proposition: Lemma postcompWithBinCoproductArrowHSET {A B : HSET} (CCAB : BinCoproduct A B) {C : HSET} (f : A --> C) (g : B --> C) {X : HSET} (k : C --> X) z: k (BinCoproductArrow CCAB f g z) = BinCoproductArrow CCAB (f · k) (g · k) z.
proof: Proof. set (H1 := postcompWithBinCoproductArrow _ CCAB f g k). apply toforallpaths in H1. now apply H1. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Coproducts UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Pushouts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Categories.HSET.Core UniMath.Combinatorics.FiniteSets UniMath.MoreFoundations.Subtypes