Definition pb_of_sfib_cleaving_cell : pb_of_sfib_cleaving_mor ==> h₂. Proof. use (pb_ump_cell H). - exact (pb_ump_mor_pr1 H pb_of_sfib_cleaving_cone • internal_sfib_cleaving_lift_cell _ _ _). - exact (pb_ump_mor_pr2 H pb_of_sfib_cleaving_cone • α). - abstract (simpl ; rewrite !vassocl ; etrans ; [ apply maponpaths_2 ; exact (pb_ump_mor_cell H pb_of_sfib_cleaving_cone) | ] ; rewrite !vassocl ; apply maponpaths ; rewrite <- !rwhisker_vcomp ; rewrite !vassocl ; apply maponpaths ; cbn ; rewrite !(maponpaths (λ z, _ • (_ • z)) (vassocr _ _ _)) ; rewrite rassociator_lassociator ; rewrite id2_left ; etrans ; [ apply maponpaths ; rewrite !vassocr ; rewrite rwhisker_vcomp ; rewrite vcomp_linv ; rewrite id2_rwhisker ; rewrite id2_left ; apply idpath | ] ; refine (!_) ; etrans ; [ apply maponpaths_2 ; apply internal_sfib_cleaving_over | ] ; rewrite !vassocl ; apply maponpaths ; rewrite !vassocl ; apply maponpaths ; rewrite !(maponpaths (λ z, _ • (_ • z)) (vassocr _ _ _)) ; rewrite lassociator_rassociator ; rewrite id2_left ; rewrite lwhisker_vcomp ; rewrite vcomp_linv ; rewrite lwhisker_id2 ; apply id2_right). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits. Section FromPBCartesian. End FromPBCartesian.