Module Int63ring := CyclicRing Int63Cyclic.
(** Unlike in the generic [CyclicRing], we can use Leibniz here. *)
Proof to_Z_inj.

Lemma ring_theory_switch_eq :
forall A (R R':A->A->Prop) zero one add mul sub opp,
(forall x y : A, R x y -> R' x y) ->
ring_theory zero one add mul sub opp R ->
ring_theory zero one add mul sub opp R'.