
theorem Th33:
  for P being pcs-Str, p, q being Element of P
  for p9, q9 being Element of pcs-reverse(P) st p = p9 & q = q9 holds
  p <= q iff q9 <= p9
proof
  let P be 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 InternalRel of R = (the InternalRel of P)~ by Def40;
  thus p <= q implies q9 <= p9
  by A1,A2,A3,RELAT_1:def 7;
  assume [q9,p9] in the InternalRel of R;
  hence [p,q] in the InternalRel of P by A1,A2,A3,RELAT_1:def 7;
end;
