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%------------------------------------------------------------------------------
% Integral domains
%
% Author: David Lester, Manchester University & NIA
% Rick Butler
%
% Version 1.0 3/1/02
% Version 1.1 12/3/03 New library structure
% Version 1.2 5/5/04 Reworked for definition files DRL
%------------------------------------------------------------------------------
integral_domain[T:Type+,+,*:[T,T->T],zero:T]: THEORY
BEGIN
ASSUMING IMPORTING integral_domain_def[T,+,*,zero]
fullset_is_integral_domain: ASSUMPTION integral_domain?(fullset[T])
ENDASSUMING
IMPORTING ring_def[T,+,*,zero],
integral_domain_def[T,+,*,zero],
commutative_ring[T,+,*,zero]
integral_domain: NONEMPTY_TYPE = (integral_domain?) CONTAINING fullset[T]
I: VAR integral_domain
integral_domain_is: LEMMA integral_domain?(I)
integral_domain_is_ring: JUDGEMENT integral_domain SUBTYPE_OF
commutative_ring
END integral_domain
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