (expand* "merge" "merge_struct")
(("7" (expand "coreduce" 1 1)
(("7" (expand "coreduce" 2 1)
(("7" (expand "coreduce" -)
(("7" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("8" (expand* "merge" "merge_struct" "coreduce")
(("8" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T formal-type-decl nil csequence_merge nil)
(coinduction formula-decl nil csequence_codt nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(eseq!1 skolem-const-decl "empty_csequence[T]" csequence_merge nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(merge const-decl "csequence" csequence_merge nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil))
shostak))
(merge_first_TCC1 0
(merge_first_TCC1-1 nil 3513693179
("" (skosimp)
(("" (rewrite "merge_nonempty") (("" (assert) nil nil)) nil)) nil)
((merge_nonempty formula-decl nil csequence_merge nil)
(T formal-type-decl nil csequence_merge nil)
(csequence type-decl nil csequence_codt nil))
nil))
(merge_first 0
(merge_first-1 nil 3513693556
("" (expand* "merge" "merge_struct" "coreduce")
(("" (reduce) nil nil)) nil)
((merge const-decl "csequence" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil))
shostak))
(merge_rest 0
(merge_rest-1 nil 3513693567
("" (skosimp)
(("" (lift-if)
(("" (prop)
(("1" (expand* "merge" "merge_struct")
(("1" (expand "coreduce" 1 1) (("1" (reduce) nil nil)) nil))
nil)
("2" (rewrite "merge_empty_left") nil nil))
nil))
nil))
nil)
((merge_empty_left formula-decl nil csequence_merge nil)
(T formal-type-decl nil csequence_merge nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(merge const-decl "csequence" csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil))
shostak))
(merge_finite 0
(merge_finite-1 nil 3513693179
("" (induct "fseq1" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (case "empty?(cseq!1)")
(("1" (skolem!)
(("1" (rewrite "merge_empty_left") (("1" (assert) nil nil))
nil))
nil)
("2" (ground)
(("2" (skolem-typepred)
(("2" (case "empty?(fseq2!1)")
(("1" (rewrite "merge_empty_right") nil nil)
("2" (assert)
(("2" (expand* "merge" "merge_struct")
(("2" (expand "coreduce" +)
(("2" (expand "is_finite" +)
(("2" (expand "coreduce" +)
(("2" (expand "is_finite" +)
(("2" (inst - "rest(fseq2!1)")
(("2" (expand "is_finite" -1)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((merge_empty_right formula-decl nil csequence_merge nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(fseq2!1 skolem-const-decl "finite_csequence[T]" csequence_merge
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(merge_empty_left formula-decl nil csequence_merge nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_merge nil)
(merge const-decl "csequence" csequence_merge nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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))
nil))
(merge_finiteness 0
(merge_finiteness-1 nil 3513696751
("" (skosimp)
(("" (lemma "is_finite_induction")
((""
(inst -
"LAMBDA cseq: FORALL cseq1, cseq2: cseq = merge(cseq1, cseq2) IMPLIES is_finite(cseq1) AND is_finite(cseq2)")
(("" (split)
(("1" (inst - "merge(cseq1!1, cseq2!1)")
(("1" (assert) (("1" (inst - "cseq1!1" "cseq2!1") nil nil))
nil))
nil)
("2" (delete -1 2)
(("2" (skosimp*)
(("2" (replace -2)
(("2" (hide -2)
(("2" (split)
(("1" (rewrite "merge_empty")
(("1" (expand "is_finite")
(("1" (ground) nil nil)) nil))
nil)
("2" (flatten)
(("2" (case "empty?(cseq1!2)")
(("1" (rewrite "merge_empty_left")
(("1" (expand "is_finite" +)
(("1" (assert) nil nil)) nil))
nil)
("2" (assert)
(("2" (inst - "cseq2!2" "rest(cseq1!2)")
(("2" (expand "is_finite" 2 1)
(("2"
(expand* "merge" "merge_struct")
(("2"
(expand "coreduce" -2 1)
(("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T formal-type-decl nil csequence_merge nil)
(is_finite_induction formula-decl nil csequence_props nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(merge_empty_left formula-decl nil csequence_merge nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(merge_empty formula-decl nil csequence_merge nil)
(is_finite inductive-decl "bool" csequence_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(merge const-decl "csequence" csequence_merge nil)
(= const-decl "[T, T -> boolean]" equalities 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))
(merge_infinite1 0
(merge_infinite1-1 nil 3513693179
("" (skolem-typepred)
(("" (forward-chain "merge_finiteness") nil nil)) nil)
((merge_finiteness formula-decl nil csequence_merge nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_merge nil))
nil))
(merge_infinite2 0
(merge_infinite2-1 nil 3513693179
("" (skolem-typepred)
(("" (forward-chain "merge_finiteness") nil nil)) nil)
((merge_finiteness formula-decl nil csequence_merge nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_merge nil))
nil))
(merge_length 0
(merge_length-1 nil 3513696918
("" (induct "fseq1" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (case "empty?(cseq!1)")
(("1" (rewrite "merge_empty_left")
(("1" (rewrite "length_empty?_rew") (("1" (ground) nil nil))
nil))
nil)
("2" (ground)
(("2" (case "empty?(fseq2!1)")
(("1" (rewrite "merge_empty_right")
(("1" (rewrite "length_empty?_rew")
(("1" (assert) nil nil)) nil))
nil)
("2" (assert)
(("2" (expand* "merge" "merge_struct")
(("2" (expand "coreduce" +)
(("2" (expand "length" 3 1)
(("2" (expand "coreduce" +)
(("2" (expand "length" +)
(("2" (inst - "rest(fseq2!1)")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4" (skosimp*)
(("4"
(lemma "merge_finite" ("fseq1" "fseq1!2" "fseq2" "fseq2!1"))
(("1" (propax) nil nil) ("2" (propax) nil nil)) nil))
nil))
nil)
((merge_finite judgement-tcc nil csequence_merge nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(merge_empty_right formula-decl nil csequence_merge nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(merge_empty_left formula-decl nil csequence_merge nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(length_empty?_rew formula-decl nil csequence_length nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_merge nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(has_length def-decl "bool" csequence_props 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)
(= const-decl "[T, T -> boolean]" equalities nil)
(number nonempty-type-decl nil numbers nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(merge const-decl "csequence" csequence_merge nil))
shostak))
(merge_index_TCC1 0
(merge_index_TCC1-1 nil 3513693179
("" (skosimp)
(("" (rewrite "index?_finite") (("" (assert) nil nil)) nil)) nil)
((index?_finite formula-decl nil csequence_nth nil)
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(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)
(T formal-type-decl nil csequence_merge nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(merge_index 0
(merge_index-1 nil 3513697065
("" (auto-rewrite "merge_length")
(("" (auto-rewrite "index?_prop")
(("" (skolem!)
(("" (smash)
(("1" (use "merge_finite") nil nil)
("2" (use "merge_infinite2") (("2" (assert) nil nil)) nil)
("3" (use "merge_infinite1") nil nil)
("4" (use "merge_infinite2") (("4" (assert) nil nil)) nil)
("5" (use "merge_infinite1") nil nil))
nil))
nil))
nil))
nil)
((T formal-type-decl nil csequence_merge nil)
(index?_prop formula-decl nil csequence_nth nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(merge_length formula-decl nil csequence_merge nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(merge_finite judgement-tcc nil csequence_merge 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)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(cseq2!1 skolem-const-decl "csequence[T]" csequence_merge nil)
(merge_infinite2 judgement-tcc nil csequence_merge nil)
(merge_infinite1 judgement-tcc nil csequence_merge nil))
shostak))
(merge_nth_TCC1 0
(merge_nth_TCC1-1 nil 3513693179 ("" (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)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil)
(T formal-type-decl nil csequence_merge nil)
(length_lt const-decl "bool" csequence_length_comp nil))
nil))
(merge_nth_TCC2 0
(merge_nth_TCC2-1 nil 3513693179
("" (skosimp :preds? t)
(("" (assert)
(("" (rewrite "merge_index")
(("" (expand "length_lt")
(("" (auto-rewrite "index?_finite") (("" (ground) nil nil))
nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(index?_finite formula-decl nil csequence_nth nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(merge_index formula-decl nil csequence_merge 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_merge nil)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(merge_nth_TCC3 0
(merge_nth_TCC3-1 nil 3513693179 ("" (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)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil)
(T formal-type-decl nil csequence_merge nil)
(length_lt const-decl "bool" csequence_length_comp nil))
nil))
(merge_nth_TCC4 0
(merge_nth_TCC4-1 nil 3513693179
("" (skosimp :preds? t)
(("" (rewrite "merge_index")
(("" (expand "length_lt")
(("" (auto-rewrite "index?_finite")
(("" (auto-rewrite "index?_infinite") (("" (reduce) nil nil))
nil))
nil))
nil))
nil))
nil)
((merge_index formula-decl nil csequence_merge nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(index?_finite formula-decl nil csequence_nth nil)
(index?_infinite formula-decl nil csequence_nth nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(length_lt const-decl "bool" csequence_length_comp 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_merge nil)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(merge_nth_TCC5 0
(merge_nth_TCC5-1 nil 3513693179
("" (skosimp :preds? t)
(("" (expand "even?")
(("" (skolem!)
(("" (assert)
(("" (expand "length_lt")
(("" (rewrite "index?_prop")
(("" (rewrite "index?_prop")
(("" (lemma "merge_finite")
(("" (lemma "merge_length") (("" (reduce) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((even? const-decl "bool" integers nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(index?_prop formula-decl nil csequence_nth nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(merge_finite judgement-tcc nil csequence_merge nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(cseq2!1 skolem-const-decl "csequence[T]" csequence_merge nil)
(merge_finite application-judgement "finite_csequence"
csequence_merge nil)
(merge_length formula-decl nil csequence_merge nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(length_lt const-decl "bool" csequence_length_comp 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_merge nil)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(merge_nth_TCC6 0
(merge_nth_TCC6-1 nil 3513693179
("" (skosimp :preds? t)
(("" (use "even_or_odd")
(("" (assert)
(("" (expand* "odd?" "length_lt")
(("" (rewrite "merge_index")
(("" (auto-rewrite "index?_prop") (("" (reduce) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((even_or_odd formula-decl nil naturalnumbers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(odd? const-decl "bool" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(index?_prop formula-decl nil csequence_nth nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(merge_index formula-decl nil csequence_merge 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_merge nil)
(csequence type-decl nil csequence_codt 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)
(merge const-decl "csequence" csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(merge_nth 0
(merge_nth-1 nil 3513697436
("" (measure-induct+ "n" ("cseq1" "cseq2" "n") :skolem-typepreds? t)
(("1" (case-replace "x!3 = 0")
(("1" (hide -3)
(("1" (expand* "index?" "nth" "length_lt")
(("1" (rewrite "merge_first")
(("1" (rewrite "merge_nonempty")
(("1" (lemma "length_nonempty?_rew")
(("1" (inst-cp - "x!2")
(("1" (inst - "x!1") (("1" (smash) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (expand "index?")
(("2" (flatten)
(("2" (lemma "merge_index_TCC1" ("cseq1" "x!1" "n" "x!3"))
(("2" (use "merge_index")
(("2" (case "is_finite(x!1)")
(("1" (assert)
(("1" (case "empty?(x!1)")
(("1" (use "length_empty?_rew")
(("1" (assert)
(("1" (rewrite "merge_empty_left")
(("1" (expand "length_lt")
(("1"
(use "length_nonempty?_rew")
(("1"
(expand "index?" -5 1)
(("1" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "nth" 3 1)
(("2" (forward-chain "merge_rest")
(("2" (assert)
(("2" (replace -1)
(("2"
(inst - "x!2" "rest(x!1)" "x!3 - 1")
(("2"
(use "length_empty?_rew")
(("2"
(assert)
(("2"
(expand "length_lt")
(("2"
(expand "is_finite" -2)
(("2"
(case-replace
"length(x!1) = length(rest(x!1)) + 1")
(("1"
(expand "nth" 4 3)
(("1"
(expand "nth" 4 4)
(("1"
(use "even_plus1")
(("1"
(lemma "index?_prop")
(("1"
(inst
-
"x!1"
"x!3")
(("1"
(expand
"is_finite"
-1)
(("1"
(expand
"length"
-1)
(("1"
(auto-rewrite
"index?_finite")
(("1"
(smash)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand "length" 1 1)
(("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide -1 -2)
(("2" (expand "length_lt")
(("2" (assert)
(("2" (expand "nth" 3 1)
(("2" (forward-chain "merge_rest")
(("2"
(use "infinite_csequence_is_nonempty")
(("2"
(assert)
(("2"
(replace -2)
(("2"
(inst
-
"x!2"
"rest(x!1)"
"x!3 - 1")
(("2"
(expand "is_finite" 1)
(("2"
(assert)
(("2"
(expand "nth" 3 2)
(("2"
(expand "nth" 3 3)
(("2"
(use "even_plus1")
(("2" (reduce) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (use "merge_nth_TCC6") (("2" (ground) nil nil)) nil)
("3" (use "merge_nth_TCC5") (("3" (ground) nil nil)) nil)
("4" (use "merge_nth_TCC4") (("4" (ground) nil nil)) nil)
("5" (forward-chain "merge_nth_TCC3") (("5" (assert) nil nil))
nil)
("6" (forward-chain "merge_nth_TCC3") (("6" (assert) nil nil))
nil)
("7" (forward-chain "merge_nth_TCC2") (("7" (assert) nil nil))
nil)
("8" (use "merge_nth_TCC1") (("8" (assert) nil nil)) nil)
("9" (use "merge_nth_TCC1") (("9" (assert) nil nil)) nil)
("10" (use "merge_nth_TCC6") (("10" (ground) nil nil)) nil)
("11" (use "merge_nth_TCC5") (("11" (ground) nil nil)) nil)
("12" (use "merge_nth_TCC4") (("12" (ground) nil nil)) nil)
("13" (forward-chain "merge_nth_TCC3") (("13" (assert) nil nil))
nil)
("14" (forward-chain "merge_nth_TCC3") (("14" (assert) nil nil))
nil)
("15" (forward-chain "merge_nth_TCC2") (("15" (assert) nil nil))
nil)
("16" (use "merge_nth_TCC1") (("16" (assert) nil nil)) nil)
("17" (use "merge_nth_TCC1") (("17" (assert) nil nil)) nil)
("18" (use "merge_nth_TCC6") (("18" (ground) nil nil)) nil)
("19" (use "merge_nth_TCC5") (("19" (ground) nil nil)) nil)
("20" (use "merge_nth_TCC4") (("20" (ground) nil nil)) nil)
("21" (forward-chain "merge_nth_TCC3") (("21" (assert) nil nil))
nil)
("22" (forward-chain "merge_nth_TCC3") (("22" (assert) nil nil))
nil)
("23" (forward-chain "merge_nth_TCC2") (("23" (assert) nil nil))
nil)
("24" (use "merge_nth_TCC1") (("24" (assert) nil nil)) nil)
("25" (use "merge_nth_TCC1") (("25" (assert) nil nil)) nil)
("26" (use "merge_nth_TCC6") (("26" (ground) nil nil)) nil)
("27" (use "merge_nth_TCC5") (("27" (ground) nil nil)) nil)
("28" (use "merge_nth_TCC4") (("28" (ground) nil nil)) nil)
("29" (forward-chain "merge_nth_TCC3") (("29" (assert) nil nil))
nil)
("30" (forward-chain "merge_nth_TCC3") (("30" (assert) nil nil))
nil)
("31" (forward-chain "merge_nth_TCC2") (("31" (assert) nil nil))
nil)
("32" (use "merge_nth_TCC1") (("32" (assert) nil nil)) nil)
("33" (use "merge_nth_TCC1") (("33" (assert) nil nil)) nil))
nil)
((merge_nth_TCC1 subtype-tcc nil csequence_merge nil)
(merge_nth_TCC2 subtype-tcc nil csequence_merge nil)
(merge_nth_TCC3 subtype-tcc nil csequence_merge nil)
(merge_nth_TCC4 subtype-tcc nil csequence_merge nil)
(merge_nth_TCC5 subtype-tcc nil csequence_merge nil)
(merge_nth_TCC6 subtype-tcc nil csequence_merge nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(merge_nonempty formula-decl nil csequence_merge nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(length_nonempty?_rew formula-decl nil csequence_length nil)
(merge_first formula-decl nil csequence_merge nil)
(merge_index_TCC1 subtype-tcc nil csequence_merge nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(merge_empty_left formula-decl nil csequence_merge nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(length_empty?_rew formula-decl nil csequence_length nil)
(merge_rest formula-decl nil csequence_merge nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(index?_prop formula-decl nil csequence_nth nil)
(index?_finite formula-decl nil csequence_nth nil)
(even_plus_even_is_even application-judgement "even_int" integers
nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(rat_minus_rat_is_rat application-judgement "rat" rationals nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(even_plus1 formula-decl nil naturalnumbers nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(infinite_csequence_is_nonempty judgement-tcc nil csequence_props
nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(merge_index formula-decl nil csequence_merge nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(nth def-decl "T" csequence_nth nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(even? const-decl "bool" integers nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(has_length def-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(wf_nat formula-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(naturalnumber type-eq-decl nil naturalnumbers nil)
(indexes type-eq-decl nil csequence_nth nil)
(merge const-decl "csequence" csequence_merge nil)
(index? def-decl "bool" csequence_nth 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)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_merge nil)
(measure_induction formula-decl nil measure_induction nil)
(well_founded? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil))
shostak))
(merge_add 0
(merge_add-1 nil 3513698074
("" (expand* "merge" "merge_struct")
(("" (expand "coreduce" 1 2) (("" (propax) nil nil)) nil)) nil)
((coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(merge const-decl "csequence" csequence_merge nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil))
shostak))
(merge_last_TCC1 0
(merge_last_TCC1-1 nil 3513693179
("" (skosimp)
(("" (rewrite "merge_nonempty")
(("" (assert)
(("" (lemma "length_nonempty?_rew")
(("" (inst-cp - "fseq2!1")
(("" (inst - "fseq1!1") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((merge_nonempty formula-decl nil csequence_merge nil)
(T formal-type-decl nil csequence_merge 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)
(length_nonempty?_rew formula-decl nil csequence_length nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(merge_last_TCC2 0
(merge_last_TCC2-1 nil 3513693179
("" (skosimp)
(("" (rewrite "merge_nonempty")
(("" (assert)
(("" (lemma "length_nonempty?_rew")
(("" (inst-cp - "fseq2!1")
(("" (inst - "fseq1!1") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((merge_nonempty formula-decl nil csequence_merge nil)
(T formal-type-decl nil csequence_merge 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)
(length_nonempty?_rew formula-decl nil csequence_length nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(merge_last 0
(merge_last-1 nil 3513698166
("" (skosimp)
(("" (expand "last")
(("" (rewrite "merge_length")
(("" (use "merge_nth")
(("1" (expand* "length_lt" "even?") (("1" (reduce) nil nil))
nil)
("2" (rewrite "merge_nonempty")
(("2" (lemma "length_nonempty?_rew")
(("2" (inst-cp - "fseq2!1")
(("2" (inst - "fseq1!1") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((last const-decl "T" csequence_nth nil)
(merge_nth formula-decl nil csequence_merge nil)
(indexes type-eq-decl nil csequence_nth nil)
(merge const-decl "csequence" csequence_merge nil)
(index? def-decl "bool" csequence_nth 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)
(>= const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(has_length def-decl "bool" csequence_props nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(fseq1!1 skolem-const-decl "finite_csequence[T]" csequence_merge
nil)
(fseq2!1 skolem-const-decl "finite_csequence[T]" csequence_merge
nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(merge_finite application-judgement "finite_csequence"
csequence_merge nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(even? const-decl "bool" integers nil)
(length_nonempty?_rew formula-decl nil csequence_length nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(merge_nonempty formula-decl nil csequence_merge nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers 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)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_merge nil)
(merge_length formula-decl nil csequence_merge nil))
shostak))
(merge_extensionality 0
(merge_extensionality-1 nil 3513698243
("" (skosimp)
(("" (split)
(("1" (lemma "coinduction")
(("1"
(inst -
"LAMBDA cseq1, cseq3: EXISTS cseq2, cseq4: length_eq(cseq1, cseq2) AND length_eq(cseq3, cseq4) AND merge(cseq1, cseq2) = merge(cseq3, cseq4)"
"cseq1!1" "cseq3!1")
(("1" (assert)
(("1" (inst + "cseq2!1" "cseq4!1") (("1" (assert) nil nil))
nil))
nil)
("2" (delete -1 -2 -3 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2" (lemma "length_eq_empty")
(("2" (inst-cp - "y!1" "cseq4!2")
(("2" (inst - "x!1" "cseq2!2")
(("2" (smash)
(("1" (rewrite "merge_empty_left")
(("1" (use "merge_empty")
(("1" (assert) nil nil)) nil))
nil)
("2"
(rewrite "merge_empty_left" :subst
("eseq" "y!1"))
(("2" (use "merge_empty")
(("2" (assert) nil nil)) nil))
nil)
("3" (inst + "rest(cseq2!2)" "rest(cseq4!2)")
(("3" (lemma "length_eq_rest")
(("3" (inst-cp - "y!1" "cseq4!2")
(("3"
(inst - "x!1" "cseq2!2")
(("3"
(assert)
(("3"
(expand* "merge" "merge_struct")
(("3"
(expand "coreduce" -)
(("3"
(expand "coreduce" -)
(("3"
(smash)
(("3"
(decompose-equality)
(("3"
(decompose-equality)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4"
(expand* "merge" "merge_struct" "coreduce")
(("4" (decompose-equality) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "coinduction")
(("2"
(inst -
"LAMBDA cseq2, cseq4: EXISTS cseq1, cseq3: length_eq(cseq1, cseq2) AND length_eq(cseq3, cseq4) AND merge(cseq1, cseq2) = merge(cseq3, cseq4)"
"cseq2!1" "cseq4!1")
(("1" (assert)
(("1" (inst + "cseq1!1" "cseq3!1") (("1" (assert) nil nil))
nil))
nil)
("2" (delete -1 -2 -3 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2" (lemma "length_eq_empty")
(("2" (inst-cp - "cseq3!2" "y!1")
(("2" (inst - "cseq1!2" "x!1")
(("2" (smash)
(("1" (rewrite "merge_empty_right")
(("1" (use "merge_empty")
(("1" (assert) nil nil)) nil))
nil)
("2"
(rewrite "merge_empty_right" :subst
("eseq" "y!1"))
(("2" (use "merge_empty")
(("2" (assert) nil nil)) nil))
nil)
("3" (inst + "rest(cseq1!2)" "rest(cseq3!2)")
(("3" (lemma "length_eq_rest")
(("3" (inst-cp - "cseq3!2" "y!1")
(("3"
(inst - "cseq1!2" "x!1")
(("3"
(assert)
(("3"
(expand* "merge" "merge_struct")
(("3"
(expand "coreduce" -)
(("3"
(expand "coreduce" -)
(("3"
(smash)
(("3"
(decompose-equality)
(("3"
(decompose-equality)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4"
(expand* "merge" "merge_struct" "coreduce"
"coreduce")
(("4" (decompose-equality)
(("4" (decompose-equality) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((merge const-decl "csequence" csequence_merge nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(length_eq const-decl "bool" csequence_length_comp nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(length_eq_empty formula-decl nil csequence_length_comp nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(coreduce adt-def-decl "{c: csequence[T] |
inj_empty?(op(x)) AND empty?(c) OR
inj_nonempty?(op(x)) AND nonempty?(c)}"
csequence_codt_coreduce nil)
(inj_add adt-constructor-decl "[[T, domain] -> (inj_nonempty?)]"
csequence_codt_coreduce nil)
(inj_empty_cseq adt-constructor-decl "(inj_empty?)"
csequence_codt_coreduce nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(inj_nonempty? adt-recognizer-decl "[csequence_struct -> boolean]"
csequence_codt_coreduce nil)
(inj_empty? adt-recognizer-decl "[csequence_struct -> boolean]"
csequence_codt_coreduce nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(csequence_struct type-decl nil csequence_codt_coreduce nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(merge_struct const-decl "csequence_struct" csequence_merge nil)
(length_eq_rest formula-decl nil csequence_length_comp nil)
(empty_csequence nonempty-type-eq-decl nil csequence_props nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(merge_empty_left formula-decl nil csequence_merge nil)
(merge_empty formula-decl nil csequence_merge nil)
(coinduction formula-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_merge nil)
(merge_empty_right formula-decl nil csequence_merge nil))
shostak))
(merge_some 0
(merge_some-1 nil 3513698604
("" (skolem!)
(("" (prop)
(("1" (lemma "some_induction")
(("1"
(inst - "p!1"
"LAMBDA cseq: FORALL cseq1, cseq2: cseq = merge(cseq1, cseq2) IMPLIES some(p!1)(cseq1) OR some(p!1)(cseq2)")
(("1" (split)
(("1" (inst - "merge(cseq1!1, cseq2!1)")
(("1" (assert)
(("1" (inst - "cseq1!1" "cseq2!1")
--> --------------------
--> maximum size reached
--> --------------------
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Lebenszyklus
Die hierunter aufgelisteten Ziele sind für diese Firma wichtig
Ziele
Entwicklung einer Software für die statische Quellcodeanalyse
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