Lemma is_precategory_binop_precategory_data : is_precategory binop_precategory_data. Proof. repeat split; cbn. intros a b f. apply idbinopfun_remove_left. intros a b f. apply idbinopfun_remove_right. intros a b c d f g h. apply pathsinv0. apply (binopfuncomp_assoc a b c d f g h). intros a b c d f g h. apply (binopfuncomp_assoc a b c d f g h). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors.