∀ {α : Type u} {β : α → Type v} [inst : BEq α] {l : List ((a : α) × β a)} {k a : α} {v : β k},
  Std.Internal.List.containsKey a (⟨k, v⟩ :: l) = false ↔ (k == a) = false ∧ Std.Internal.List.containsKey a l = false