(* OK: weak rcp *)

(* Specifications: *)
Lemma expf_planar_rcp_1: forall (m:fmap)(x y:dart),
inv_hmap m -> prec_L m one x y ->
planar (L m one x y) ->
expf m x (cA m zero y) -> planar m.
Theorem weak_planarity_criterion_0: forall (m:fmap)(x y:dart),
inv_hmap m -> prec_L m zero x y ->
expf m (cA_1 m one x) y ->
(planar m <-> planar (L m zero x y)).
Theorem weak_planarity_criterion_1: forall (m:fmap)(x y:dart),
inv_hmap m -> prec_L m one x y ->
expf m x (cA m zero y) ->
(planar m <-> planar (L m one x y)).