Quelle constant_continuity.prf Sprache: Lisp

(constant_continuity
(const_continuous_at 0
  (const_continuous_at-1 nil 3301542630
   ("" (expand "continuous_at?")
    (("" (expand "neighbourhood?")
      (("" (expand "interior_point?")
        (("" (skosimp*)
          (("" (typepred "U!2")
            (("" (assert)
              (("" (inst + "inverse_image(const_fun(a!1), U!2)")
                (("1"
                  (lemma "inverse_image_subset[T1,T2]"
                   ("Y1" "U!2" "Y2" "U!1" "f" "const_fun[T1,T2](a!1)"))
                  (("1" (assert)
                    (("1" (lemma "topology1")
                      (("1" (lemma "open_fullset[T1,S]")
                        (("1" (expand "inverse_image")
                          (("1" (assert) nil nil)) nil)
                         ("2" (propax) nil nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "inverse_image")
                  (("2" (expand "const_fun")
                    (("2" (expand "member")
                      (("2" (replace -3)
                        (("2" (lemma "open_fullset[T1,S]")
                          (("1" (expand "fullset")
                            (("1" (propax) nil nil)) nil)
                           ("2" (lemma "topology1")
                            (("2" (propax) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((neighbourhood? const-decl "bool" topology nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (member const-decl "bool" sets nil)
    (fullset const-decl "set" sets nil)
    (inverse_image_subset formula-decl nil function_image nil)
    (open_fullset formula-decl nil topology nil)
    (fullset_is_clopen name-judgement "clopen" constant_continuity nil)
    (T1 formal-type-decl nil constant_continuity nil)
    (S formal-const-decl "topology[T1]" constant_continuity nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (const_fun const-decl "[S -> T]" const_fun_def "structures/")
    (a!1 skolem-const-decl "T2" constant_continuity nil)
    (U!2 skolem-const-decl "open[T2, T]" constant_continuity nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T2 formal-type-decl nil constant_continuity nil)
    (set type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (setofsets type-eq-decl nil sets nil)
    (topology? const-decl "bool" topology_prelim nil)
    (topology nonempty-type-eq-decl nil topology_prelim nil)
    (T formal-const-decl "topology[T2]" constant_continuity nil)
    (open? const-decl "bool" topology nil)
    (open nonempty-type-eq-decl nil topology nil)
    (interior_point? const-decl "bool" topology nil)
    (continuous_at? const-decl "bool" continuity_def nil))
   shostak))
(const_continuous 0
  (const_continuous-1 nil 3301542853
   ("" (expand "continuous?")
    (("" (skosimp*)
      (("" (lemma "const_continuous_at" ("a" "a!1" "x" "x!1"))
        (("" (propax) nil nil)) nil))
      nil))
    nil)
   ((const_continuous_at formula-decl nil constant_continuity nil)
    (T2 formal-type-decl nil constant_continuity nil)
    (T1 formal-type-decl nil constant_continuity nil)
    (continuous? const-decl "bool" continuity_def nil))
   shostak))
(const_is_continuous 0
  (const_is_continuous-1 nil 3358747663
   ("" (skosimp)
    (("" (lemma "const_continuous" ("a" "a!1")) (("" (propax) nil nil))
      nil))
    nil)
   ((T2 formal-type-decl nil constant_continuity nil)
    (const_continuous formula-decl nil constant_continuity nil))
   nil)))

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