proposition: Lemma rhs_right_inv_cell {a b : C} {f g h : a --> b} (x : f ==> g) (y : g ==> h) (z : f ==> h) (inv_y : is_invertible_2cell y) : x • y = z -> x = z • inv_y^-1.
proof: Proof. intro H1. apply (vcomp_rcancel _ inv_y). etrans. { apply H1. } etrans. 2: apply vassocr. apply pathsinv0. etrans. { apply maponpaths. apply vcomp_linv. } apply id2_right. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct