pith. machine review for the scientific record. sign in
theorem proved tactic proof

J_bit_eq_phi_minus

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

  88theorem J_bit_eq_phi_minus : J_bit_val = phi - 3/2 := by

proof body

Tactic-mode proof.

  89  unfold J_bit_val J
  90  -- Key identity: 1/φ = φ - 1 (from φ² = φ + 1)
  91  have h_inv : phi⁻¹ = phi - 1 := by
  92    have hphi_ne : phi ≠ 0 := phi_pos.ne'
  93    have hsq : phi^2 = phi + 1 := phi_sq_eq
  94    have : phi * phi = phi + 1 := by rw [← sq]; exact hsq
  95    field_simp at this ⊢
  96    linarith
  97  rw [h_inv]
  98  ring
  99
 100/-- **Numerical Bound**: J_bit ≈ 0.118.
 101    Since 1.61 < φ < 1.62, we have 0.11 < J_bit < 0.12. -/

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (6)

Lean names referenced from this declaration's body.