∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Inhabited α] {k : α}, t.erase k ≠ ∅ → ¬cmp k t.maxKey! = Ordering.eq → (t.erase k).maxKey! = t.maxKey!