Use ListBox properties for TreeView implementation.

src/Avalonia.Controls/ListBox.cs

@@ -30,13 +30,13 @@ namespace Avalonia.Controls
         /// <summary>
         /// Defines the <see cref="SelectedItems"/> property.
         /// </summary>
-        public static readonly new AvaloniaProperty<IList> SelectedItemsProperty =
+        public static readonly new DirectProperty<SelectingItemsControl, IList> SelectedItemsProperty =
             SelectingItemsControl.SelectedItemsProperty;
 
         /// <summary>
         /// Defines the <see cref="SelectionMode"/> property.
         /// </summary>
-        public static readonly new AvaloniaProperty<SelectionMode> SelectionModeProperty = 
+        public static readonly new StyledProperty<SelectionMode> SelectionModeProperty = 
             SelectingItemsControl.SelectionModeProperty;
 
         /// <summary>

src/Avalonia.Controls/TreeView.cs

@@ -40,8 +40,7 @@ namespace Avalonia.Controls
         /// Defines the <see cref="SelectedItems"/> property.
         /// </summary>
         public static readonly DirectProperty<TreeView, IList> SelectedItemsProperty =
-            AvaloniaProperty.RegisterDirect<TreeView, IList>(
+            ListBox.SelectedItemsProperty.AddOwner<TreeView>(
-                nameof(SelectedItems),
                 o => o.SelectedItems,
                 (o, v) => o.SelectedItems = v);
 
@@ -49,8 +48,7 @@ namespace Avalonia.Controls
         /// Defines the <see cref="SelectionMode"/> property.
         /// </summary>
         public static readonly StyledProperty<SelectionMode> SelectionModeProperty =
-            AvaloniaProperty.Register<TreeView, SelectionMode>(
+            ListBox.SelectionModeProperty.AddOwner<TreeView>();
-                nameof(SelectionMode));
 
         private static readonly IList Empty = new object[0];
         private object _selectedItem;