Definition is_precategory_one_assoc_to_two (C : precategory_data) : is_precategory_one_assoc C -> is_precategory C := λ i, (pr11 i,,pr21 i),,(pr2 i,,λ a b c d f g h, pathsinv0 (pr2 i a b c d f g h)).
Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations.