proposition: Lemma length_map (f : A -> A) : ∏ xs, length (map f xs) = length xs.
proof: Proof. apply listIndProp. - intros l; apply isasetnat. - now unfold map; rewrite foldr_nil. - simpl; unfold map, length; simpl; intros a l Hl. now rewrite !foldr_cons, <- Hl. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.Combinatorics.Lists UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PrecategoryBinProduct