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