∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp]
  [inst : Inhabited α] {k a : α} {v : β k}, (t.insert k v).getKey! a = if cmp k a = Ordering.eq then k else t.getKey! a