proposition: Lemma to_ring_involutive Z `{Integers Z} Z2 `{Integers Z2} x : integers_to_ring Z2 Z (integers_to_ring Z Z2 x) = x.
proof: Proof. change (Compose (integers_to_ring Z2 Z) (integers_to_ring Z Z2) x = id x). apply to_ring_unique_alt;apply _. Qed.
imports: HoTT.Basics.Decidable HoTT.Classes.theory.nat_distance HoTT.Classes.implementations.peano_naturals HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.orders HoTT.Classes.implementations.natpair_integers HoTT.Classes.theory.rings HoTT.Classes.isomorphisms.rings HoTT.Classes.interfaces.integers