(* IDENTITY between A, A_1 on the closure and the closure of A, A_1: *)

Theorem A_clos_eq_cA :
forall (m:fmap)(k:dim)(z:dart),
inv_qhmap m -> exd m z ->
A (clos m) k z = cA m k z
/\ A_1 (clos m) k z = cA_1 m k z.