proposition: Lemma transportf_cancel {X : UU} (P : X → UU) {x x' : X} (e : x = x') (y0 y1 : P x): transportf P e y0 = transportf P e y1 -> y0 = y1.
proof: Proof. induction e. apply idfun. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.Foundations.All UniMath.CategoryTheory.DisplayedCats.MoreFibrations.Prefibrations UniMath.CategoryTheory.DisplayedCats.MoreFibrations.CartesiannessOfComposites