%------------------------------------------------------------------------------
% 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