|
(csequence_unzip
(unzip_left_struct_TCC1 0
(unzip_left_struct_TCC1-1 nil 3513780110 ("" (subtype-tcc) nil nil)
nil nil))
(unzip_finite 0
(unzip_finite-1 nil 3513780110
("" (induct "fseq" :name "is_finite_induction[[T1, T2]]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (assert) nil nil) ("4" (assert) nil nil)
("5" (skosimp)
(("5" (expand "is_finite" +)
(("5"
(expand* "unzip" "unzip_left_struct" "unzip_right_struct")
(("5" (expand "coreduce" +) (("5" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil)
((unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil)
(AND const-decl "[bool, bool -> bool]" booleans 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))
(unzip_infinite 0
(unzip_infinite-1 nil 3513780110
(""
(case "FORALL iseq, n: NOT has_length(unzip(iseq)`1, n) AND NOT has_length(unzip(iseq)`2, n)")
(("1" (skolem!)
(("1" (split)
(("1" (rewrite "is_finite_def")
(("1" (skolem!)
(("1" (inst - "iseq!1" "n!1") (("1" (flatten) nil nil))
nil))
nil))
nil)
("2" (rewrite "is_finite_def")
(("2" (skolem!)
(("2" (inst - "iseq!1" "n!1") (("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (delete 2)
(("2" (induct "n")
(("1" (skolem-typepred)
(("1"
(expand* "has_length" "unzip" "unzip_left_struct"
"unzip_right_struct" "coreduce" "is_finite")
(("1" (reduce) nil nil)) nil))
nil)
("2" (skosimp* t)
(("2" (expand "has_length" +)
(("2" (expand "is_finite" +)
(("2"
(expand* "unzip" "unzip_left_struct"
"unzip_right_struct")
(("2" (expand "coreduce" +)
(("2" (smash)
(("1" (inst - "rest(iseq!1)")
(("1" (flatten) nil nil)) nil)
("2" (inst - "rest(iseq!1)")
(("2" (flatten) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip 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)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(nat_induction formula-decl nil naturalnumbers nil)
(pred type-eq-decl nil defined_types nil)
(is_finite_def formula-decl nil csequence_props nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(infinite_csequence 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)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(has_length def-decl "bool" csequence_props nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
nil))
(unzip_nonempty 0
(unzip_nonempty-1 nil 3513780110
(""
(expand* "unzip" "unzip_left_struct" "unzip_right_struct"
"coreduce")
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)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
nil))
(unzip_empty_left 0
(unzip_empty_left-1 nil 3513780336
("" (expand* "unzip" "unzip_left_struct" "coreduce")
(("" (reduce) nil nil)) nil)
((unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_empty_right 0
(unzip_empty_right-1 nil 3513780348
("" (expand* "unzip" "unzip_right_struct" "coreduce")
(("" (reduce) nil nil)) nil)
((unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_first_left 0
(unzip_first_left-1 nil 3513780362
("" (expand* "unzip" "unzip_left_struct" "coreduce") 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)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_first_right 0
(unzip_first_right-1 nil 3513780369
("" (expand* "unzip" "unzip_right_struct" "coreduce") 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)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_rest_left 0
(unzip_rest_left-1 nil 3513780376
("" (expand* "unzip" "unzip_left_struct")
(("" (expand "coreduce" 1 1) (("" (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)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_rest_right 0
(unzip_rest_right-1 nil 3513780388
("" (expand* "unzip" "unzip_right_struct")
(("" (expand "coreduce" 1 1) (("" (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)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_length_left 0
(unzip_length_left-1 nil 3513780408
("" (induct "fseq" :name "is_finite_induction[[T1, T2]]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (expand "length" +)
(("3" (expand* "unzip" "unzip_left_struct")
(("3" (expand "coreduce" +) (("3" (reduce) nil nil)) nil))
nil))
nil))
nil)
("4" (skosimp)
(("4" (assert)
(("4" (lemma "unzip_finite" ("fseq" "fseq!2"))
(("4" (flatten) nil nil)) nil))
nil))
nil))
nil)
((unzip_finite judgement-tcc nil csequence_unzip nil)
(unzip_finite application-judgement
"[finite_csequence[T1], finite_csequence[T2]]" csequence_unzip
nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers 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)
(is_finite_induction formula-decl nil csequence_props nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_length_right 0
(unzip_length_right-1 nil 3513780457
("" (induct "fseq" :name "is_finite_induction[[T1, T2]]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (expand "length" +)
(("3" (expand* "unzip" "unzip_right_struct")
(("3" (expand "coreduce" +) (("3" (reduce) nil nil)) nil))
nil))
nil))
nil)
("4" (skosimp)
(("4" (assert)
(("4" (lemma "unzip_finite" ("fseq" "fseq!2"))
(("4" (flatten) nil nil)) nil))
nil))
nil))
nil)
((unzip_finite judgement-tcc nil csequence_unzip nil)
(unzip_finite application-judgement
"[finite_csequence[T1], finite_csequence[T2]]" csequence_unzip
nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers 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)
(is_finite_induction formula-decl nil csequence_props nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_index_left 0
(unzip_index_left-1 nil 3513780499
("" (skolem!)
(("" (rewrite "index?_prop")
(("" (rewrite "index?_prop")
(("" (rewrite "unzip_length_left")
(("" (ground)
(("1" (use "unzip_finite") (("1" (flatten) nil nil)) nil)
("2" (use "unzip_infinite") (("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((index?_prop formula-decl nil csequence_nth nil)
(csequence type-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(T1 formal-type-decl nil csequence_unzip nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(unzip_length_left formula-decl nil csequence_unzip nil)
(unzip_infinite judgement-tcc nil csequence_unzip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(unzip_finite judgement-tcc nil csequence_unzip nil))
shostak))
(unzip_index_right 0
(unzip_index_right-1 nil 3513780534
("" (skolem!)
(("" (rewrite "index?_prop")
(("" (rewrite "index?_prop")
(("" (rewrite "unzip_length_right")
(("" (ground)
(("1" (use "unzip_finite") (("1" (flatten) nil nil)) nil)
("2" (use "unzip_infinite") (("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((index?_prop formula-decl nil csequence_nth nil)
(csequence type-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(T2 formal-type-decl nil csequence_unzip nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(unzip_length_right formula-decl nil csequence_unzip nil)
(unzip_infinite judgement-tcc nil csequence_unzip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(unzip_finite judgement-tcc nil csequence_unzip nil))
shostak))
(unzip_nth_left_TCC1 0
(unzip_nth_left_TCC1-1 nil 3513780110
("" (skolem!) (("" (rewrite "unzip_index_left") nil nil)) nil)
((unzip_index_left formula-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(csequence type-decl nil csequence_codt 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)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(unzip_nth_left 0
(unzip_nth_left-1 nil 3513780751
("" (measure-induct+ "n" ("cseq" "n") :skolem-typepreds? t)
(("1" (expand "index?" -)
(("1" (expand "nth" +)
(("1" (expand* "unzip" "unzip_left_struct")
(("1" (expand "coreduce" +) (("1" (reduce) nil nil)) nil))
nil))
nil))
nil)
("2" (use "unzip_nth_left_TCC1") nil nil)
("3" (use "unzip_nth_left_TCC1") nil nil)
("4" (use "unzip_nth_left_TCC1") nil nil)
("5" (use "unzip_nth_left_TCC1") nil nil))
nil)
((unzip_nth_left_TCC1 subtype-tcc nil csequence_unzip nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(x!2 skolem-const-decl "indexes[[T1, T2]](x!1)" csequence_unzip
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)
(x!1 skolem-const-decl "csequence[[T1, T2]]" csequence_unzip nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(nth def-decl "T" csequence_nth nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(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)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip 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))
(unzip_nth_right_TCC1 0
(unzip_nth_right_TCC1-1 nil 3513780110
("" (skolem!) (("" (rewrite "unzip_index_right") nil nil)) nil)
((unzip_index_right formula-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(csequence type-decl nil csequence_codt 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)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil))
nil))
(unzip_nth_right 0
(unzip_nth_right-1 nil 3513780801
("" (measure-induct+ "n" ("cseq" "n") :skolem-typepreds? t)
(("1" (expand "index?" -)
(("1" (expand "nth" +)
(("1" (expand* "unzip" "unzip_right_struct")
(("1" (expand "coreduce" +) (("1" (reduce) nil nil)) nil))
nil))
nil))
nil)
("2" (use "unzip_nth_right_TCC1") nil nil)
("3" (use "unzip_nth_right_TCC1") nil nil)
("4" (use "unzip_nth_right_TCC1") nil nil)
("5" (use "unzip_nth_right_TCC1") nil nil))
nil)
((unzip_nth_right_TCC1 subtype-tcc nil csequence_unzip nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(x!2 skolem-const-decl "indexes[[T1, T2]](x!1)" csequence_unzip
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)
(x!1 skolem-const-decl "csequence[[T1, T2]]" csequence_unzip nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(nth def-decl "T" csequence_nth nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
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)
(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)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip 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))
(unzip_map 0
(unzip_map-1 nil 3513780879
("" (skolem!)
(("" (decompose-equality)
(("1" (lemma "coinduction[T1]")
(("1"
(inst -
"LAMBDA (cseq1, cseq2: csequence[T1]): EXISTS cseq: cseq1 = unzip(cseq)`1 AND cseq2 = map[[T1, T2], T1](PROJ_1, cseq)"
"unzip(cseq!1)`1" "map[[T1, T2], T1](PROJ_1, cseq!1)")
(("1" (assert) (("1" (inst + "cseq!1") nil nil)) nil)
("2" (delete 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2" (replace*)
(("2" (hide -1 -2)
(("2"
(expand* "unzip" "unzip_left_struct" "coreduce"
"map")
(("2" (smash)
(("2" (inst + "rest(cseq!2)")
(("2" (expand "map" 2 1)
(("2" (expand "coreduce" 2 1)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "coinduction[T2]")
(("2"
(inst -
"LAMBDA (cseq1, cseq2: csequence[T2]): EXISTS cseq: cseq1 = unzip(cseq)`2 AND cseq2 = map[[T1, T2], T2](PROJ_2, cseq)"
"unzip(cseq!1)`2" "map[[T1, T2], T2](PROJ_2, cseq!1)")
(("1" (assert) (("1" (inst + "cseq!1") nil nil)) nil)
("2" (delete 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2" (replace*)
(("2" (hide -1 -2)
(("2"
(expand* "unzip" "unzip_right_struct" "coreduce"
"map")
(("2" (smash)
(("2" (inst + "rest(cseq!2)")
(("2" (expand "map" 2 1)
(("2" (expand "coreduce" 2 1)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(T2 formal-type-decl nil csequence_unzip nil)
(csequence type-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_unzip nil)
(= const-decl "[T, T -> boolean]" equalities 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)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip 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)
(coinduction formula-decl nil csequence_codt nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_extensionality 0
(unzip_extensionality-1 nil 3513781049
("" (skosimp)
(("" (lemma "coinduction[[T1, T2]]")
((""
(inst - "LAMBDA cseq1, cseq2: unzip(cseq1) = unzip(cseq2)"
"cseq1!1" "cseq2!1")
(("1" (assert) nil nil)
("2" (delete -1 2)
(("2" (expand "bisimulation?")
(("2" (skosimp)
(("2" (reduce)
(("1"
(expand* "unzip" "unzip_left_struct"
"unzip_right_struct" "coreduce")
nil nil)
("2"
(expand* "unzip" "unzip_left_struct"
"unzip_right_struct" "coreduce")
nil nil)
("3"
(expand* "unzip" "unzip_left_struct"
"unzip_right_struct")
(("3" (expand "coreduce" -)
(("3" (reduce)
(("1" (decompose-equality -2) nil nil)
("2" (decompose-equality) nil nil))
nil))
nil))
nil)
("4"
(expand* "unzip" "unzip_left_struct"
"unzip_right_struct" "coreduce")
(("4" (reduce)
(("4" (reduce-with-ext)
(("1" (decompose-equality) nil nil)
("2" (decompose-equality -2) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil)
(coinduction formula-decl nil csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
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)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
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)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip 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)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_add 0
(unzip_add-1 nil 3513781223
("" (expand* "unzip" "unzip_left_struct" "unzip_right_struct")
(("" (expand "coreduce" 1 1)
(("" (expand "coreduce" 1 1) (("" (propax) nil 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)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil)
(unzip_right_struct const-decl
"csequence_struct[T2, csequence[[T1, T2]]]" csequence_unzip nil)
(unzip_left_struct const-decl
"csequence_struct[T1, csequence[[T1, T2]]]" csequence_unzip nil))
shostak))
(unzip_last_left_TCC1 0
(unzip_last_left_TCC1-1 nil 3513780110
("" (skolem!)
(("" (use "unzip_nonempty") (("" (flatten) nil nil)) nil)) nil)
((unzip_nonempty judgement-tcc nil csequence_unzip nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props 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)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil))
nil))
(unzip_last_left 0
(unzip_last_left-1 nil 3513781279
("" (skolem-typepred)
(("" (rewrite "length_nonempty?_rew")
(("" (expand "last")
(("" (rewrite "unzip_length_left")
(("" (rewrite "unzip_nth_left") nil nil)) nil))
nil))
nil))
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)
(unzip_length_left formula-decl nil csequence_unzip nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(has_length def-decl "bool" csequence_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(indexes type-eq-decl nil csequence_nth nil)
(index? def-decl "bool" csequence_nth 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)
(unzip_nth_left formula-decl nil csequence_unzip nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(last const-decl "T" csequence_nth nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(csequence type-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
shostak))
(unzip_last_right_TCC1 0
(unzip_last_right_TCC1-1 nil 3513780110
("" (skolem!)
(("" (use "unzip_nonempty") (("" (flatten) nil nil)) nil)) nil)
((unzip_nonempty judgement-tcc nil csequence_unzip nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props 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)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil))
nil))
(unzip_last_right 0
(unzip_last_right-1 nil 3513781314
("" (skolem-typepred)
(("" (rewrite "length_nonempty?_rew")
(("" (expand "last")
(("" (rewrite "unzip_length_right")
(("" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
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)
(unzip_length_right formula-decl nil csequence_unzip nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(has_length def-decl "bool" csequence_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(indexes type-eq-decl nil csequence_nth nil)
(index? def-decl "bool" csequence_nth 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)
(unzip_nth_right formula-decl nil csequence_unzip nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(last const-decl "T" csequence_nth nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(csequence type-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_unzip nil)
(T1 formal-type-decl nil csequence_unzip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
shostak))
(unzip_some 0
(unzip_some-1 nil 3513781344
("" (skolem!)
(("" (use "nth_some[[T1, T2]]")
(("" (use "nth_some[T2]")
(("" (use "nth_some[T1]")
(("" (smash)
(("1" (skosimp* t)
(("1" (rewrite "unzip_index_right")
(("1" (inst + "i!2")
(("1" (flatten)
(("1" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
nil)
("2" (skolem-typepred)
(("2" (rewrite "unzip_index_left")
(("2" (inst 4 "i!1")
(("2" (flatten)
(("2" (rewrite "unzip_nth_left") nil nil)) nil))
nil))
nil))
nil)
("3" (skolem-typepred)
(("3" (rewrite "unzip_index_right")
(("3" (inst 4 "i!1")
(("3" (flatten)
(("3" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
nil)
("4" (skolem-typepred)
(("4" (split)
(("1" (rewrite "unzip_index_left" :dir rl)
(("1" (inst + "i!1")
(("1" (rewrite "unzip_nth_left") nil nil)) nil))
nil)
("2" (rewrite "unzip_index_right" :dir rl)
(("2" (inst 4 "i!1")
(("2" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nth_some formula-decl nil csequence_nth nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(OR const-decl "[bool, bool -> bool]" booleans 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)
(i!1 skolem-const-decl "indexes[[T1, T2]](cseq!1)" csequence_unzip
nil)
(i!1 skolem-const-decl "indexes[T2](unzip(cseq!1)`2)"
csequence_unzip nil)
(i!1 skolem-const-decl "indexes[T1](unzip(cseq!1)`1)"
csequence_unzip nil)
(unzip_nth_left formula-decl nil csequence_unzip nil)
(unzip_index_left formula-decl nil csequence_unzip nil)
(indexes type-eq-decl nil csequence_nth nil)
(index? def-decl "bool" csequence_nth 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(cseq!1 skolem-const-decl "csequence[[T1, T2]]" csequence_unzip
nil)
(i!2 skolem-const-decl "indexes[T2](unzip(cseq!1)`2)"
csequence_unzip nil)
(unzip_nth_right formula-decl nil csequence_unzip nil)
(unzip_index_right formula-decl nil csequence_unzip nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak))
(unzip_every 0
(unzip_every-1 nil 3513781474
("" (skolem!)
(("" (use "nth_every[[T1, T2]]")
(("" (use "nth_every[[T2]]")
(("" (use "nth_every[[T1]]")
(("" (smash)
(("1" (skolem-typepred)
(("1" (split)
(("1" (rewrite "unzip_index_left" :dir rl)
(("1" (inst - "i!1")
(("1" (rewrite "unzip_nth_left" :dir rl) nil nil))
nil))
nil)
("2" (rewrite "unzip_index_right" :dir rl)
(("2" (inst -5 "i!1")
(("2" (rewrite "unzip_nth_right" :dir rl) nil nil))
nil))
nil))
nil))
nil)
("2" (skolem-typepred)
(("2" (rewrite "unzip_index_right")
(("2" (inst -5 "i!1")
(("2" (flatten)
(("2" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
nil)
("3" (skolem-typepred)
(("3" (rewrite "unzip_index_left")
(("3" (inst -5 "i!1")
(("3" (flatten)
(("3" (rewrite "unzip_nth_left") nil nil)) nil))
nil))
nil))
nil)
("4" (skosimp* t)
(("4" (rewrite "unzip_index_right")
(("4" (inst - "i!2")
(("4" (flatten)
(("4" (rewrite "unzip_nth_right") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nth_every formula-decl nil csequence_nth nil)
(T1 formal-type-decl nil csequence_unzip nil)
(T2 formal-type-decl nil csequence_unzip nil)
(AND const-decl "[bool, bool -> bool]" booleans 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)
(i!2 skolem-const-decl "indexes[T2](unzip(cseq!1)`2)"
csequence_unzip nil)
(i!1 skolem-const-decl "indexes[T1](unzip(cseq!1)`1)"
csequence_unzip nil)
(i!1 skolem-const-decl "indexes[T2](unzip(cseq!1)`2)"
csequence_unzip nil)
(NOT const-decl "[bool -> bool]" booleans 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)
(unzip_index_right formula-decl nil csequence_unzip nil)
(unzip_nth_right formula-decl nil csequence_unzip nil)
(unzip_index_left formula-decl nil csequence_unzip nil)
(unzip_nth_left formula-decl nil csequence_unzip nil)
(i!1 skolem-const-decl "indexes[[T1, T2]](cseq!1)" csequence_unzip
nil)
(cseq!1 skolem-const-decl "csequence[[T1, T2]]" csequence_unzip
nil)
(unzip const-decl "[csequence[T1], csequence[T2]]" csequence_unzip
nil))
shostak)))
¤ Dauer der Verarbeitung: 0.28 Sekunden
(vorverarbeitet)
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