
theorem Th21:
  for P being pcs-Str, a being set holds
  the carrier of P c= the carrier of pcs-extension(P,a) &
  the InternalRel of P c= the InternalRel of pcs-extension(P,a) &
  the ToleranceRel of P c= the ToleranceRel of pcs-extension(P,a)
proof
  let P be pcs-Str, a be set;
  set R = pcs-extension(P,a);
A1: the carrier of R = {a} \/ the carrier of P by Def39;
A2: the InternalRel of R = [:{a},the carrier of R:] \/ the InternalRel of P
  by Def39;
  the ToleranceRel of R = [:{a},the carrier of R:] \/ [:the carrier of R,{
  a}:] \/ the ToleranceRel of P by Def39;
  hence thesis by A1,A2,XBOOLE_1:7;
end;
