proposition: Theorem mul_two_iso : forall a, a * two ≅ a + a.
proof: Proof. intros. exists (fun (p : a * bool) => if snd p then inl (fst p) else inr (fst p)). exists (fun p => match p with | inl x => (x, true) | inr x => (x, false) end). extensionalize. Qed.
imports: Hask.Ltac Hask.Prelude Hask.Control.Applicative Hask.Control.Monad Hask.Control.Monad.Cont Hask.Control.Monad.State Hask.Data.Functor.Contravariant Hask.Data.Functor.Identity Hask.Data.Functor.Kan Hask.Data.Functor.Yoneda Hask.Control.Lens Coq.Classes.Morphisms Coq.Setoids.Setoid Coq.Init.Datatypes Coq.Relations.Relation_Definitions FunctionalExtensionality