Quellcode-Bibliothek permutation_ops.prf Sprache: Lisp

(permutation_ops
(sorted_iff_id_lem 0
  (sorted_iff_id_lem-1 nil 3262700911
   ("" (induct "m")
    (("1" (skosimp*) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)
     ("2" (skosimp*)
      (("2" (inst?)
        (("2" (replace -4)
          (("2" (assert)
            (("2" (skosimp*)
              (("2" (case-replace "i!1 = jb!1")
                (("1" (case "pi!1(jb!1) > jb!1")
                  (("1" (inst - "pi!1(jb!1)")
                    (("1" (assert)
                      (("1" (typepred "pi!1")
                        (("1" (expand "bijective?")
                          (("1" (flatten)
                            (("1" (expand "injective?")
                              (("1"
                                (inst - "jb!1" "pi!1(jb!1)")
                                (("1" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (typepred "pi!1")
                    (("2" (expand "bijective?")
                      (("2" (flatten)
                        (("2" (expand "surjective?")
                          (("2" (inst - "jb!1")
                            (("2" (skosimp*)
                              (("2"
                                (inst -7 "x!1" "jb!1")
                                (("2"
                                  (assert)
                                  (("2"
                                    (case-replace "x!1 = jb!1")
                                    (("2"
                                      (inst - "x!1")
                                      (("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (inst?) (("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((injective? const-decl "bool" functions nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (surjective? const-decl "bool" functions 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (below_induction formula-decl nil bounded_nat_inductions 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)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" permutation_ops nil)
    (<= const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (permutation nonempty-type-eq-decl nil permutation nil)
    (bijective? const-decl "bool" functions nil)
    (pred type-eq-decl nil defined_types nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   shostak))
(sorted_iff_id 0
  (sorted_iff_id-1 nil 3262700349
   ("" (skosimp*)
    (("" (prop)
      (("1" (decompose-equality)
        (("1" (expand* "sorted?" "id")
          (("1" (lemma "sorted_iff_id_lem")
            (("1" (inst - "x!1" "N" "pi!1") (("1" (assert) nil nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (replace -1 :hide? t)
        (("2" (expand* "sorted?" "id")
          (("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((sorted? const-decl "bool" sort_array nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (sorted_iff_id_lem formula-decl nil permutation_ops 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)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" permutation_ops nil)
    (below type-eq-decl nil naturalnumbers nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (permutation nonempty-type-eq-decl nil permutation nil)
    (bijective? const-decl "bool" functions nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak)))

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