Definition s0 := (perm (inv_inj S0_inv)).Definition is_iso3 (p : {perm cube}) := forall fi, p (s0 fi) = s0 (p fi).Definition sop (p : {perm cube}) : seq cube := val (val (val p)).

(* Specifications: *)
Lemma sop_inj : injective sop.
Lemma prod_t_correct : forall (x y : {perm cube}) (i : cube), (x * y) i = nth F0 (prod_tuple (sop x) (sop y)) i.
Lemma ecubes_def : ecubes = enum (@predT cube).
Lemma seqs1 : forall f injf, sop (@perm _ f injf) = map f ecubes.
Lemma iso0_1 : dir_iso3 =i dir_iso3l.