iSup_pow_of_ne_zero — Mathlib

English

The real-valued iSup_pow_of_ne_zero: for Real-valued f with 0 ≤ f(i) and n ≠ 0, iSup hPow equals hPow of iSup.

Русский

Для f(i) ≥ 0 и n ≠ 0: iSup f(i)^n = (iSup f(i))^n.

LaTeX

$$iSup_pow_of_ne_zero {f : ι → Real} (hf : ∀ i, 0 ≤ f i) (hn : n ≠ 0) : (⨆ i, f i)^n = ⨆ i, f i^n$$

Lean4

theorem iSup_pow_of_ne_zero {f : ι → ℝ} (hf : ∀ i, 0 ≤ f i) (hn : n ≠ 0) : (⨆ i, f i) ^ n = ⨆ i, f i ^ n :=
  by
  cases isEmpty_or_nonempty ι
  · simp [hn]
  · exact iSup_pow hf _

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