proposition: Lemma fiber_paths_transposed {A : UU} {B : A → UU} {a1 : A} {a2 : A} (b1 : B a1) (b2 : B a2) : ∏ p : a1,, b1 = a2,, b2, b1 = transportb B (base_paths _ _ p) b2 .
proof: Proof. intro q. use transportb_transpose_right. apply (fiber_paths q). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Adjunctions UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.TotalAdjunction UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispPseudofunctor UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.PseudoFunctors.Biadjunction UniMath.Bicategories.Modifications.Modification UniMath.Bicategories.PseudoFunctors.UniversalArrow UniMath.Bicategories.DisplayedBicats.DispBiadjunction UniMath.Bicategories.DisplayedBicats.DispInvertibles