(*========================================================== (PRE-)DOUBLE-LINKS AND BREAKING ===========================================================*)
(* BREAKING A PRE-DOUBLE-LINK (x x'): GENERAL *)
Definition Br1(m:fmap)(x x':dart):fmap:=
if succ_dec m zero x
then if succ_dec m zero x'
then B (L (B m zero x)
zero (top m zero x) (bottom m zero x)) zero x'
else B m zero x
else B m zero x'.
(* OK !! *)

(* Specifications: *)
Lemma exd_Br1:forall(m:fmap)(x x' z:dart),
exd m z <-> exd (Br1 m x x') z.
Lemma inv_hmap_Br1:forall(m:fmap)(x x':dart),
inv_hmap m -> inv_hmap (Br1 m x x').
Lemma planar_Br1:forall(m:fmap)(x x':dart),
inv_hmap m -> planar m -> x <> x' ->
planar (Br1 m x x').