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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(** * Proofs about standard combinators, exports functional extensionality.  Author: Matthieu Sozeau Institution: LRI, CNRS UMR 8623 - University Paris Sud *)
Require Export FunctionalExtensionality.
Open Scope program_scope.
(** Composition has [id] for neutral element and is associative. *)
Hint Rewrite @compose_id_left @compose_id_right : core.
Hint Rewrite <- @compose_assoc : core.
(** [flip] is involutive. *)
(** [prod_curry] and [prod_uncurry] are each others inverses. *)

Lemma prod_uncurry_curry : forall A B C, @prod_uncurry A B C ∘ prod_curry = id.