induction m.
simpl in |- *.
tauto.
simpl in |- *.
intros.
generalize (IHm k x z).
tauto.
simpl in |- *.
intros k x z.
elim (eq_dim_dec d k).
elim (eq_dart_dec d1 x).
generalize (IHm k x z).
tauto.
simpl in |- *.
generalize (IHm k x z).
tauto.
simpl in |- *.
intro.
apply IHm.
Qed.

Lemma not_succ_B:forall(m:fmap)(k:dim)(z:dart),
inv_hmap m -> ~succ m k z -> B m k z = m.