proposition: Lemma precompWithLimArrow {g : graph} (D : diagram g C^op) (CC : LimCone D) (c : C) (cc : cone D c) (d : C) (k : C⟦d,c⟧) : k · limArrow CC c cc = limArrow CC d (make_cone (λ u, k · coneOut cc u) (Cone_precompose cc d k)).
proof: Proof. apply limArrowUnique. now intro u; rewrite <- assoc, limArrowCommutes. Qed.
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