proposition: Lemma is_precategory_slice_precat_data : is_precategory slice_precat_data.
proof: Proof. repeat split; simpl. * intros a b f. induction f as [h hP]. apply subtypePairEquality; [ intro; apply C | apply id_left ]. * intros a b f. induction f as [h hP]. apply subtypePairEquality; [ intro; apply C | apply id_right ]. * intros a b c d f g h. apply subtypePairEquality; [ intro; apply C | apply assoc ]. * intros a b c d f g h. apply subtypePairEquality; [ intro; apply C | apply assoc' ]. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis