fact: Definition total_functor_commute {C₁ C₂ : category} {F : C₁ ⟶ C₂} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} (FF : disp_functor F D₁ D₂) : pr1_category D₁ ∙ F ⟹ total_functor FF ∙ pr1_category D₂.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.AxiomOfChoice UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence