(* cA_cA_1_B is defined *)
(* COROLLARIES : *)

Lemma cA_cA_1_B_bis : forall (m:fmap)(k:dim)(x z:dart),
inv_hmap m -> ~succ m k x ->
cA (B m k x) k z = cA m k z
/\ cA_1 (B m k x) k z = cA_1 m k z.