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theorem proved term proof

eigenvalue_pos

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formal statement (Lean)

  85theorem eigenvalue_pos {σ : ℝ} (hσ : 0 < σ) (p : Nat.Primes) :
  86    0 < (p : ℝ) ^ (-σ) := by

proof body

Term-mode proof.

  87  exact Real.rpow_pos_of_pos (by exact_mod_cast p.prop.pos) _
  88
  89/-! ### §2. The regularized Fredholm determinant -/
  90
  91/-- The per-prime factor of det₂:
  92    det₂_factor(p, s) = (1 − p^{−s}) · exp(p^{−s}).
  93    This is entire in s. -/

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