
theorem Th28:
  for P being pcs-Str, a being set, p, q being Element of P,
  p1, q1 being Element of pcs-extension(P,a) st p = p1 & q = q1 &
  p (--) q holds p1 (--) q1
proof
  let P be pcs-Str, a be set, p, q be Element of P,
  p1, q1 be Element of pcs-extension(P,a) such that
A1: p = p1 and
A2: q = q1 and
A3: [p,q] in the ToleranceRel of P;
  the ToleranceRel of P c= the ToleranceRel of pcs-extension(P,a) by Th21;
  hence [p1,q1] in the ToleranceRel of pcs-extension(P,a) by A1,A2,A3;
end;
