proposition: Lemma InitialToCoproduct (I : Initial C): ∏ (a : stn 0 -> C), Coproduct (stn 0) C a.
proof: Proof. intros a. use (make_Coproduct _ _ _ I (λ i : stn 0, fromempty (weqstn0toempty i))). intros c g. use unique_exists. - apply (InitialArrow I c). - intros i. apply (fromempty (weqstn0toempty i)). - intro; apply impred_isaprop. intro; apply homset_property. - intros. apply InitialArrowUnique. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial