theorem Th11:
  - (g - c) = -g + c
proof
A1: dom -(g-c) = dom(g-c) by VALUED_1:8;
A2: dom(g-c) = dom g & dom(-g+c) = dom -g by VALUED_1:def 2;
  hence dom -(g-c) = dom(-g+c) by A1,VALUED_1:8;
  let x be object;
  assume
A3: x in dom -(g-c);
A4: dom -g = dom g by VALUED_1:8;
  thus (-(g-c)).x = -(g-c).x by VALUED_1:8
    .= -(g.x-c) by A1,A3,VALUED_1:def 2
    .= -g.x+c
    .= (-g).x+c by VALUED_1:8
    .= (-g+c).x by A2,A1,A4,A3,VALUED_1:def 2;
end;
