∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] (x : R) (y : ↥(ValuativeRel.posSubmonoid R)),
  ValuativeRel.ValueGroupWithZero.lift (fun a b => ValuativeRel.ValueGroupWithZero.mk (a ^ 0) (b ^ 0)) ⋯
      (ValuativeRel.ValueGroupWithZero.mk x y) =
    1