∀ {α : Type u_2} {β : Type u_1} {r : α → β → Prop} {a : α} {as : Multiset α} {bs : Multiset β}
  (motive : (∃ b bs', r a b ∧ Multiset.Rel r as bs' ∧ bs = b ::ₘ bs') → Prop)
  (x : ∃ b bs', r a b ∧ Multiset.Rel r as bs' ∧ bs = b ::ₘ bs'),
  (∀ (b : β) (bs' : Multiset β) (hab : r a b) (h : Multiset.Rel r as bs') (Eq : bs = b ::ₘ bs'), motive ⋯) → motive x