Quelle denumerable_enumeration.prf Sprache: Lisp

(denumerable_enumeration
(denumerable_enumeration_TCC1 0
  (denumerable_enumeration_TCC1-1 nil 3322365875
   ("" (skosimp)
    (("" (typepred "X!1")
      (("" (expand "is_countably_infinite")
        (("" (skosimp)
          (("" (typepred "f!1")
            (("" (lemma "bijective_inverse_exists" ("f" "f!1"))
              (("" (expand "exists1")
                (("" (flatten)
                  (("" (skolem - "g")
                    ((""
                      (lemma "bij_inv_is_bij_alt" ("f" "f!1" "g" "g"))
                      (("1" (expand "nonempty?")
                        (("1" (expand "empty?")
                          (("1" (inst - "g")
                            (("1" (expand "member")
                              (("1" (propax) nil nil)) nil))
                            nil))
                          nil))
                        nil)
                       ("2" (propax) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((countably_infinite_set type-eq-decl nil countability "sets_aux/")
    (is_countably_infinite const-decl "bool" countability "sets_aux/")
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil denumerable_enumeration nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (empty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (nonempty? const-decl "bool" sets nil)
    (exists1 const-decl "bool" exists1 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)
    (bijective? const-decl "bool" functions nil))
   shostak))
(denumerable_enumeration_bij 0
  (denumerable_enumeration_bij-1 nil 3322366032
   ("" (skosimp)
    (("" (expand "denumerable_enumeration") (("" (propax) nil nil))
      nil))
    nil)
   ((denumerable_enumeration const-decl "[nat -> (X)]"
     denumerable_enumeration nil))
   shostak))
(denumerable_enumeration_image 0
  (denumerable_enumeration_image-1 nil 3322366048
   ("" (skosimp)
    (("" (expand "restrict")
      (("" (expand "fullset")
        (("" (expand "image")
          (("" (apply-extensionality :hide? t)
            (("" (lemma "denumerable_enumeration_bij" ("X" "X!1"))
              (("" (expand "bijective?")
                (("" (flatten)
                  (("" (expand "surjective?")
                    (("" (inst - "x!1")
                      (("" (skosimp)
                        (("" (inst + "x!2") (("" (assert) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((restrict const-decl "R" restrict nil)
    (image const-decl "set[R]" function_image nil)
    (denumerable_enumeration_bij formula-decl nil
     denumerable_enumeration nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions 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)
    (TRUE const-decl "bool" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (denumerable_enumeration const-decl "[nat -> (X)]"
     denumerable_enumeration nil)
    (countably_infinite_set type-eq-decl nil countability "sets_aux/")
    (is_countably_infinite const-decl "bool" countability "sets_aux/")
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil denumerable_enumeration nil)
    (fullset const-decl "set" sets nil))
   shostak)))

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