(* pre_ring1_Br1 is defined *)
(*============================================================ NEW pre_ring2 PROPERTIES : OK =============================================================*)
(* NEW, OK: VERY USEFUL *)

Lemma expf_Br1_link:forall (m : fmap) (x x': dart),
inv_hmap m -> planar m -> double_link m x x' ->
let y :=cA m zero x in
let y':=cA m zero x' in
~expf m y y' -> expf (Br1 m x x') y y'.