theorem Th19:
  dom f c= dom g implies f +* g = g
proof
  assume dom f c= dom g;
  then dom f \/ dom g = dom g by XBOOLE_1:12;
  then dom(f +* g) = dom g &
   for x being object st x in dom g holds (f +* g).x = g.x by Def1;
  hence thesis;
end;
