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

theorem Th1:
  0 + f = f
  proof
    thus dom(0+f) = dom f by VALUED_1:def 2;
    let x be object;
    assume x in dom (0+f);
    hence (0+f).x = 0+f.x by VALUED_1:def 2
    .= f.x;
  end;
