
theorem
  for X,Y being non empty set, Z being non empty Poset for T being non
empty full SubRelStr of Z|^[:X,Y:] for S being non empty full SubRelStr of (Z|^
  Y)|^X for f being Function of S, T st f is uncurrying one-to-one onto holds f
  is isomorphic
proof
  let X,Y be non empty set, Z be non empty Poset;
  let T be non empty full SubRelStr of Z|^[:X,Y:];
  let S be non empty full SubRelStr of (Z|^Y)|^X;
  let f be Function of S, T;
  assume
A1: f is uncurrying one-to-one onto;
  then
A2: f*f" = id T & f"*f = id S by GRCAT_1:41;
  f is monotone & f" is monotone by A1,Th2,WAYBEL27:20,21;
  hence thesis by A2,YELLOW16:15;
end;
