
theorem
  for P, Q being non empty pcs-Str, p, q being Element of P --> Q
  for p1, p2 being Element of P, q1, q2 being Element of Q st
  p = [p1,q1] & q = [p2,q2] holds not p1 (--) p2 or q1 (--) q2 implies p (--) q
proof
  let P, Q be non empty pcs-Str, p, q be Element of P --> Q;
  let p1, p2 be Element of P, q1, q2 be Element of Q such that
A1: p = [p1,q1] and
A2: q = [p2,q2];
  reconsider r1 = p1, r2 = p2 as Element of pcs-reverse P by Def40;
  reconsider w1 = [r1,q1], w2 = [r2,q2] as
  Element of (pcs-reverse P) pcs-times Q by A1,A2;
  assume not p1 (--) p2 or q1 (--) q2;
  then r1 (--) r2 or q1 (--) q2 by Th35;
  then w1 (--) w2 by Th38;
  hence thesis by A1,A2;
end;
