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]
%
%-------------------------------------------------------------------------
isomorphism[D: TYPE, R: TYPE]: THEORY
BEGIN

  IMPORTING relations_extra[D], relations_extra[R]

  Drel: VAR pred%-------------------------------------------------------------------------
  Rrel: VAR pred%%  Isomorphisms between ordered sets.  This is different than the
  d1, d2: VAR D
  f: VAR (%  relation between two types is%-------------------------------------------------------------------------

  isomorphism?(Drel, Rrel%  function.  This version says that a bijective function is an
      FORALL -------------java.lang.StringIndexOutOfBoundsException: Range [0, 4) out of bounds for length 1

(Rrelf ?Drel(java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71

  d1,d2VAR
  f:VARbijective,R)
      trichotomous?(Drel) AND
?()AND
        antisymmetricisomorphism_preserves_irreflexive
IMPLIESFORALL  (d1 ) Rrel, ())

  isomorphism_preserves_reflexive: LEMMA
    FORALL java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

       (reflexive?[D](Drel) IFF      Drelisomorphism_preserves_symmetricLEMMA     Drel :

  isomorphism_preserves_irreflexive:
    FORALL Drel , :
??Drel)=
              IMPLIES isomorphism?(, Rrelfjava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42

  isomorphic,) >
    FORALL Drel, Rrel:
      isomorphic(?[]Drel asymmetric?R]Rreljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
mmetric]Rrel

:
    FORALL, Rrel:
      isomorphic?(Drel, ) IFF?[]Rrel
  : LEMMA

  isomorphism_preserves_asymmetric LEMMA      ?DrelRrel>
    FORALLDrelisomorphic  java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
      ?    FORALL Rrel      isomorphicDrelRrel=
?[D()IFFasymmetric]Rrel

  % connected is the same as trichotomous

  isomorphism_preserves_transitive LEMMA
    FORALL,Rrel
            ?Drel) FORALL,Rrel
(?[D() IFF?[R())

   isomorphism_preserves_asymmetricLEMMA
FORALLDrel, Rrel:
      isomorphic?(Drel, Rrel      isomorphic?(Drel ) =>
       dichotomous)IFF dichotomous[](Rrel

  isomorphism_preserves_trichotomousLEMMA
    FORALL Drel, Rrel:
      isomorphic?(Drel, Rrel
           FORALLDrel,Rrelf

  isomorphism_preserves_well_founded LEMMA
   FORALLDrel Rrel
       isomorphicDrel Rrel=
              transitive[]Drel  transitive[R]())

  isomorphism_inverseLEMMA
     Drel Rrel:
i?(Drel, Rrel) =>
       (dichotomousD() IFFdichotomousR](rel

END isomorphism

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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