SSL IUnion_extra.prf Sprache: Lisp

(IUnion_extra
(upto?_TCC1 0
  (upto?_TCC1-1 nil 3415314220 ("" (subtype-tcc) nil nil) nil nil))
(disjoint_subset 0
  (disjoint_subset-1 nil 3415314271
   ("" (skosimp*)
    (("" (expand* "disjoint?" "empty?" "intersection")
      (("" (skeep)
        (("" (inst?)
          (("" (expand* "subset?" "member")
            (("" (inst?) (("" (inst?) (("" (prop) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((empty? const-decl "bool" sets nil)
    (intersection const-decl "set" sets nil)
    (disjoint? const-decl "bool" sets nil)
    (T formal-type-decl nil IUnion_extra nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil))
   shostak))
(disjoint_commute 0
  (disjoint_commute-1 nil 3415314299
   ("" (skeep)
    (("" (expand* "disjoint?" "empty?" "intersection")
      (("" (skosimp*)
        (("" (inst?) (("" (expand "member") (("" (prop) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((empty? const-decl "bool" sets nil)
    (intersection const-decl "set" sets nil)
    (disjoint? const-decl "bool" sets nil)
    (T formal-type-decl nil IUnion_extra nil)
    (member const-decl "bool" sets nil))
   shostak))
(IUnion_of_finite_is_finite 0
  (IUnion_of_finite_is_finite-1 nil 3415314322
   ("" (induct "n")
    (("1" (typepred "n!1") (("1" (propax) nil nil)) nil)
     ("2" (assert) nil nil)
     ("3" (skosimp*)
      (("3" (case "j!1 = 0")
        (("1" (hide -2)
          (("1" (expand "IUnion")
            (("1" (inst -3 "1")
              (("1"
                (case-replace
                 "{x: T | EXISTS (i_1: upto?(1 + j!1)): f!1(i_1)(x)} = f!1(1)"
                 :hide? T)
                (("1" (hide 2)
                  (("1" (decompose-equality 1)
                    (("1" (iff)
                      (("1" (prop)
                        (("1" (skosimp*)
                          (("1" (typepred "i!1")
                            (("1" (replaces -4)
                              (("1" (assert) nil nil)) nil))
                            nil))
                          nil)
                         ("2" (inst 1 "1") nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assert)
          (("2"
            (inst -1
             "restrict[upto?(1 + j!1), upto?(j!1), set[T]](f!1)")
            (("2" (prop)
              (("1" (expand "restrict")
                (("1"
                  (case-replace
                   "IUnion(LAMBDA (i: upto?(1 + j!1)): f!1(i)) = union(f!1(j!1 + 1),IUnion(LAMBDA (i: upto?(j!1)): f!1(i)))"
                   :hide? T)
                  (("1" (inst -3 "j!1 + 1")
                    (("1" (rewrite "finite_union" 2) nil nil)) nil)
                   ("2" (hide (-1 -3 3))
                    (("2" (decompose-equality 1)
                      (("2" (iff)
                        (("2" (prop)
                          (("1" (expand "IUnion" -1)
                            (("1" (skosimp*)
                              (("1"
                                (expand* "union" "member")
                                (("1"
                                  (flatten)
                                  (("1"
                                    (case-replace "i!1 = 1 + j!1")
                                    (("1"
                                      (expand "IUnion")
                                      (("1"
                                        (inst 3 "i!1")
                                        (("1"
                                          (typepred "i!1")
                                          (("1" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (expand* "union" "member")
                            (("2" (prop)
                              (("1"
                                (expand "IUnion")
                                (("1" (inst 1 "1 + j!1") nil nil))
                                nil)
                               ("2"
                                (expand "IUnion")
                                (("2"
                                  (skosimp*)
                                  (("2" (inst 1 "i!1") nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (skosimp*)
                (("2" (expand "restrict")
                  (("2" (inst -2 "i!1") nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((union const-decl "set" sets nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (finite_union judgement-tcc nil finite_sets nil)
    (i!1 skolem-const-decl "upto?(1 + j!1)" IUnion_extra nil)
    (j!1 skolem-const-decl "nat" IUnion_extra nil)
    (member const-decl "bool" sets nil)
    (restrict const-decl "R" restrict nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil IUnion_extra nil)
    (upto? nonempty-type-eq-decl nil IUnion_extra nil)
    (<= const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types 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))
   shostak))
(IUnion_of_finite_is_finite1 0
  (IUnion_of_finite_is_finite1-1 nil 3415319375
   ("" (induct "n")
    (("1" (typepred "n!1") (("1" (propax) nil nil)) nil)
     ("2" (assert) nil nil)
     ("3" (skosimp*)
      (("3" (case "j!1 = 0")
        (("1" (hide -2)
          (("1" (expand "IUnion")
            (("1" (inst -3 "0")
              (("1"
                (case-replace
                 "{x: T | EXISTS (i_1: below[1 + j!1]): f!1(i_1)(x)} = f!1(0)"
                 :hide? T)
                (("1" (hide 2)
                  (("1" (decompose-equality 1)
                    (("1" (iff)
                      (("1" (prop)
                        (("1" (skosimp*)
                          (("1" (typepred "i!1")
                            (("1" (replaces -3)
                              (("1" (assert) nil nil)) nil))
                            nil))
                          nil)
                         ("2" (inst 1 "0") nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assert)
          (("2"
            (inst -1
             "restrict[below[1 + j!1], below[j!1], set[T]](f!1)")
            (("2" (prop)
              (("1" (expand "restrict")
                (("1"
                  (case-replace
                   "IUnion(LAMBDA (i: below[1 + j!1]): f!1(i)) = union(f!1(j!1),IUnion(LAMBDA (i: below[j!1]): f!1(i)))"
                   :hide? T)
                  (("1" (inst -3 "j!1")
                    (("1" (rewrite "finite_union" 2) nil nil)) nil)
                   ("2" (hide (-1 -3 3))
                    (("2" (decompose-equality 1)
                      (("2" (iff)
                        (("2" (prop)
                          (("1" (expand "IUnion" -1)
                            (("1" (skosimp*)
                              (("1"
                                (expand* "union" "member")
                                (("1"
                                  (flatten)
                                  (("1"
                                    (case-replace "i!1 = j!1")
                                    (("1"
                                      (expand "IUnion")
                                      (("1"
                                        (inst 3 "i!1")
                                        (("1"
                                          (typepred "i!1")
                                          (("1" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (expand* "union" "member")
                            (("2" (prop)
                              (("1"
                                (expand "IUnion")
                                (("1" (inst 1 "j!1") nil nil))
                                nil)
                               ("2"
                                (expand "IUnion")
                                (("2"
                                  (skosimp*)
                                  (("2" (inst 1 "i!1") nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (skosimp*)
                (("2" (expand "restrict")
                  (("2" (inst -2 "i!1") nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((union const-decl "set" sets nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (finite_union judgement-tcc nil finite_sets nil)
    (i!1 skolem-const-decl "below[1 + j!1]" IUnion_extra nil)
    (j!1 skolem-const-decl "nat" IUnion_extra nil)
    (member const-decl "bool" sets nil)
    (restrict const-decl "R" restrict 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)
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil IUnion_extra nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil) (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types 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))
   shostak)))

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