proposition: Lemma is_precategory_binop_precategory_data : is_precategory binop_precategory_data.
proof: 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.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors