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ofScalars_norm_eq_mul
simp
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Mathlib/Analysis/Analytic/OfScalars.lean
@@ -175,6 +175,7 @@ open scoped Topology NNReal
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variable {𝕜 : Type*} (E : Type*) [NontriviallyNormedField 𝕜] [SeminormedRing E]
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[NormedAlgebra 𝕜 E] (c : ℕ → 𝕜) (n : ℕ)
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+@[simp]
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theorem ofScalars_norm_eq_mul :
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‖ofScalars E c n‖ = ‖c n‖ * ‖ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n E‖ := by
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rw [ofScalars, norm_smul]
@@ -184,9 +185,8 @@ theorem ofScalars_norm_le (hn : n > 0) : ‖ofScalars E c n‖ ≤ ‖c n‖ :=
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exact (mul_le_of_le_one_right (norm_nonneg _)
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(ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos hn))
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-@[simp]
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theorem ofScalars_norm [NormOneClass E] : ‖ofScalars E c n‖ = ‖c n‖ := by
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- simp [ofScalars_norm_eq_mul]
+ simp
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end Seminormed
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