Valuation Δ base Change lt one

theorem valuation_Δ_baseChange_lt_one [HasMultiplicativeReduction 𝒪[k] E] :    (IsDiscreteValuationRing.maximalIdeal 𝒪[l]).valuation l (E.baseChange l).Δ < 1 := by  have hk : valuation k E.Δ < 1 := by    have hbad := HasMultiplicativeReduction.badReduction (R := 𝒪[k]) (W := E)    rw [← integralModel_Δ_eq 𝒪[k] E] at hbad ⊢    exact adicValuation_lt_one_iff.mp hbad  have hl : valuation l (E.baseChange l).Δ < 1 := by    rw [show (E.baseChange l).Δ = algebraMap k l E.Δ from E.map_Δ (algebraMap k l)]    exact valuation_algebraMap_lt_one hk  rw [← integralModel_Δ_eq 𝒪[l] (E.baseChange l)] at hl ⊢  exact adicValuation_lt_one_iff.mpr hl