∀ {R : Type u_2} {Γ : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R]
  [inst_2 : LinearOrderedCommGroupWithZero Γ] (v : Valuation R Γ) [h : v.Compatible],
  ValuativeRel.ValueGroupWithZero.lift
      (fun r s => (MonoidWithZeroHom.ValueGroup₀.restrict₀ v) r / (MonoidWithZeroHom.ValueGroup₀.restrict₀ v) ↑s) ⋯ 0 =
    0