proposition: Lemma CoproductInLiftingProblemsEqCod {C : category} {J : morphism_class C} {f : arrow C} {CCa : Coproduct _ _ (λ lp, arrow_cod (pr1 (morcls_lp_map lp)))} {g : total_category (morcls_disp J)} {S S' : (pr1 g) --> f} : S = S' -> CoproductIn CCa (g,, S) = CoproductIn CCa (g,, S').
proof: Proof. apply (CoproductInLiftingProblemsEq (a := λ f, arrow_cod (pr1 f))). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monads.ComonadCoalgebras UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.Opposite UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.MorphismClass UniMath.ModelCategories.Retract UniMath.ModelCategories.Lifting UniMath.ModelCategories.NWFS UniMath.ModelCategories.NWFSisWFS UniMath.ModelCategories.Generated.LiftingWithClass UniMath.CategoryTheory.DisplayedCats.Examples.MonadAlgebras