(* NEW, OK!! WITH THE LEMMA ABOVE: *)

Lemma distinct_face_list_Br1_aux_bis:
forall(m:fmap)(x x' xs xs' xf xf':dart)(l:list),
inv_hmap m -> planar m ->
let l1 := cons x x' (cons xs xs' (cons xf xf' l)) in
double_link_list m l1 ->
pre_ring0 m l1 ->
face_adjacent m x x' xs xs' ->
pre_ring3 m l1 ->
distinct_face_list (Br1 m x x') xf xf' l.