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Datei: sum_orders.pvs Sprache: PVS

Original von: PVS^©

%------------------------------------------------------------------------------
% Pointwise Ordering in Disjoint Union types
%
%       Author: David Lester <[email protected]> Manchester University
%
%       Version 1.0          03/30/06
%------------------------------------------------------------------------------

sum_orders[T1,T2:TYPE]: THEORY

BEGIN

  r1:  VAR pred[[T1,T1]]
  r2:  VAR pred[[T2,T2]]
  x,y: VAR union[T1,T2]

  ; % syntax

  +(r1,r2)(x,y):bool = (inl?(x) AND inl?(y) AND r1(left(x), left(y))) OR
                       (inr?(x) AND inr?(y) AND r2(right(x),right(y)))

  sum_preserves_reflexive: JUDGEMENT
   +(r1:(reflexive?[T1]),r2:(reflexive?[T2]))
                                           HAS_TYPE (reflexive?[union[T1,T2]])

  sum_preserves_transitive: JUDGEMENT
   +(r1:(transitive?[T1]),r2:(transitive?[T2]))
                                           HAS_TYPE (transitive?[union[T1,T2]])

  sum_preserves_antisymmetric: JUDGEMENT
   +(r1:(antisymmetric?[T1]),r2:(antisymmetric?[T2]))
                                        HAS_TYPE (antisymmetric?[union[T1,T2]])

  sum_preserves_preorder: JUDGEMENT
   +(r1:(preorder?[T1]),r2:(preorder?[T2]))
                           HAS_TYPE (preorder?[union[T1,T2]])

  sum_preserves_partial_order: JUDGEMENT
   +(r1:(partial_order?[T1]),r2:(partial_order?[T2]))
                                        HAS_TYPE (partial_order?[union[T1,T2]])

  IMPORTING directed_orders[T1], directed_orders[T2],
            directed_orders[union[T1,T2]]

  sum_preserves_directed_complete: JUDGEMENT
   +(r1:(directed_complete?[T1]),r2:(directed_complete?[T2]))
                   HAS_TYPE (directed_complete?[union[T1,T2]])

  sum_preserves_directed_complete_partial_order: JUDGEMENT
   +(r1:(directed_complete_partial_order?[T1]),
     r2:(directed_complete_partial_order?[T2]))
                   HAS_TYPE (directed_complete_partial_order?[union[T1,T2]])

END sum_orders

¤ Dauer der Verarbeitung: 0.12 Sekunden (vorverarbeitet) ¤

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