(* PLANARITY CRITERION / B0: OK! *)

Theorem planarity_crit_B0: forall (m:fmap)(x:dart),
inv_hmap m -> succ m zero x ->
let m0 := B m zero x in
let y := A m zero x  in
(planar m <->
(planar m0 /\ (~eqc m0 x y \/ expf m0 (cA_1 m0 one x) y))).