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