∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : BEq α] [Std.LawfulBEqCmp cmp] [inst_3 : Inhabited α] {l : List ((a : α) × β a)} {k : α},
  (List.map Sigma.fst l).contains k = false → (t.insertMany l).getKey! k = t.getKey! k