Quelle infinite_card.prf Sprache: Lisp

(infinite_card
(finite_card_eq 0
  (finite_card_eq-1 nil 3316971041
   ("" (skosimp)
    (("" (use "card_eq_symmetric[T1, T2]")
      (("" (expand* "card_eq" "is_finite" "bijective?")
        (("" (smash)
          (("1" (skosimp*)
            (("1"
              (use "composition_injective[(S2!1), (S1!1), below[N!1]]")
              (("1" (inst + "N!1" "f!3 o f!2") nil nil)) nil))
            nil)
           ("2" (skosimp*)
            (("2"
              (use "composition_injective[(S1!1), (S2!1), below[N!1]]")
              (("2" (inst + "N!1" "f!3 o f!1") nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((card_eq_symmetric formula-decl nil card_comp_set_props nil)
    (T1 formal-type-decl nil infinite_card nil)
    (T2 formal-type-decl nil infinite_card nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (composition_injective judgement-tcc nil function_props 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)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S1!1)]" infinite_card nil)
    (injective? const-decl "bool" functions nil)
    (S1!1 skolem-const-decl "set[T1]" infinite_card nil)
    (S2!1 skolem-const-decl "set[T2]" infinite_card nil)
    (f!3 skolem-const-decl "[(S1!1) -> below[N!1]]" infinite_card nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (O const-decl "T3" function_props nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" infinite_card nil)
    (f!3 skolem-const-decl "[(S2!1) -> below[N!1]]" infinite_card nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (bijective? const-decl "bool" functions nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak))
(infinite_card_eq 0
  (infinite_card_eq-1 nil 3316971153
   ("" (skosimp)
    (("" (forward-chain "finite_card_eq") (("" (prop) nil nil)) nil))
    nil)
   ((finite_card_eq formula-decl nil infinite_card nil)
    (T1 formal-type-decl nil infinite_card nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil infinite_card nil))
   shostak))
(infinite_card_le 0
  (infinite_card_le-1 nil 3316971171
   ("" (expand* "card_le" "is_finite")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S2!1), below[N!1]]")
        (("" (inst + "N!1" "f!2 o f!1") nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (f!2 skolem-const-decl "[(S2!1) -> below[N!1]]" infinite_card nil)
    (S1!1 skolem-const-decl "set[T1]" infinite_card nil)
    (S2!1 skolem-const-decl "set[T2]" infinite_card nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" infinite_card nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (T2 formal-type-decl nil infinite_card nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil infinite_card nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_le const-decl "bool" card_comp_set nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak))
(infinite_card_ge 0
  (infinite_card_ge-1 nil 3316971198
   ("" (expand* "card_ge" "is_finite")
    (("" (skosimp*)
      (("" (use "composition_injective[(S2!1), (S1!1), below[N!1]]")
        (("" (inst + "N!1" "f!2 o f!1") nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (f!2 skolem-const-decl "[(S1!1) -> below[N!1]]" infinite_card nil)
    (S2!1 skolem-const-decl "set[T2]" infinite_card nil)
    (S1!1 skolem-const-decl "set[T1]" infinite_card nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]" infinite_card nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (T1 formal-type-decl nil infinite_card nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T2 formal-type-decl nil infinite_card nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak))
(finite_card_le 0
  (finite_card_le-1 nil 3316971226
   ("" (expand* "card_le" "is_finite")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S2!1), below[N!1]]")
        (("" (inst + "N!1" "f!2 o f!1") nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (f!2 skolem-const-decl "[(S2!1) -> below[N!1]]" infinite_card nil)
    (S1!1 skolem-const-decl "set[T1]" infinite_card nil)
    (S2!1 skolem-const-decl "set[T2]" infinite_card nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" infinite_card nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (T2 formal-type-decl nil infinite_card nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil infinite_card nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_le const-decl "bool" card_comp_set nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak))
(finite_card_ge 0
  (finite_card_ge-1 nil 3316971246
   ("" (expand* "card_ge" "is_finite")
    (("" (skosimp*)
      (("" (use "composition_injective[(S2!1), (S1!1), below[N!1]]")
        (("" (inst + "N!1" "f!2 o f!1") nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (N!1 skolem-const-decl "nat" infinite_card nil)
    (f!2 skolem-const-decl "[(S1!1) -> below[N!1]]" infinite_card nil)
    (S2!1 skolem-const-decl "set[T2]" infinite_card nil)
    (S1!1 skolem-const-decl "set[T1]" infinite_card nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]" infinite_card nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (T1 formal-type-decl nil infinite_card nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T2 formal-type-decl nil infinite_card nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak)))

quality100%

¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.