proposition: Lemma are_inverses_from_Pullback_to_Pullback {a b c : C} {f : C⟦b, a⟧} {g : C⟦c, a⟧} (Pb Pb': Pullback f g) : is_inverse_in_precat (from_Pullback_to_Pullback Pb Pb') (from_Pullback_to_Pullback Pb' Pb).
proof: Proof. split; apply pathsinv0; apply PullbackEndo_is_identity; rewrite <- assoc; unfold from_Pullback_to_Pullback; repeat rewrite PullbackArrow_PullbackPr1; repeat rewrite PullbackArrow_PullbackPr2; auto. 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