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theorem proved tactic proof

one_sub_eulerPrimePowerComplex_ne_zero

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formal statement (Lean)

 450theorem one_sub_eulerPrimePowerComplex_ne_zero {s : ℂ} (hs : 0 < s.re)
 451    (p : Nat.Primes) :
 452    1 - eulerPrimePowerComplex p s ≠ 0 := by

proof body

Tactic-mode proof.

 453  have hone : eulerPrimePowerComplex p s ≠ 1 := by
 454    intro h
 455    have hnorm : ‖eulerPrimePowerComplex p s‖ = 1 := by
 456      simpa [h]
 457    have hlt := norm_eulerPrimePowerComplex_lt_one hs p
 458    linarith
 459  exact sub_ne_zero.mpr (by simpa [eq_comm] using hone)
 460
 461/-- Each regularized Euler factor is nonzero on the open right half-plane. -/

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