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

theorem
  #Z 0 = REAL --> 1
  proof
    reconsider s = 1 as Element of REAL by XREAL_0:def 1;
    #Z 0 = REAL --> s
    proof
      let r be Element of REAL;
      thus ( #Z 0).r = r #Z 0 by TAYLOR_1:def 1
      .= s by PREPOWER:34
      .= (REAL --> s).r;
    end;
    hence thesis;
  end;
