reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem
  name-r x, name-y x, name-ord x name_like x
proof
  name-ord x = dom name-r x by Th105;
  then
A2: name-r x, name-y x, name-ord x name_like Sum(name-r x, name-y x)
   by Def23,Th101;
 Sum(name-r x,name-y x)==x by Def23;
  hence thesis by A2,Th103;
end;
