Theorem FinOrdProducts_from_Terminal_and_BinProducts : Terminal C -> BinProducts C -> FinOrdProducts C. Proof. intros T BinProds n. induction n as [|n IHn]. - exact(TerminalToProduct T). - apply products_stn_Sn. now apply products_stn_unit. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal.