proposition: Lemma PullbackArrowUnique {a b c d : C} (f : C⟦b, a⟧) (g : C⟦c, a⟧) (Pb : Pullback f g) e (h : C⟦e, b⟧) (k : C⟦e, c⟧) (Hcomm : h · f = k · g) (w : C⟦e, PullbackObject Pb⟧) (H1 : w · PullbackPr1 Pb = h) (H2 : w · PullbackPr2 Pb = k) : w = PullbackArrow Pb _ h k Hcomm.
proof: Proof. apply path_to_ctr. use three_rec_dep; try assumption. set (X:= limOutCommutes Pb Three Two tt). eapply pathscomp0. eapply maponpaths, pathsinv0, X. simpl. rewrite assoc. eapply pathscomp0. apply cancel_postcomposition, H2. apply (!Hcomm). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits