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 Th36:
  o in Day(No_Ord A,B) & B c= A implies o in Day B
proof
  assume A1:o in Day(No_Ord A,B) & B c= A;
  then No_Ord A /\ [:BeforeGames B,BeforeGames B:] =
  No_Ord B /\ [:BeforeGames B,BeforeGames B:] by Th31;
  hence thesis by A1,Th10;
end;
