reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X c= Y \/ Z implies X \ Y c= Z
proof
  assume
A1: X c= Y \/ Z;
  let x be object;
  assume
A2: x in X \ Y;
  then x in X by XBOOLE_0:def 5;
  then
A3: x in Y \/ Z by A1;
  not x in Y by A2,XBOOLE_0:def 5;
  hence thesis by A3,XBOOLE_0:def 3;
end;
