Remark permutation_norepet:
forall (A: Type) (l l': list A), Permutation l l' -> list_norepet l -> list_norepet l'.

Lemma assign_variables_domain:
forall id vars cesz,
(fst (assign_variables cesz vars))!id <> None ->
(fst cesz)!id <> None \/ In id (map fst vars).