(* NEW, OK: *)

(* Specifications: *)
Lemma not_expf_Br1:forall (m:fmap)(x x' z t:dart),
inv_hmap m -> planar m -> double_link m x x' ->
let y  := cA m zero x in
let y' := cA m zero x' in
(~expf m y z /\ ~expf m y' z
\/ ~expf m y t /\ ~expf m y' t) ->
~expf m z t -> ~expf (Br1 m x x') z t.
Lemma distinct_faces_Br1:
forall(m:fmap)(x x' xs xs' z z' zs zs':dart)(l:list),
inv_hmap m -> planar m ->
let l1:= cons x x' (cons xs xs' (cons z z'
(cons zs zs' l))) in
double_link_list m l1 ->
pre_ring0 m l1 ->
pre_ring3 m l1 ->
face_adjacent m x x' xs xs' ->
distinct_faces (Br1 m x x') z z' zs zs'.
Lemma pre_ring3_Br1_aux_bis:
forall(m:fmap)(x x' xs xs':dart)(l:list),
inv_hmap m -> planar m ->
let l1 := cons x x' (cons xs xs' l) in
double_link_list m l1 ->
pre_ring0 m l1 ->
pre_ring1 m l1 ->
pre_ring3 m l1 ->
pre_ring3 (Br1 m x x') (cons xs xs' l).