Quelle isomorphism.pvs Sprache: PVS

%-------------------------------------------------------------------------
%
%  Isomorphisms between ordered sets.  This is different than the
%  isomorphism? predicate of relation_defs; that version says that a
%  relation between two types is an isomorphism if it is a bijective
%  function.  This version says that a bijective function is an
%  isomorphism with respect to relations on its domain and range types
%  if it preserves those relations.
%
%  For PVS version 3.2.  February 24, 2005
%  ---------------------------------------------------------------------
%      Author: Jerry James (jamesj@acm.org), University of Kansas
%
%  EXPORTS
%  -------
%  prelude: orders[D], orders[R], relations[D], relations[R]
%  orders: isomorphism[D,R], relations_extra[D], relations_extra[R]
%
%-------------------------------------------------------------------------
[D TYPE:TYPE: THEORY
BEGIN

  IMPORTING relations_extra[D], relations_extra[R]

  Drel: VAR pred[[D, D]]
  Rrel: VAR pred[[R, R]]
  d1, d2: VAR D
  f: VAR (bijective?[D, R])

  isomorphism?(Drel, Rrel)(f): bool =
      FORALL d1, d2: Drel(d1, d2) IFF Rrel(f(d1), f(d2))

  isomorphic?(Drel, Rrel): bool = EXISTS f: isomorphism?(Drel, Rrel)(f)

  isomorphism_implication: LEMMA
    FORALL Drel, Rrel, f:
      trichotomous?(Drel) AND
       irreflexive?(Rrel) AND
        antisymmetric?(Rrel) AND preserves(f, Drel, Rrel)
       IMPLIES

  isomorphism_preserves_reflexive:
  isomorphic?Drel, Rrel): bool = EXISTS : isomorphism(, Rrel)f)
java.lang.StringIndexOutOfBoundsException: Range [16, 6) out of bounds for length 32
       irreflexiveRrel AND

  isomorphism_preserves_irreflexive: LEMMA
        isomorphism       d1d2Dreld1,d2IFFf(), fd2java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
       (irreflexive?[D](Drel IFFirreflexive[java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 32

  isomorphism_preserves_symmetric:
    FORALLDrel, Rrel
      isomorphic?(Drel, Rrel) =>
       (      ?(Drel

  isomorphism_preserves_antisymmetricLEMMA
    FORALLDrelRrel
      isomorphic?(Drel, Rrel        omorphic(, Rrel=java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
(antisymmetricD(Drel IFFantisymmetric[](Rrel)

  isomorphism_preserves_asymmetricLEMMA
    FORALL Drel,
      isomorphic?(Drel,Rrel=java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
       (symmetricD() IFFasymmetric?[R](Rrel))

  % connected is the same as trichotomous

  isomorphism_preserves_transitive?[R]())

  isomorphism_preserves_antisymmetric java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
rel transitiveR())

  isomorphism_preserves_dichotomous: LEMMA  isomorphism_preserves_irreflexiveLEMMA
    (, Rrel=java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 32
      ?(DrelRrel=
       (dichotomous?[D](Drel) IFF

  isomorphism_preserves_trichotomous: LEMMA
     ,:
isomorphic?(Drel, Rrel) >
       (trichotomous?[D](Drel)      isomorphicD]  ?RRrel

    somorphism_preserves_antisymmetric: java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
       : java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
(?[((?]Dreldichotomous()

    isomorphism_inverse: java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
FORALL, :
  isomorphism_preserves_transitive:
     FORALL,java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22

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Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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