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theorem proved tactic proof

phi_pow_residue_mu_upper

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formal statement (Lean)

 570theorem phi_pow_residue_mu_upper :
 571    phi ^ predicted_residue_mu < (0.0098 : ℝ) := by

proof body

Tactic-mode proof.

 572  have h_mu := predicted_residue_mu_bounds
 573  have h_phi_gt : phi = Real.goldenRatio := rfl
 574  rw [h_phi_gt]
 575  have h_mono := Numerics.phi_rpow_strictMono
 576  have h_lt : Real.goldenRatio ^ predicted_residue_mu < Real.goldenRatio ^ (-9.62 : ℝ) :=
 577    h_mono h_mu.2
 578  calc Real.goldenRatio ^ predicted_residue_mu < Real.goldenRatio ^ (-9.62 : ℝ) := h_lt
 579    _ < (0.0098 : ℝ) := by
 580        simpa [phi_pow_neg962_upper_hypothesis] using phi_pow_neg962_upper_proved
 581
 582/-- Bounds on φ^(predicted_residue_mu). -/

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