
theorem Th25:
  for P being pcs-Str, a being set,
  p being Element of pcs-extension(P,a) st p <> a holds p in the carrier of P
proof
  let P be pcs-Str, a be set, p be Element of pcs-extension(P,a) such that
A1: p <> a;
  the carrier of pcs-extension(P,a) = {a} \/ the carrier of P by Def39;
  then p in {a} or p in the carrier of P by XBOOLE_0:def 3;
  hence thesis by A1,TARSKI:def 1;
end;
