reserve x, y for object, X, X1, X2 for set;
reserve Y, Y1, Y2 for complex-functions-membered set,
  c, c1, c2 for Complex,
  f for PartFunc of X,Y,
  f1 for PartFunc of X1,Y1,
  f2 for PartFunc of X2, Y2,
  g, h, k for complex-valued Function;

theorem
  - (g /" h) = (-g) /" h
proof
A1: dom -(g/"h) = dom(g/"h) by VALUED_1:8;
  dom(g/"h) = dom g /\ dom h & dom((-g)/"h) = dom(-g) /\ dom h by VALUED_1:16;
  hence dom -(g/"h) = dom((-g)/"h) by A1,VALUED_1:8;
  let x be object;
  assume x in dom -(g/"h);
  thus (-(g/"h)).x = -(g/"h).x by VALUED_1:8
    .= -(g.x/h.x) by VALUED_1:17
    .= (-g.x)/h.x
    .= (-g).x/h.x by VALUED_1:8
    .= ((-g)/"h).x by VALUED_1:17;
end;
