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

(* Specifications: *)
Lemma exd_B_1_r : forall (m:fmap)(k:dim)(x y:dart),
exd m y -> exd (B_1 m k x) y.
Lemma exd_B_1_l : forall (m:fmap)(k:dim)(x y:dart),
exd (B_1 m k x) y ->  exd m y.