(* IDEM, SYMMETRIC: *)

(* Specifications: *)
Lemma cA_1_L_B_top_bot:forall(m:fmap)(k:dim)(x z:dart),
inv_hmap m -> succ m k x ->
cA_1 (L (B m k x) k (top m k x) (bottom m k x)) k z =
cA_1 m k z.
Lemma cA_1_L_B_top_bot_ter:forall(m:fmap)(k:dim)(x z:dart),
inv_hmap m -> succ m k x ->
let k1 := dim_opp k in
cA_1 (L (B m k x) k (top m k x) (bottom m k x)) k1 z =
cA_1 m k1 z.
Lemma A_1_L_B_top_bot:forall(m:fmap)(k:dim)(x z:dart),
inv_hmap m -> succ m k x ->
A_1 (L (B m k x) k (top m k x) (bottom m k x)) k z =
if eq_dart_dec (A m k x) z then nil
else if eq_dart_dec (bottom m k x) z then (top m k x)
else A_1 m k z.
Lemma A_1_L_B_top_bot_ter:forall(m:fmap)(k:dim)(x z:dart),
inv_hmap m -> succ m k x -> let k1:=dim_opp k in
A_1 (L (B m k x) k (top m k x) (bottom m k x)) k1 z =
A_1 m k1 z.