proposition: Lemma terminal_product_arrow_unique (t : ∑ k, ∏ i : I, k · terminal_product_projection i = cone' i) : t = terminal_product_arrow ,, terminal_product_arrow_commutes.
proof: Proof. use subtypePairEquality. { intro i. apply impred_isaprop. intro. apply homset_property. } apply TerminalArrowUnique. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Monics