reserve A,A1,A2,B,B1,B2,C,O for Ordinal,
      R,S for Relation,
      a,b,c,o,l,r for object;
reserve x,y,z,t,r,l for Surreal,
        X,Y,Z for set;

theorem Th32:
  A c= B implies
    ClosedProd(No_Ord A,A,A) = ClosedProd(No_Ord B,A,A)
proof
  assume A c= B;
  then No_Ord A /\ [:BeforeGames A,BeforeGames A:] =
  No_Ord B /\ [:BeforeGames A,BeforeGames A:] by Th31;
  hence thesis by Th15;
end;
