proposition: Lemma postCompWithLimOfArrows_subproof {C : precategory} {g : graph} {d1 d2 : diagram g C} (CC1 : LimCone d1) (CC2 : LimCone d2) (f : ∏ (u : vertex g), C⟦dob d1 u,dob d2 u⟧) (fNat : ∏ u v (e : edge u v), f u · dmor d2 e = dmor d1 e · f v) (x : C) (cc : cone d1 x) u v (e : edge u v) : (coneOut cc u · f u) · dmor d2 e = coneOut cc v · f v.
proof: Proof. now rewrite <- (coneOutCommutes cc u v e), <- assoc, fNat, assoc. 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