(* IDEM: *)

(* Specifications: *)
Lemma B_1_not_exd : forall (m:fmap)(k:dim)(x:dart),
inv_qhmap m -> ~ exd m x -> B_1 m k x = m.
Lemma B_1_nil : forall (m:fmap)(k:dim),
inv_qhmap m -> B_1 m k nil = m.