proposition: Lemma nwfs_is_wfs {C : category} (n : nwfs C) : wfs C.
proof: Proof. use make_wfs. - exact ((nwfs_L_maps_class n)^cl). - exact ((nwfs_R_maps_class n)^cl). - use make_is_wfs. * apply morphism_class_subset_antisymm. + exact (nwfs_L_maps_cl_subs_llp_R_maps_cl _). + exact (nwfs_llp_R_maps_cl_subs_L_maps_cl _). * apply morphism_class_subset_antisymm. + exact (nwfs_R_maps_cl_subs_rlp_L_maps_cl _). + exact (nwfs_rlp_L_maps_cl_subs_R_maps_cl _). * intros x y f. set (fact := fact_functor n f). set (f01 := three_mor01 fact). set (f12 := three_mor12 fact). apply hinhpr. exists (three_ob1 fact), f01, f12. repeat split. + apply in_morcls_retc_if_in_morcls. exact (nwfs_Lf_is_L_map n (three_mor02 fact)). + apply in_morcls_retc_if_in_morcls. exact (nwfs_Rf_is_R_map n (three_mor02 fact)). + exact (three_comp fact). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monads.ComonadCoalgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.MorphismClass UniMath.ModelCategories.Retract UniMath.ModelCategories.Lifting UniMath.ModelCategories.WFS UniMath.ModelCategories.NWFS UniMath.ModelCategories.Helpers