proposition: Lemma iscontr_prod (A B : UU) : iscontr A -> iscontr B -> iscontr (A × B).
proof: Proof. intros p q. exists (pr1 p ,, pr1 q). intro t. use total2_paths_f. { apply (pr2 p). } rewrite transportf_const. apply (pr2 q). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.precomp_ess_surj UniMath.CategoryTheory.precomp_fully_faithful UniMath.CategoryTheory.PrecategoryBinProduct