(* MORE SIMPLE: *)

(* Specifications: *)
Lemma ring_Br1: forall(m:fmap)(l:list),
inv_hmap m -> planar m ->
let x:= fst (first l) in let x' := snd (first l) in
let m1 := Br1 m x x' in
ring m l -> (emptyl (tail l) \/ ring m1 (tail l)).