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theorem proved term proof

phi_zpow_ne_one

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formal statement (Lean)

  49theorem phi_zpow_ne_one {n : ℤ} (hn : n ≠ 0) : PhiForcing.φ ^ n ≠ 1 := by

proof body

Term-mode proof.

  50  have hφ_gt := PhiForcing.phi_gt_one
  51  intro heq
  52  have h0 : PhiForcing.φ ^ (0 : ℤ) = 1 := zpow_zero _
  53  have hmono : StrictMono fun m : ℤ => PhiForcing.φ ^ m :=
  54    zpow_right_strictMono₀ hφ_gt
  55  exact hn (hmono.injective (heq.trans h0.symm))
  56

used by (2)

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