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;
reserve A,B for set;

theorem
  for f,g,h being Function st dom g = dom h holds f +* g +* h = f +* h
proof
  let f,g,h be Function;
  assume
A1: dom g = dom h;
  thus f +* g +* h = f +* (g +* h) by Th14
    .= f +* h by A1,Th19;
end;
