reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;

theorem
  (id REAL)`| = REAL --> 1
  proof
    set f = id REAL;
    reconsider z = 1 as Element of REAL by XREAL_0:def 1;
    f`| = REAL --> z
    proof
      let r be Element of REAL;
      f|REAL = f;
      hence f`|.r = z by Lm1,FDIFF_1:17
      .= (REAL --> z).r;
    end;
    hence thesis;
  end;
