
theorem
  for S1, S2 being non empty TolStr, x, y being Element of [^S1,S2^] holds
  x (--) y iff x^`1 (--) y^`1 or x^`2 (--) y^`2
proof
  let S1, S2 be non empty TolStr, x, y be Element of [^S1,S2^];
A1: ex a, b being object st a in the carrier of S1 & b in the carrier of S2 &
  x = [a,b] by ZFMISC_1:def 2;
A2: ex c, d being object st c in the carrier of S1 & d in the carrier of S2 &
  y = [c,d] by ZFMISC_1:def 2;
A3: x = [x^`1,x^`2] by A1;
  y = [y^`1,y^`2] by A2;
  hence thesis by A3,Th6;
end;
