proposition: Lemma postCompWithPullbackArrow (c d : C) (k0 : C⟦c,d⟧) {a b x : C} {f : C⟦a,x⟧} {g : C⟦b,x⟧} (Pb : Pullback f g) (h : C ⟦ d, a ⟧) (k : C ⟦ d, b ⟧) (H : h · f = k · g) : k0 · PullbackArrow Pb d h k H = PullbackArrow Pb _ (k0 · h) (k0 · k) (postCompWithPullbackArrow_subproof k0 H).
proof: Proof. apply PullbackArrowUnique. - now rewrite <- assoc, PullbackArrow_PullbackPr1. - now rewrite <- assoc, PullbackArrow_PullbackPr2. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Monics