proposition: Proposition pstrans_id_inv {B₁ B₂ : bicat} {F G : psfunctor B₁ B₂} (τ : pstrans F G) (x : B₁) : (psnaturality_of τ (id₁ x))^-1 • (τ x ◃ (psfunctor_id G x)^-1) = ((psfunctor_id F x)^-1 ▹ τ x) • lunitor _ • rinvunitor _.
proof: Proof. use vcomp_move_L_pM ; [ is_iso | ]. use vcomp_move_R_Mp ; [ is_iso | ]. use vcomp_move_L_pM; [ is_iso | ]. cbn -[psfunctor_id]. rewrite !vassocr. exact (!(pstrans_id τ x)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.PseudoFunctors.Display.Base UniMath.Bicategories.PseudoFunctors.Display.Map1Cells UniMath.Bicategories.PseudoFunctors.Display.Map2Cells UniMath.Bicategories.PseudoFunctors.Display.Identitor UniMath.Bicategories.PseudoFunctors.Display.Compositor UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor