∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α} {v : β}
  {km kmi : α}, t.maxKey? = some km → (t.insert k v).maxKey?.get ⋯ = kmi → (cmp km kmi).isLE = true