proposition: Theorem add_one_mul_iso : forall a b, (a + one) * b ≅ (a * b) + b.
proof: Proof. intros. exists (fun p => match p with | (inl a, b) => inl (a, b) | (inr tt, b) => inr b end). exists (fun p => match p with | inl (a, b) => (inl a, b) | inr b => (inr tt, b) 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