let A, B be Ordinal; ( A c= B implies ClosedProd ((No_Ord A),A,A) = ClosedProd ((No_Ord B),A,A) )
assume
A c= B
; ClosedProd ((No_Ord A),A,A) = ClosedProd ((No_Ord B),A,A)
then
(No_Ord A) /\ [:(BeforeGames A),(BeforeGames A):] = (No_Ord B) /\ [:(BeforeGames A),(BeforeGames A):]
by Th31;
hence
ClosedProd ((No_Ord A),A,A) = ClosedProd ((No_Ord B),A,A)
by Th15; verum