intros d; elim d; simpl in |- *; auto.
intros n H' a b c.
rewrite (H' (pmon2 (S n) a) (pmon2 (S n) b) (pmon2 (S n) c)); auto.
rewrite (plus_assoc (pmon1 (S n) a) (pmon1 (S n) b) (pmon1 (S n) c)); auto.
Qed.
(* Zero *)
Definition zero_mon : forall d : nat, mon d.
intros d; elim d.
exact n_0.
intros n Rec; exact (c_n n 0 Rec).
Defined.

Theorem mult_mon_zero_r :
forall (d : nat) (a : mon d), mult_mon d a (zero_mon d) = a.