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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: csequence_unzip.prf Sprache: LispOriginal von: PVS© |
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(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( (("1" (skolem!) 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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 cs "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 cs "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!) 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