∀ {α : Type u} {β : α → Type v} [inst : Ord α] [Std.TransOrd α] [inst_2 : BEq α] [Std.LawfulBEqOrd α]
  {l : List ((a : α) × β a)},
  Std.Internal.List.DistinctKeys l →
    ∀ {k : α} {he : l.isEmpty = false},
      (compare (Std.Internal.List.maxKey l he) k).isLE = true ↔
        ∀ (k' : α), Std.Internal.List.containsKey k' l = true → (compare k' k).isLE = true