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theorem proved tactic proof

eigenvalue_lt_one

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formal statement (Lean)

  78theorem eigenvalue_lt_one {σ : ℝ} (hσ : 0 < σ) (p : Nat.Primes) :
  79    (p : ℝ) ^ (-σ) < 1 := by

proof body

Tactic-mode proof.

  80  have hp_one : (1 : ℝ) < p := by
  81    exact_mod_cast p.prop.one_lt
  82  exact Real.rpow_lt_one_of_one_lt_of_neg hp_one (by linarith)
  83
  84/-- Each eigenvalue p^{−s} is positive for σ > 0. -/

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depends on (6)

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