∀ (R : Type u_1) [inst : CommRing R] [inst_1 : ValuativeRel R],
  ValuativeRel.valuation R =
    { toFun := fun r => ValuativeRel.ValueGroupWithZero.mk r 1, map_zero' := ⋯, map_one' := ⋯, map_mul' := ⋯,
      map_add_le_max' := ⋯ }