∀ {α : Type u_1},
  Function.RightInverse
    (fun s =>
      ((Equiv.subtypeQuotientEquivQuotientSubtype (fun x => x.length = 1) (fun x => Multiset.card x = 1) ⋯ ⋯) s).liftOn
        (fun l => (↑l).head ⋯) ⋯)
    fun a => ⟨{a}, ⋯⟩