(*========================================================== ============================================================ 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.

(* Specifications: *)
Lemma ndZ_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
nd (B m k x) = nd m.
Lemma ndZ_L_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
let m1:= L (B m k x) k x (A m k x) in
nd m1 = nd m.
Lemma ne_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
ne (B m k x) = ne m +
if (eq_dim_dec k zero) then 1 else 0.
Lemma ne_L_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
let m1 := L (B m k x) k x (A m k x) in
ne m1 = ne m.
Lemma nv_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
nv (B m k x) = nv m +
if (eq_dim_dec k one) then 1 else 0.
Lemma nv_L_B:forall (m:fmap)(k:dim)(x:dart),
inv_hmap m -> succ m k x ->
let m1 := L (B m k x) k x (A m k x) in
nv m1 = nv m.