proposition: Lemma lifting_coprod_lp_red_impl_lifting_coprod_lp : filler (arrow_mor_comm (morcls_lp_coprod_diagram_red)) -> filler (arrow_mor_comm (morcls_lp_coprod_diagram)).
proof: Proof. intro H. destruct H as [l [Hl1 Hl2]]. exists ((PushoutIn1 morcls_lp_coprod_diagram_pushout) · l). split. - etrans. apply assoc. etrans. apply cancel_postcomposition. apply (PushoutSqrCommutes (morcls_lp_coprod_diagram_pushout)). etrans. apply assoc'. etrans. apply maponpaths. exact Hl1. apply id_right. - etrans. apply assoc'. etrans. apply maponpaths. exact Hl2. use PushoutArrow_PushoutIn1. 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.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Equivalences 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.Helpers