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%%%%%%%%%%%%%%%%%%%%%%  The {log} library  %%%%%%%%%%%%%%%%%%%%
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%
%                   Oct. 1996 - by Gianfranco Rossi
%
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less(R,X,S) :-                  % S = R\{X}
        R = {X/S} & X nin S.

subset(S1,S2) :-                % subset
    forall(X in S1,X in S2).
	  
size(S,N) :- in_size(S,0,N).    % cardinality
in_size('{}',N,N).
in_size(S,N,M) :-
	    N neq M &
		less(S,_,SS) & 
	    NN is N + 1 &
	    in_size(SS,NN,M).    

union('{}',X,X).                % union
union(R,S,{A/U}) :-
        less(R,A,RR) &
	    union(RR,S,U).

int('{}',_,'{}').               % intersection
int(R,S,{X/U}) :-
	    less(R,X,RR) &
        X in S &
	    int(RR,S,U).
int(R,S,U) :-
	    less(R,X,RR) &
        X nin S &
	    int(RR,S,U).
	   
diff('{}',_,'{}').              % difference
diff(R,S,U) :-
	    less(R,X,RR) &
        X in S &
	    diff(RR,S,U).
diff(R,S,{X/U}) :-
	    less(R,X,RR) &
        X nin S &
	    diff(RR,S,U).
		

powerset(S,PS) :-               % powerset
        PS = {SS : subset(SS,S)}.