(*========================================================== ============================================================ 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? *)
(*========================================================= cF / L, expf / L, CNS ===========================================================*)
(* expf IS AN EQUIVALENCE (NEW PLACE): *)
(* OK!: *)
(* OK: *)
(* OK: *)
(* OK: *)
(* RENAMING of MF.between: *)
Definition betweenf:= MF.between.

Lemma cF_L0_1:forall (m:fmap)(x y z:dart),
inv_hmap (L m zero x y) ->
let x_1 := cA_1 m one x in
betweenf m x_1 z y ->
cF (L m zero x y) z =
if eq_dart_dec y z then x_1 else cF m z.