proposition: Lemma isaprop_Coproducts {C : category} (Cuniv : Univalence.is_univalent C) (I : UU) : isaprop (Coproducts I C).
proof: Proof. use invproofirrelevance. intros C1 C2. apply funextsec ; intro ind. use eq_Coproduct. - refine (Univalence.isotoid _ Cuniv _). apply z_iso_from_coproduct_to_coproduct. - intro. rewrite Univalence.idtoiso_isotoid ; cbn. apply pathsinv0, CoproductInCommutes. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.Combinatorics.Lists UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Groupoids UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCoalgebras UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Chains.Cochains UniMath.CategoryTheory.Chains.CoAdamek UniMath.CategoryTheory.Chains.OmegaContFunctors UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Monoidal.Examples.MonadsAsMonoidsElementary UniMath.SubstitutionSystems.EquivalenceLaxLineatorsHomogeneousCase UniMath.SubstitutionSystems.MultiSorted_alt UniMath.SubstitutionSystems.MultiSorted_actegorical UniMath.SubstitutionSystems.MultiSortedMonadConstruction_alt UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems UniMath.SubstitutionSystems.ConstructionOfGHSS UniMath.SubstitutionSystems.SigmaMonoids UniMath.SubstitutionSystems.ContinuitySignature.ContinuityOfMultiSortedSigToFunctor UniMath.SubstitutionSystems.ContinuitySignature.MultiSortedSignatureFunctorEquivalence UniMath.SubstitutionSystems.ContinuitySignature.CommutingOfOmegaLimitsAndCoproducts UniMath.SubstitutionSystems.ContinuitySignature.InstantiateHSET