
theorem lemfinset:
for X1,X2 being finite set st X1 c= X2 & card X1 = card X2 holds X1 = X2
proof
let X1,X2 be finite set;
assume AS: X1 c= X2 & card X1 = card X2;
then card (X2 \ X1) = card X2 - card X1 by CARD_2:44 .= 0 by AS;
then X2 \ X1 = {};
then X2 c= X1 by XBOOLE_1:37;
hence thesis by AS,XBOOLE_0:def 10;
end;
