proposition: Lemma lhs_left_invert_cell {a b : C} {f g h : a --> b} (x : f ==> g) (y : g ==> h) (z : f ==> h) (inv_x : is_invertible_2cell x) : y = inv_x^-1 • z -> x • y = z.
proof: Proof. intro H1. etrans. { apply maponpaths. apply H1. } etrans. { apply vassocr. } etrans. { apply maponpaths_2. apply (vcomp_rinv inv_x). } apply id2_left. 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