lemma
proved
tactic proof
phi_gt_onePointFive
show as:
view Lean formalization →
formal statement (Lean)
78lemma phi_gt_onePointFive : (1.5 : ℝ) < phi := by
proof body
Tactic-mode proof.
79 simp only [phi]
80 have h5 : (2 : ℝ) < Real.sqrt 5 := by
81 have h : (2 : ℝ)^2 < 5 := by norm_num
82 rw [← Real.sqrt_sq (by norm_num : (0 : ℝ) ≤ 2)]
83 exact Real.sqrt_lt_sqrt (by norm_num) h
84 linarith
85
86/-- Tighter upper bound: φ < 1.62 (since √5 < 2.24). -/
used by (40)
-
over_damped_below_one -
acceptanceBandRatio_gt_one -
adjacencyGap_pos -
coronalTime_strictly_increasing -
shell_radius_increases_with_period -
fragility_one_lt_zero -
catalyticBarrierRatio_pos -
tempAtRung_strictly_increasing -
transition_cohesive_gt_alkali -
horizonAtRung_strictly_decreasing -
flameSpeed_strictly_increasing -
criticalDamkohler_in_empirical_band -
J_phi_pos -
phi_cubed_bounds -
phi_fourth_bounds -
phi_squared_bounds -
etaBAt_strictly_decreasing -
delta_w0_max_pos -
crossSectionRatio_pos -
reductionFactor_lt_one -
coolingFraction_pos -
alphaProvenanceCert -
octave_sufficient_for_4_hop -
phi_blend_5_hop_weak -
phi_four_power_lower -
canonicalThreshold_pos -
full_cooperation_cascades -
cooperatorThreshold_lt_one -
subduction_faster_than_ridge -
echoAmplitude_strictly_decreasing