proposition: Lemma treeIndProp (P : pr1 Tree -> UU) (HP : ∏ l, isaprop (P l)) : P leaf -> (∏ a l1 l2, P l1 → P l2 → P (node (a,,l1,,l2))) -> ∏ l, P l.
proof: Proof. intros Pnil Pcons. apply treeInd; try assumption. intro l; apply isasetaprop, HP. Defined.
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