
theorem Th22:
  for S being non empty RelStr for T being non empty reflexive
antisymmetric RelStr holds the carrier of UPS(S, T) c= Funcs(the carrier of S,
  the carrier of T)
proof
  let S be non empty RelStr;
  let T be non empty reflexive antisymmetric RelStr;
  UPS(S, T) is SubRelStr of T|^the carrier of S by Def4;
  then the carrier of UPS(S, T) c= the carrier of T|^the carrier of S by
YELLOW_0:def 13;
  hence thesis by YELLOW_1:28;
end;
