
theorem Th2:
  for S being 1-sorted, T being non empty 1-sorted, f being Function of S,T
  for X being Subset of T holds (f"X)` = f"X`
proof
  let S be 1-sorted, T be non empty 1-sorted, f be Function of S,T;
  let X be Subset of T;
  thus (f"X)` = (the carrier of S)\(f"X) by SUBSET_1:def 4
    .= f"(the carrier of T)\(f"X) by FUNCT_2:40
    .= f"((the carrier of T)\X) by FUNCT_1:69
    .= f"X` by SUBSET_1:def 4;
end;
