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;
