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. use subtypePairEquality. { intro i. apply impred_isaprop. intro. apply homset_property. } apply TerminalArrowUnique. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Monics.