(* ========================================================== PLANARITY CRITERIA (SUFFICIENT CONDITIONS) =============================================================*)

(* Specifications: *)
Lemma planar_dec:forall m:fmap,
{planar m} + {~planar m}.
Lemma planar_V: planar V.
Lemma planar_I: forall (m:fmap)(x:dart)(t:tag)(p:point),
inv_hmap m -> planar m -> prec_I m x ->
planar (I m x t p).
Lemma expf_planar_0: forall (m:fmap)(x y:dart),
inv_hmap m -> planar m ->
prec_L m zero x y ->
expf m (cA_1 m one x) y ->
planar (L m zero x y).