enorm_compContinuousLinearMap_le — Mathlib

English

Radius is preserved under taking additive inverse: radius(-p) = radius(p).

Русский

Радиус сохраняется при взятии противоположной серии: radius(-p) = radius(p).

LaTeX

$$$(-p).radius = p.radius.$$$

Lean4

theorem enorm_compContinuousLinearMap_le (p : FormalMultilinearSeries 𝕜 F G) (u : E →L[𝕜] F) (n : ℕ) :
    ‖p.compContinuousLinearMap u n‖ₑ ≤ ‖p n‖ₑ * ‖u‖ₑ ^ n :=
  by
  rw [← ofReal_norm, ← ofReal_norm, ← ofReal_norm, ← ENNReal.ofReal_pow (by simp), ← ENNReal.ofReal_mul (by simp)]
  gcongr
  apply norm_compContinuousLinearMap_le

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