From Undecidability.SystemF.Util Require Import typing_facts term_facts step.
Definition pw_iff {X} p q := (forall x : X, p x <-> q x).
Notation "p == q" := (pw_iff p q) (at level 70).
Instance Equiv_pw_iff {X} : Equivalence (@pw_iff X).

Lemma pw {X : Type} P Q :
(forall x : X, P x <-> Q x) ->
(forall x, P x) <-> (forall x, Q x).