theorem Th64: INTERSECTION(X,Y) is_finer_than X
proof
now
let xy be set;assume xy in INTERSECTION(X,Y);then consider x,y such that
A1: x in X & y in Y & xy=x/\y by SETFAM_1:def 5;
take x; thus x in X & xy c= x by A1;
end;
hence thesis by SETFAM_1:def 2;
end;
