∀ {α : Type u} {β : Type v} {key : α} {value : β} {tail : Batteries.AssocList α β} {key_1 : α} {value_1 : β}
  {tail_1 : Batteries.AssocList α β},
  Batteries.AssocList.cons key value tail = Batteries.AssocList.cons key_1 value_1 tail_1 →
    key = key_1 ∧ value = value_1 ∧ tail = tail_1