(* OK: USEFULL?  Lemma cA_cA_1_L_B_top_bot:forall(m:fmap)(k:dim)(x:dart), inv_hmap m -> succ m k x -> (forall z:dart, exd m z -> cA (L (B m k x) k (top m k x) (bottom m k x)) k z = cA m k z) -> (forall z:dart, exd m z -> cA_1 (L (B m k x) k (top m k x) (bottom m k x)) k z = cA_1 m k z). *)

Lemma inv_hmap_L_B_top_bot:forall(m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
inv_hmap (L (B m k x) k (top m k x) (bottom m k x)).