reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem
  A c= X & B c= Y implies [:A,Y:] /\ [:X,B:] = [:A,B:]
proof
  assume that
A1: A c= X and
A2: B c= Y;
A3: [:A,Y:] /\ [:X,B:] = [:A /\ X, Y /\ B:] by Th99;
  A /\ X = A by A1,XBOOLE_1:28;
  hence thesis by A2,A3,XBOOLE_1:28;
end;
