(* DEFINITION OF eqco WHICH ALLOWS TO PUT AHEAD 
ANY 0-LINK: *)

Definition eqco(m:fmap)(k:dim)(x z t:dart):=
  eqc (L (B m k x) k x (A m k x)) z t.

(* Specifications: *)
Lemma eqco_eqc:forall(m:fmap)(k:dim)(x z t:dart), inv_hmap m -> succ m k x -> (eqco m k x z t <-> eqc m z t).
Lemma eqc_B_eqc :forall(m:fmap)(k:dim)(x z t:dart), inv_hmap m -> succ m k x -> eqc (B m k x) z t -> eqc m z t.
Lemma eqc_eqc_B : forall(m:fmap)(k:dim)(x z t:dart), inv_hmap m -> succ m k x -> eqc (B m k x) x (A m k x) -> eqc m z t -> eqc (B m k x) z t.