unfold modNat.
intuition.
rewrite Nnat.Nat2N.inj_add.
rewrite <- N.add_mod_idemp_l.
f_equal.
rewrite <- (Nnat.Nat2N.id n2) at 2.
rewrite Nnat.Nat2N.inj_add.
repeat rewrite Nnat.N2Nat.id.
trivial.
destruct p.
simpl.
destruct x;
simpl.
omega.
apply Npos_nz.
Qed.

Lemma modNat_arg_eq : forall (p : posnat),
modNat p p = O.