proposition: Lemma to_ring_twice `{Integers Z} `{IsRing R1} `{IsRing R2} (f : R1 -> R2) (g : Z -> R1) (h : Z -> R2) `{!IsSemiRingPreserving f} `{!IsSemiRingPreserving g} `{!IsSemiRingPreserving h} x : f (g x) = h x.
proof: Proof. exact (to_ring_unique_alt (f ∘ g) h _). 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