(*=========================================================== cF, expf on L and B ============================================================*)
(* OK, TRIVIAL: USEFUL? *)

(* Specifications: *)
Lemma nf_L_B_aux :forall(m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
let y := A m k x in
let m0 := B m k x in
let m1 := L m0 k x (A m k x) in
nf m1 =
match k with
| zero =>
let x_1 := cA_1 m0 one x in
nf m0 +
(if expf_dec m0 x_1 y then 1 else -1)
| one =>
let y0 := cA m0 zero y in
nf m0 +
(if expf_dec m0 x y0 then 1 else -1)
end.
Lemma cA_I:forall(m:fmap)(k:dim)(x z:dart)(u:tag)(p:point),
inv_hmap m -> prec_I m x -> x <> z ->
(cA (I m x u p) k z = cA m k z).
Lemma cA_1_I:forall(m:fmap)(k:dim)(x z:dart)(u:tag)(p:point),
inv_hmap m -> prec_I m x -> x <> z ->
(cA_1 (I m x u p) k z = cA_1 m k z).