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 Th25:
  g c= f +* g
proof
  dom(f +* g) = dom f \/ dom g by Def1;
  then
A1: dom g c= dom(f +* g) by XBOOLE_1:7;
  for x being object st x in dom g holds (f+*g).x = g.x by Th13;
  hence thesis by A1,GRFUNC_1:2;
end;
