intros.
inversion_clear H.
rename x into beta.
inversion_clear H0.
inversion_clear H.
rename x into n.
exists n.
red in |- *.
exists beta; auto.
red in |- *.
exists x0; auto.
Qed.

Lemma has_dim_inj :
forall (F : field) (V : vectorspace F) (n m : Nat),
has_dim n V -> has_dim m V -> n =' m in _.