proposition: Proposition dfl_full_comp_cat_nat_trans_eq {C₁ C₂ : dfl_full_comp_cat} {F G : dfl_full_comp_cat_functor C₁ C₂} (τ₁ τ₂ : dfl_full_comp_cat_nat_trans F G) (p : ∏ (x : C₁), τ₁ x = τ₂ x) (p' := nat_trans_eq (homset_property _) _ _ _ _ p) (pp : ∏ (x : C₁) (xx : disp_cat_of_types C₁ x), transportf _ (nat_trans_eq_pointwise p' x) (comp_cat_type_nat_trans τ₁ x xx) = comp_cat_type_nat_trans τ₂ x xx) : τ₁ = τ₂.
proof: Proof. use subtypePath. { intro. repeat (use isapropdirprod) ; apply isapropunit. } exact (full_comp_nat_trans_eq p pp). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.DependentSums UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Preservation UniMath.Bicategories.Core.Bicat UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations UniMath.Bicategories.ComprehensionCat.TypeFormers.UnitTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.ProductTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.EqualizerTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.Democracy UniMath.Bicategories.ComprehensionCat.TypeFormers.SigmaTypes