∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {α : Type u_2} {β : Type u_3}
  (a : Matrix α β (NumberField.RingOfIntegers K)) [inst_2 : Fintype β] {A : ℝ},
  (∀ (k : α) (l : β), NumberField.house ((algebraMap (NumberField.RingOfIntegers K) K) (a k l)) ≤ A) →
    ∀ [inst_3 : DecidableEq (K →+* ℂ)] [inst_4 : Fintype α],
      0 ≤ A → ‖NumberField.house.asiegel✝ K a‖ ≤ NumberField.house.c₂✝ K * A