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Datei: lower_semilattices.prf Sprache: Lisp

Original von: PVS^©

(lower_semilattices
(finite_set_is_greatest_bounded_below 0
  (finite_set_is_greatest_bounded_below-1 nil 3315157450
   ("" (skolem!)
    (("" (typepred "<=")
      (("" (expand "lower_semilattice?")
        (("" (flatten) (("" (inst?) nil nil)) nil)) nil))
      nil))
    nil)
   ((<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (empty? const-decl "bool" sets nil)
    (non_empty_finite_set type-eq-decl nil finite_sets nil))
   nil))
(greatest_lower_bound_singleton 0
  (greatest_lower_bound_singleton-1 nil 3315157495
   ("" (skolem!)
    (("" (expand "greatest_lower_bound?")
      (("" (split)
        (("1" (typepred "<=")
          (("1"
            (expand* "singleton" "lower_bound?" "lower_semilattice?"
             "partial_order?" "preorder?" "reflexive?")
            (("1" (skosimp :preds? t)
              (("1" (inst?) (("1" (assert) nil nil)) nil)) nil))
            nil))
          nil)
         ("2" (skosimp)
          (("2" (expand* "singleton" "lower_bound?")
            (("2" (inst?) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (singleton const-decl "(singleton?)" sets nil)
    (preorder? const-decl "bool" orders nil)
    (reflexive? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (lower_bound? const-decl "bool" bounded_orders nil))
   shostak))
(glb_singleton 0
  (glb_singleton-1 nil 3315157548
   ("" (skolem!)
    (("" (invoke (typepred "%1") (! 1 l))
      (("" (rewrite "unique_greatest_lower_bound")
        (("" (rewrite "greatest_lower_bound_singleton") nil nil)) nil))
      nil))
    nil)
   ((nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil lower_semilattices nil)
    (set type-eq-decl nil sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (glb const-decl "(LAMBDA (t): greatest_lower_bound?(t, S, <=))"
     bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil)
    (greatest_lower_bound_singleton formula-decl nil lower_semilattices
     nil)
    (antisymmetric? const-decl "bool" relations nil)
    (PRED type-eq-decl nil defined_types nil)
    (unique_greatest_lower_bound formula-decl nil bounded_orders nil))
   shostak))
(le_glb 0
  (le_glb-1 nil 3315157580
   ("" (skolem!)
    (("" (expand "glb")
      (("" (invoke (typepred "%1") (! 1 l r))
        (("" (invoke (name-replace "L" "%1") (! 1 l r))
          (("" (typepred "<=")
            (("" (expand "greatest_lower_bound?")
              (("" (prop)
                (("1" (hide -4)
                  (("1" (expand "lower_bound?")
                    (("1" (inst - "t!1")
                      (("1"
                        (expand* "lower_semilattice?" "partial_order?"
                         "preorder?" "transitive?")
                        (("1" (flatten)
                          (("1" (inst - "s!1" "L" "t!1")
                            (("1" (assert) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (expand* "union" "singleton" "member") nil
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide -4)
                  (("2" (expand "lower_bound?")
                    (("2" (inst - "u!1")
                      (("1"
                        (expand* "lower_semilattice?" "partial_order?"
                         "preorder?" "transitive?")
                        (("1" (flatten)
                          (("1" (inst - "s!1" "L" "u!1")
                            (("1" (assert) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (expand* "union" "singleton" "member") nil
                        nil))
                      nil))
                    nil))
                  nil)
                 ("3" (hide -4)
                  (("3" (inst - "s!1")
                    (("3" (assert)
                      (("3"
                        (expand* "union" "singleton" "member"
                         "lower_bound?")
                        (("3" (skolem-typepred)
                          (("3" (assert) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((glb const-decl "T" lower_semilattices nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (t!1 skolem-const-decl "T" lower_semilattices nil)
    (u!1 skolem-const-decl "T" lower_semilattices nil)
    (preorder? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (member const-decl "bool" sets nil)
    (lower_bound? const-decl "bool" bounded_orders nil)
    (singleton const-decl "(singleton?)" sets nil)
    (singleton? const-decl "bool" sets nil)
    (union const-decl "set" sets nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (glb const-decl "(LAMBDA (t): greatest_lower_bound?(t, S, <=))"
     bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nonempty_finite_union1 application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil))
   shostak))
(glb_le_1 0
  (glb_le_1-1 nil 3315157701
   ("" (skosimp)
    (("" (expand "glb")
      (("" (invoke (typepred "%1") (! 1 l))
        (("" (invoke (name-replace "L" "%1") (! 1 l))
          (("" (expand* "greatest_lower_bound?" "lower_bound?")
            (("" (flatten)
              (("" (inst - "t!1")
                (("1" (typepred "<=")
                  (("1"
                    (expand* "lower_semilattice?" "partial_order?"
                     "preorder?" "transitive?")
                    (("1" (flatten)
                      (("1" (inst - "L" "t!1" "s!1")
                        (("1" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand* "union" "singleton" "member") nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((glb const-decl "T" lower_semilattices nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (member const-decl "bool" sets nil)
    (preorder? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (u!1 skolem-const-decl "T" lower_semilattices nil)
    (t!1 skolem-const-decl "T" lower_semilattices nil)
    (lower_bound? const-decl "bool" bounded_orders nil)
    (singleton const-decl "(singleton?)" sets nil)
    (singleton? const-decl "bool" sets nil)
    (union const-decl "set" sets nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (glb const-decl "(LAMBDA (t): greatest_lower_bound?(t, S, <=))"
     bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nonempty_finite_union1 application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil))
   shostak))
(glb_le_2 0
  (glb_le_2-1 nil 3315157757
   ("" (skosimp)
    (("" (expand "glb")
      (("" (invoke (typepred "%1") (! 1 l))
        (("" (invoke (name-replace "L" "%1") (! 1 l))
          (("" (expand* "greatest_lower_bound?" "lower_bound?")
            (("" (flatten)
              (("" (inst - "u!1")
                (("1" (typepred "<=")
                  (("1"
                    (expand* "lower_semilattice?" "partial_order?"
                     "preorder?" "transitive?")
                    (("1" (flatten)
                      (("1" (inst - "L" "u!1" "s!1")
                        (("1" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand* "union" "singleton" "member") nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((glb const-decl "T" lower_semilattices nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (member const-decl "bool" sets nil)
    (preorder? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (u!1 skolem-const-decl "T" lower_semilattices nil)
    (t!1 skolem-const-decl "T" lower_semilattices nil)
    (lower_bound? const-decl "bool" bounded_orders nil)
    (singleton const-decl "(singleton?)" sets nil)
    (singleton? const-decl "bool" sets nil)
    (union const-decl "set" sets nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (glb const-decl "(LAMBDA (t): greatest_lower_bound?(t, S, <=))"
     bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nonempty_finite_union1 application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil))
   shostak))
(union_preserves_bounded_below 0
  (union_preserves_bounded_below-1 nil 3315157450
   ("" (skolem-typepred)
    (("" (expand "bounded_below?")
      (("" (skosimp*)
        (("" (inst + "glb(t!1, t!2)")
          (("" (expand "lower_bound?")
            (("" (skolem-typepred)
              (("" (expand* "union" "member")
                (("" (inst?)
                  (("1" (rewrite "glb_le_1") nil nil)
                   ("2" (assert)
                    (("2" (inst?) (("2" (rewrite "glb_le_2") nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((glb const-decl "T" lower_semilattices nil)
    (union const-decl "set" sets nil)
    (S1!1 skolem-const-decl
     "(LAMBDA (S: set[T]): bounded_below?(S, <=))" lower_semilattices
     nil)
    (S2!1 skolem-const-decl
     "(LAMBDA (S: set[T]): bounded_below?(S, <=))" lower_semilattices
     nil)
    (r!1 skolem-const-decl "(union[T](S1!1, S2!1))" lower_semilattices
     nil)
    (glb_le_1 formula-decl nil lower_semilattices nil)
    (glb_le_2 formula-decl nil lower_semilattices nil)
    (member const-decl "bool" sets nil)
    (lower_bound? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (bounded_below? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
(add_preserves_bounded_below 0
  (add_preserves_bounded_below-1 nil 3315157450
   ("" (skolem-typepred)
    (("" (rewrite "add_as_union")
      (("" (rewrite "union_preserves_bounded_below") nil nil)) nil))
    nil)
   ((add_as_union formula-decl nil sets_lemmas nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (union_preserves_bounded_below application-judgement
     "(LAMBDA (S: set[T]): bounded_below?(S, <=))" lower_semilattices
     nil)
    (union_preserves_bounded_below judgement-tcc nil lower_semilattices
     nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (bounded_below? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
(greatest_lower_bound_union 0
  (greatest_lower_bound_union-1 nil 3315157910
   ("" (skosimp)
    (("" (expand "greatest_lower_bound?")
      (("" (prop)
        (("1" (hide -4 -2)
          (("1" (expand "lower_bound?")
            (("1" (skolem-typepred)
              (("1" (expand* "union" "member")
                (("1" (inst - "r!1")
                  (("1" (rewrite "glb_le_1") nil nil)
                   ("2" (assert)
                    (("2" (inst - "r!1")
                      (("2" (rewrite "glb_le_2") nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (skosimp)
          (("2" (rewrite "le_glb")
            (("2" (split)
              (("1" (hide -5 -4 -2)
                (("1" (inst?)
                  (("1" (assert)
                    (("1" (expand "lower_bound?")
                      (("1" (skolem!)
                        (("1" (inst - "r!2")
                          (("1" (expand* "union" "member") nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (hide -4 -3 -2)
                (("2" (inst?)
                  (("2" (assert)
                    (("2" (expand "lower_bound?")
                      (("2" (skolem!)
                        (("2" (inst - "r!2")
                          (("2" (expand* "union" "member") nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (r!2 skolem-const-decl "(S1!1)" lower_semilattices nil)
    (union_preserves_bounded_below application-judgement
     "(LAMBDA (S: set[T]): bounded_below?(S, <=))" lower_semilattices
     nil)
    (r!2 skolem-const-decl "(S2!1)" lower_semilattices nil)
    (le_glb formula-decl nil lower_semilattices nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil lower_semilattices nil)
    (set type-eq-decl nil sets nil) (union const-decl "set" sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (S1!1 skolem-const-decl
     "(LAMBDA (S: set[T]): greatest_bounded_below?(S, <=))"
     lower_semilattices nil)
    (S2!1 skolem-const-decl
     "(LAMBDA (S: set[T]): greatest_bounded_below?(S, <=))"
     lower_semilattices nil)
    (r!1 skolem-const-decl "(union(S1!1, S2!1))" lower_semilattices
     nil)
    (glb_le_1 formula-decl nil lower_semilattices nil)
    (glb_le_2 formula-decl nil lower_semilattices nil)
    (member const-decl "bool" sets nil)
    (lower_bound? const-decl "bool" bounded_orders nil))
   shostak))
(greatest_lower_bound_add 0
  (greatest_lower_bound_add-1 nil 3315158032
   ("" (skosimp)
    (("" (rewrite "add_as_union")
      (("" (rewrite "greatest_lower_bound_union")
        (("" (rewrite "greatest_lower_bound_singleton") nil nil)) nil))
      nil))
    nil)
   ((add_as_union formula-decl nil sets_lemmas nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (T formal-type-decl nil lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (union_preserves_bounded_below application-judgement
     "(LAMBDA (S: set[T]): bounded_below?(S, <=))" lower_semilattices
     nil)
    (greatest_lower_bound_singleton formula-decl nil lower_semilattices
     nil)
    (greatest_lower_bound_union formula-decl nil lower_semilattices
     nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil))
   shostak))
(union_preserves_greatest_bounded_below 0
  (union_preserves_greatest_bounded_below-1 nil 3315157450
   ("" (skolem-typepred)
    (("" (expand "greatest_bounded_below?")
      (("" (skosimp*)
        (("" (inst + "glb(t!1, t!2)")
          (("" (rewrite "greatest_lower_bound_union") nil nil)) nil))
        nil))
      nil))
    nil)
   ((glb const-decl "T" lower_semilattices nil)
    (greatest_lower_bound_union formula-decl nil lower_semilattices
     nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil lower_semilattices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
(add_preserves_greatest_bounded_below 0
  (add_preserves_greatest_bounded_below-1 nil 3315157450
   ("" (skolem!)
    (("" (rewrite "add_as_union")
      (("" (rewrite "union_preserves_greatest_bounded_below") nil nil))
      nil))
    nil)
   ((add_as_union formula-decl nil sets_lemmas nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (T formal-type-decl nil lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (union_preserves_greatest_bounded_below application-judgement
     "(LAMBDA (S: set[T]): greatest_bounded_below?(S, <=))"
     lower_semilattices nil)
    (union_preserves_greatest_bounded_below judgement-tcc nil
     lower_semilattices nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil))
   nil))
(glb_union 0
  (glb_union-1 nil 3315158151
   ("" (skolem!)
    (("" (invoke (typepred "%1" "%2" "%3") (! 1 l) (! 1 r 1) (! 1 r 2))
      (("" (invoke (name-replace "GU" "%1") (! 1 l))
        (("" (invoke (name-replace "G1" "%1") (! 1 r 1))
          (("" (invoke (name-replace "G2" "%1") (! 1 r 2))
            (("" (use "greatest_lower_bound_union")
              (("" (assert)
                (("" (use "unique_greatest_lower_bound") nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((union_preserves_greatest_bounded_below application-judgement
     "(LAMBDA (S: set[T]): greatest_bounded_below?(S, <=))"
     lower_semilattices nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil lower_semilattices nil)
    (set type-eq-decl nil sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_lower_bound? const-decl "bool" bounded_orders nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (glb const-decl "(LAMBDA (t): greatest_lower_bound?(t, S, <=))"
     bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (union const-decl "set" sets nil)
    (greatest_lower_bound_union formula-decl nil lower_semilattices
     nil)
    (PRED type-eq-decl nil defined_types nil)
    (antisymmetric? const-decl "bool" relations nil)
    (glb const-decl "T" lower_semilattices nil)
    (unique_greatest_lower_bound formula-decl nil bounded_orders nil)
    (= const-decl "[T, T -> boolean]" equalities nil))
   shostak))
(glb_add 0
  (glb_add-1 nil 3315158200
   ("" (skolem!)
    (("" (rewrite "add_as_union")
      (("" (rewrite "glb_union")
        (("" (rewrite "glb_singleton") nil nil)) nil))
      nil))
    nil)
   ((add_as_union formula-decl nil sets_lemmas nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (pred type-eq-decl nil defined_types nil)
    (greatest_bounded_below? const-decl "bool" bounded_orders nil)
    (lower_semilattice? const-decl "bool" bounded_orders nil)
    (<= formal-const-decl "(lower_semilattice?[T])" lower_semilattices
        nil)
    (T formal-type-decl nil lower_semilattices nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" lower_semilattices nil)
    (nonempty_union2 application-judgement "(nonempty?)"
     lower_semilattices nil)
    (union_preserves_greatest_bounded_below application-judgement
     "(LAMBDA (S: set[T]): greatest_bounded_below?(S, <=))"
     lower_semilattices nil)
    (glb_singleton formula-decl nil lower_semilattices nil)
    (glb_union formula-decl nil lower_semilattices nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.28 Sekunden (vorverarbeitet) ¤

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