proposition: Lemma size_map (f : nat -> nat) : ∏ l, size (map f l) = size l.
proof: Proof. apply treeIndProp. - intros l. apply isasetnat. - now unfold map; rewrite foldr_leaf. - intros a l1 l2 ih1 ih2; unfold map. now rewrite foldr_node, !size_node, <- ih1, <- ih2. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers 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.Inductives.Lists