∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] {x y : R} {t s : ↥(ValuativeRel.posSubmonoid R)},
  ValuativeRel.ValueGroupWithZero.mk x t = ValuativeRel.ValueGroupWithZero.mk y s ↔ x * ↑s ≤ᵥ y * ↑t ∧ y * ↑t ≤ᵥ x * ↑s