(* COROLLARIES: *)

(* Specifications: *)
Lemma cA_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.
Lemma cA_1_B_bis : forall (m:fmap)(k:dim)(x z:dart),
inv_hmap m -> ~succ m k x ->
cA_1 (B m k x) k z = cA_1 m k z.
Lemma cA_cA_1_B_ter : forall (m:fmap)(k j:dim)(x z:dart),
inv_hmap m -> k <> j ->
cA (B m k x) j z = cA m j z
/\ cA_1 (B m k x) j z = cA_1 m j z.