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%------------------------------------------------------------------------------
% Topology
%
% All references are to WA Sutherland "Introduction to Metric and
% Topological Spaces", OUP, 1981
%
% Author: David Lester, Manchester University, NIA, Université Perpignan
%
% Version 1.0 8/10/04 Initial Version
% Version 1.1 9/06/06 Interface change, added type judgement
%------------------------------------------------------------------------------
identity_continuity[T:TYPE, (IMPORTING topology_def[T]) S:topology]: THEORY
BEGIN
IMPORTING continuity[T,S,T,S]
x: VAR T
id_continuous_at: LEMMA continuous_at?(I[T],x)
id_continuous : LEMMA continuous?(I[T])
I_is_continuous : JUDGEMENT I[T] HAS_TYPE continuous
END identity_continuity
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