reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

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;
