
theorem Th48:
  for P being pcs-Str, X being set holds X in pcs-coherent-power(P)
  implies X is pcs-self-coherent Subset of P
proof
  let P be pcs-Str, X be set;
  assume X in pcs-coherent-power(P);
  then ex Y being Subset of P st X = Y & Y is pcs-self-coherent;
  hence thesis;
end;
