(*========================================================== eqc_B : eqc on B, L_B ===========================================================*)
(* RECALL: eqc = fix eqc (m : fmap) (x y : dart) {struct m} : Prop := match m with | V => False | I m0 x0 => x = x0 /\ y = x0 \/ eqc m0 x y | L m0 _ x0 y0 => eqc m0 x y \/ eqc m0 x x0 /\ eqc m0 y0 y \/ eqc m0 x y0 /\ eqc m0 x0 y end *)
(* OK: LONG... *)

Lemma eqc_B_CN: forall(m:fmap)(k:dim)(x z t:dart),
inv_hmap m -> succ m k x ->
let xk:= A m k x in
let m0:= B m k x in
eqc m z t ->
(eqc m0 z t \/
eqc m0 z x /\ eqc m0 xk t \/
eqc m0 z xk /\ eqc m0 x t).