intuition.
destruct (modNat_correct x p).
rewrite H in H0.
econstructor.
rewrite plus_0_r in H0.
eauto.
Qed.
Local Open Scope nat_scope.

Lemma modNatAddInverse_sum_0 : forall x y p,
modNat (x + (modNatAddInverse y p)) p = O ->
modNat x p = modNat y p.