(*==========================================================  TOPOLOGICAL FMAPS, HMAPS - WITH TAGS AND EMBEDDINGS  PART 6:.  PROPERTIES OF MERGING AND SPLITTING FACES expf / L1  COMPLETE: OK! ============================================================*)
(* Load Jordan1. Load Jordan2. Load Jordan3. Load Jordan4. Load Jordan5. *)
Require Export Jordan5.
(*========================================================== 1. MERGING FACES BY L1 (CASE ~expf m x y0) ===========================================================*)
(* CASE k = one IN cF_L (from Jordan5) : OK *)

Lemma cF_L1:forall(m:fmap)(x y z:dart),
inv_hmap m -> prec_L m one x y ->
let x10 := cF_1 m x in
let y0 := cA m zero y in
let y_1 := cA_1 m one y in
let m1:= L m one x y in
cF m1 z =
if eq_dart_dec y0 z then x
else if eq_dart_dec x10 z then y_1
else cF m z.