
theorem thre1:
for X,Y being set st card X c= card Y
ex Z being set st Z c= Y & card Z = card X
proof
let X,Y be set;
assume card X c= card Y; then
consider f being Function such that
A: f is one-to-one & dom f = X & rng f c= Y by CARD_1:10;
take Z = rng f;
thus thesis by A,CARD_1:70;
end;
