
theorem Th35:
  for P being non empty pcs-Str, p, q being Element of P
  for p9, q9 being Element of pcs-reverse(P) st p = p9 & q = q9 holds
  not p9 (--) q9 implies p (--) q
proof
  let P be non empty pcs-Str, p, q be Element of P;
  set R = pcs-reverse(P);
  let p9, q9 be Element of R such that
A1: p = p9 and
A2: q = q9;
A3: the ToleranceRel of R = (the ToleranceRel of P)` by Def40;
  assume
A4: not [p9,q9] in the ToleranceRel of R;
  [p,q] in [:the carrier of P,the carrier of P:] by ZFMISC_1:87;
  hence [p,q] in the ToleranceRel of P by A1,A2,A3,A4,XBOOLE_0:def 5;
end;
