lemma
proved
tactic proof
phi_lt_onePointSixTwo
show as:
view Lean formalization →
formal statement (Lean)
87lemma phi_lt_onePointSixTwo : phi < (1.62 : ℝ) := by
proof body
Tactic-mode proof.
88 simp only [phi]
89 have h5 : Real.sqrt 5 < (2.24 : ℝ) := by
90 have h : (5 : ℝ) < (2.24 : ℝ)^2 := by norm_num
91 have h24_pos : (0 : ℝ) ≤ 2.24 := by norm_num
92 rw [← Real.sqrt_sq h24_pos]
93 exact Real.sqrt_lt_sqrt (by norm_num) h
94 linarith
95
96/-- Even tighter lower bound: φ > 1.61. -/
used by (40)
-
optimalT60_band -
Jphi_numerical_band -
adolescenceChildhoodRatio_near_phi -
E_PBM_bounds -
phi_eighth_in_gamma_band -
adjacencyGap_band -
settlementPopRatio_in_Christaller_band -
BIT_carrier_period_band -
r_orbit_adjacent_ratio_band -
f_Schumann_RS_band -
J_phi_ceiling_band -
mercury_deviation_in_J_phi_band -
phi_cubed_band -
hcp_ratio_near_phi -
activation_energy_Fe_approx -
optimalTemp_in_industrial_range -
phi_ratio_bounds -
stratopause_tropopause_ratio_band -
predictability_threshold_band -
ignition_threshold_band -
J_phi_band -
phi_critical_numeric -
sc_prediction -
freezingRatio3D_band -
hbar_bounds -
phi_approx -
phi_cubed_bounds -
phi_fifth_bounds -
phi_fourth_bounds -
phi_squared_bounds