proposition: Lemma add_mod_bound p m n : (0 <= [m] < [p] -> 0 <= [n] < [p] -> 0 <= [add_mod p m n] < [p])%Z.
proof: Proof. intros H1 H2; rewrite add_mod_correct; auto. apply Z_mod_lt; auto with zarith. Qed.
imports: List ZArith Znumtheory Uint63 Cyclic63