proposition: Lemma PL_fold_and : ∏ p q, fold (PL_and (make_dirprod p q)) = and (fold p) (fold q).
proof: Proof. intros p q. do 2 apply (maponpaths (λ x, (inl : HSET ⟦_, BinCoproductsHSET _ _⟧) · x)) in comm. apply (maponpaths (λ x, (inr : HSET ⟦_, BinCoproductsHSET _ _⟧) · x)) in comm. apply eqtohomot in comm. specialize (comm (make_dirprod p q)). exact comm. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.Bool UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.Adamek