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:, R ]:
BEGIN

java.lang.StringIndexOutOfBoundsException: Range [6, 2) out of bounds for length 6

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        isomorphic?(Drel, Rrel) =>
d1 :  D
f  (?[D ]java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
, :d1  (d1))

  isomorphic?(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  isomorphism_implication: LEMMA       irreflexive])  ?R
FORALLjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
trichotomous) AND
  java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
omorphicR >
IMPLIESisomorphism?Drel)()

         ?[])  ?R())
    FORALL Drel: java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
mmetricRrel
:LEMMA Dreljava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22

isomorphism_preserves_irreflexive
:
isomorphic) >
       (irreflexive?[D     Drel(,)=

  isomorphism_preserves_symmetricisomorphism_preserves_trichotomous
    isomorphicDreljava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
             (asymmetricDrel[())


ijava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    FORALL Drel Rrel:
isomorphic(, Rrel     Drel :
       (antisymmetric?[D](Drel)        transitiveD]Drel transitive]Rrel

  isomorphism_preserves_asymmetric
    FORALL Drel,     DrelRrel
,Rrel
       asymmetricD]Drel??D( IFF?[])java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56

Drel,

isomorphism_preserves_transitive:
FORALL  :
     ?(, ) =
(?D()IFF?R]Rrel

  isomorphism_preserves_dichotomous:
FORALL,Rrel
      somorphicRrel=>
(?[]Drel ?[]())

  isomorphism_preserves_trichotomousisomorphism
    FORALL Drel, Rrel:
      isomorphic?(Drel, Rrel) =>
       (trichotomous?[D](Drel) IFF trichotomous?[R](Rrel))

  isomorphism_preserves_well_founded: LEMMA
    FORALL Drel, Rrel:
      isomorphic?(Drel, Rrel) =>
       (well_founded?[D](Drel) IFF well_founded?[R](Rrel))

  isomorphism_inverse: LEMMA
    FORALL Drel, Rrel, f:
      isomorphism?(Drel, Rrel)(f) IFF
       preserves%%  Isomorphisms between ordered sets.  This is different than the

END isomorphism

quality96%

¤ Dauer der Verarbeitung: 0.6 Sekunden ¤

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.