
theorem
  for n be Element of NAT for f be onto isometric Function of RLMSpace n,
  RLMSpace n holds rng f = REAL n
proof
  let n be Element of NAT;
  let f be onto isometric Function of RLMSpace n,RLMSpace n;
  thus rng f = the carrier of RLMSpace n by FUNCT_2:def 3
    .= REAL n by Def8;
end;
