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 Th37:
  for f,g being Function of X,Y holds f +* g = g
proof
  let f,g be Function of X,Y;
  per cases;
  suppose Y = {} implies X = {};
    then dom f = X & dom g = X by FUNCT_2:def 1;
    hence thesis by Th19;
  end;
  suppose Y = {} & X <> {};
    then f = {} & g = {};
    hence thesis;
  end;
end;
