
theorem
  for P being pcs-Str, a being set,
  p, q being Element of pcs-extension(P,a) st p = a holds p <= q
proof
  let P be pcs-Str, a be set;
  set R = pcs-extension(P,a);
  let p, q be Element of R such that
A1: p = a;
A2: the InternalRel of R =
  [:{a},the carrier of R:] \/ the InternalRel of P by Def39;
  [a,q] in [:{a},the carrier of R:] by ZFMISC_1:105;
  hence [p,q] in the InternalRel of R by A1,A2,XBOOLE_0:def 3;
end;
