term_nonneg — Mathlib

English

The topological sum is defined by term_tsum(s) = sum' n, term(n+1,s).

Русский

Псевдо-сумма задаётся как term_tsum(s) = \\\\sum' n, term(n+1,s).

LaTeX

$$$\\\\operatorname{term\\_tsum}(s) = \\\\sum'_{n \\\\in \\\\mathbb{N}} \\\\operatorname{term}(n+1,s)$$$

Lean4

theorem term_nonneg (n : ℕ) (s : ℝ) : 0 ≤ term n s :=
  by
  rw [term, intervalIntegral.integral_of_le (by simp)]
  refine setIntegral_nonneg measurableSet_Ioc (fun x hx ↦ ?_)
  refine div_nonneg ?_ (rpow_nonneg ?_ _)
  all_goals linarith [hx.1]

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