(* IDEM, FOR nf_L0L1 : *)

(* Specifications: *)
Lemma inv_hmap_L0L1:forall (m:fmap)(x y x' y':dart),
let m1:= L (L m zero x y) one x' y' in
let m2:= L (L m one x' y') zero x y in
inv_hmap m1 -> inv_hmap m2.
Lemma betweenf_expf:forall(m:fmap)(z v t:dart),
inv_hmap m -> exd m z ->
betweenf m z v t -> (expf m z v /\ expf m z t).
Lemma B0_L0_L0:forall (m:fmap)(x y x' y':dart),
let m1 := L (L m zero x y) zero x' y' in
inv_hmap m1 -> B m1 zero x = L m zero x' y'.
Lemma B0_L1_L0:forall (m:fmap)(x y x' y':dart),
let m1 := L (L m zero x y) one x' y' in
inv_hmap m1 -> B m1 zero x = L m one x' y'.
Lemma B1_L0_L1:forall (m:fmap)(x y x' y':dart),
let m1 := L (L m one x y) zero x' y' in
inv_hmap m1 -> B m1 one x = L m zero x' y'.