
theorem
  for P being pcs-Str, D being non empty Subset-Family of P
  for p, q being Element of pcs-general-power(D) st
  for p9, q9 being Element of P st p9 in p & q9 in q holds p9 (--) q9
  holds p (--) q
proof
  let P be pcs-Str, D be non empty Subset-Family of P;
  set R = pcs-general-power(D);
  let p, q be Element of R;
  assume
A1: for p9, q9 being Element of P st p9 in p & q9 in q holds p9 (--) q9;
A2: p in D;
A3: q in D;
   for a,b being set st a in p & b in q
    holds [a,b] in the ToleranceRel of P by A1,A2,A3,Def7;
  hence [p,q] in the ToleranceRel of R by Def46;
end;
