
theorem Th5:
  for A,B being finite set st card A < card B ex x being set st x in B \ A
proof
  let A,B be finite set;
  assume card A < card B;
  then not B c= A by NAT_1:43;
  then consider x being object such that
A1: x in B and
A2: x nin A;
  take x;
  thus thesis by A1,A2,XBOOLE_0:def 5;
end;
