generalize h; clear h.
elim m.
intros h; elim h; auto.
intros; simpl in |- *; unfold recomp in |- *; auto.
Qed.

Lemma proj_ok :
forall (d : nat) (m : mon (S d)), c_n d (pmon1 (S d) m) (pmon2 (S d) m) = m.