
theorem Th49:
  for L being complete antisymmetric non empty RelStr,
      F be Function holds
    \\/(F, L) = //\(F, L opp) & //\(F, L) = \\/(F, L opp)
proof
  let L be complete antisymmetric non empty RelStr, F be Function;
  thus \\/(F, L) = "\/"(rng F, L) by YELLOW_2:def 5
    .= "/\"(rng F, L opp) by YELLOW_0:17,Th12
    .= //\(F, L opp) by YELLOW_2:def 6;
  thus //\(F,L) = "/\"(rng F, L) by YELLOW_2:def 6
    .= "\/"(rng F, L opp) by YELLOW_0:17,Th13
    .= \\/(F, L opp) by YELLOW_2:def 5;
end;
