
theorem Th23:
  for S being non empty RelStr for T being non empty reflexive
antisymmetric RelStr for f,g being Element of UPS(S, T) holds f <= g iff for s
  being Element of S holds f.s <= g.s
proof
  let S be non empty RelStr;
  let T be non empty reflexive antisymmetric RelStr;
  let f,g be Element of UPS(S, T);
A1: UPS(S, T) is full SubRelStr of T|^the carrier of S by Def4;
  then reconsider a = f, b = g as Element of T|^the carrier of S by YELLOW_0:58
;
A2: f <= g iff a <= b by A1,YELLOW_0:59,60;
  hence f <= g implies for s being Element of S holds f.s <= g.s by Th14;
  assume for s being Element of S holds f.s <= g.s;
  hence thesis by A2,Th14;
end;
