
theorem Th42:
  for X being non empty set, S,T being non empty Poset holds UPS(S
  , T|^X), UPS(S, T)|^X are_isomorphic
proof
  let X be non empty set, S, T be non empty Poset;
  consider F being Function of UPS(S, T|^X), UPS(S, T)|^X such that
A1: F is commuting isomorphic by Th41;
  take F;
  thus thesis by A1;
end;
