lemma
proved
tactic proof
phi_ne_zero
show as:
view Lean formalization →
formal statement (Lean)
28lemma phi_ne_zero : Constants.phi ≠ 0 := by
proof body
Tactic-mode proof.
29 -- goldenRatio = (1+√5)/2 ≠ 0
30 have : Real.goldenRatio ≠ 0 := by
31 have hpos : 0 < Real.goldenRatio := Real.goldenRatio_pos
32 exact ne_of_gt hpos
33 simpa [phi_def] using this
34
35/-- φ^2 = φ + 1 using the closed form. -/
used by (40)
-
adjacencyGap_eq -
goldenDivision_ratio -
phi_ladder_step -
lyapunovAt_succ_ratio -
r_orbit_gap_skip_band -
forecastSkill_decay -
horizonAtRung_succ_ratio -
predictability_threshold_band -
ignition_threshold_band -
Jcost_phi_val -
kappa_einstein_eq -
phi_ne_zero -
mass_ratio_structural -
phiRung_add -
etaBAt_succ_ratio -
crossSectionRatio_band -
phi_cost_fixed_point -
recidivismRate_decay -
ledgerConservation_eq_one -
cycleDuration_succ_ratio -
policy_balance -
giniCeiling_eq_phi_minus_one -
mobility_threshold_band -
inv_phi_eq -
phi_rung_energy_ratio -
phi_ladder_tc_monotone -
compression_has_cost -
fibonacci_compression_step -
phi_is_optimal_compression -
eventRate_ratio