(* FINALLY: FULL PLANARITY CRITERION: *)

(* Specifications: *)
Theorem planarity_criterion_0: forall (m:fmap)(x y:dart),
inv_hmap m -> prec_L m zero x y -> planar m ->
(planar (L m zero x y) <->
(~ eqc m x y \/ expf m (cA_1 m one x) y)).
Theorem planarity_criterion_1: forall (m:fmap)(x y:dart),
inv_hmap m -> prec_L m one x y -> planar m ->
(planar (L m one x y) <->
(~ eqc m x y \/ expf m x (cA m zero y))).