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

theorem
  X /\ (X \/ Y) = X
proof
  thus X /\ (X \/ Y) c= X
  by XBOOLE_0:def 4;
  let x be object;
  assume
A1: x in X;
  then x in X \/ Y by XBOOLE_0:def 3;
  hence thesis by A1,XBOOLE_0:def 4;
end;
