∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] {motive : ValuativeRel.ValueGroupWithZero R → Prop},
  (∀ (x : R) (y : ↥(ValuativeRel.posSubmonoid R)), motive (ValuativeRel.ValueGroupWithZero.mk x y)) →
    ∀ (t : ValuativeRel.ValueGroupWithZero R), motive t