ofScalars_eq_zero — Mathlib

English

The snd projection is analytic on t: AnalyticOn 𝕜 (snd) t.

Русский

Проекция snd аналитична на t: AnalyticOn 𝕜 (snd) t.

LaTeX

$$$AnalyticOn 𝕜 (\\lambda p : E \\times F. p.2) t$$$

Lean4

@[simp]
theorem ofScalars_eq_zero [Nontrivial E] (n : ℕ) : ofScalars E c n = 0 ↔ c n = 0 :=
  by
  rw [ofScalars, smul_eq_zero (c := c n) (x := ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n E)]
  refine or_iff_left (ContinuousMultilinearMap.ext_iff.1.mt <| not_forall_of_exists_not ?_)
  use fun _ ↦ 1
  simp

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