%-------------------------------------------------------------------------
%
% Equivalence classes of automorphisms.
%
% For PVS version 3.2. November 4, 2004
% ---------------------------------------------------------------------
% Author: Jerry James (jamesj@acm.org), University of Kansas
%
% EXPORTS
% -------
% prelude: orders[T], relations[pred[[T, T]]], relations[T]
% orders: isomorphism[T,T], isomorphism_equivalence[T], relations_extra[T]
%
%-------------------------------------------------------------------------
isomorphism_equivalence[T: TYPE ]: THEORY
EXPORTING ALL WITH orders[T], relations[pred[[T, T]]], relations[T],
isomorphism[T, T], relations_extra[T]
BEGIN
IMPORTING function_inverse_def[T, T] % Proofs only
IMPORTING relations[pred[[T, T]]], isomorphism[T, T]
isomorphism_reflexive: THEOREM reflexive?(isomorphic?)
isomorphism_symmetric: THEOREM symmetric?(isomorphic?)
isomorphism_transitive: THEOREM transitive?(isomorphic?)
isomorphism_equivalence: JUDGEMENT
isomorphic? HAS_TYPE equivalence[pred[[T, T]]]
END isomorphism_equivalence
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