theorem
  g * A c= (-A) + g + A
proof
  let x be object;
  assume x in g * A;
  then consider a such that
A1: x = g * a and
A2: a in A by ThB42;
  (-a) in (-A) by A2;
  then (-a) + g in (-A) + g by Th28;
  hence thesis by A1,A2;
end;
