(*========================================================== ============================================================ TOPOLOGICAL FMAPS, HMAPS -  WITH TAGS AND EMBEDDINGS  PART 5:  characteristics, eqc, expf / L0, L_B  COMPLETE FOR DIM 0 (DIM 1 IN THE NEXT FILE): OK! ============================================================ ==========================================================*)
Require Export Jordan4.
(* OK: *)
(* OK: *)
(* LEMMA, USEFUL: *)
(*=========================================================== cF, expf on L and B ============================================================*)
(* OK, TRIVIAL: USEFUL? *)

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.