Definition rightI (d:nat)(x:TypeI) : nat :=
 match x with
 | I _ n => n
 | E _ => d
 end.

Lemma conv_correct : forall (e : BCI) (vnl vsl : list bs) n s n' s', n' <= n -> s' <= s -> inf e = I n' s' -> sem (conv n s e) vnl vsl = semI e vnl vsl.