fact: Definition is_inverse_in_precat1 {C : precategory_data} {a b : C} {f : a --> b} {g : b --> a} (H : is_inverse_in_precat f g) : f · g = identity a := dirprod_pr1 H.
imports: UniMath.Foundations.PartA UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories