intros.
unfold cast_seq, cast_fin in |- *.
destruct v.
simpl in |- *.
destruct i.
apply Map_compatible_prf; auto with algebra.
Qed.

Lemma cast_seq_cast_fin' :
forall (i : fin n') (H : n =' n' in _) (H' : n' =' n in _),
cast_seq v H i =' v (cast_fin i H') in _.