proposition: Lemma LimFunctorCone : LimCone D.
proof: Proof. use make_LimCone. - exact LimFunctor. - use make_cone. + now apply lim_nat_trans_in_data. + abstract (now intros u v e; apply (nat_trans_eq C); intro a; apply (limOutCommutes (HCg a))). - now intros F cc; simpl; apply (LimFunctor_unique _ cc). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.Graphs.Colimits