Notation infE := (sameP afix1P eqP).

Lemma card_n3s : forall x y z t u v: cube, uniq [:: x; y; z; t; u; v] ->
#|[set p : col_cubes | (p x == p y) && (p z == p t)&& (p u == p v )]|
= (n ^ 3)%N.