{K : Type u_1} →
  [inst : Field K] →
    (archAbsVal : Multiset (AbsoluteValue K ℝ)) →
      (nonarchAbsVal : Set (AbsoluteValue K ℝ)) →
        (∀ v ∈ nonarchAbsVal, IsNonarchimedean ⇑v) →
          (∀ {x : K}, x ≠ 0 → Function.HasFiniteMulSupport fun v => ↑v x) →
            (∀ {x : K}, x ≠ 0 → (Multiset.map (fun x_2 => x_2 x) archAbsVal).prod * ∏ᶠ (v : ↑nonarchAbsVal), ↑v x = 1) →
              Height.AdmissibleAbsValues K