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 Th35:
  A c= B implies Day A c= Day B
proof
  assume A1:A c= B;
  set R=No_Ord A, S= No_Ord B;
  R /\ [:BeforeGames A,BeforeGames A:] =
  S /\ [:BeforeGames A,BeforeGames A:] by A1,Th31;
  then Day(R,A) = Day(S,A) by Th10;
  hence thesis by A1,Th9;
end;
