theorem
proved
tactic proof
row_fermi_pred_lower
show as:
view Lean formalization →
formal statement (Lean)
65theorem row_fermi_pred_lower :
66 (1.16e-5 : ℝ) < row_fermi_pred := by
proof body
Tactic-mode proof.
67 unfold row_fermi_pred
68 rw [lt_div_iff₀ fermi_den_pos]
69 have hs : Real.sqrt 2 < (1.4143 : ℝ) := sqrt2_lt_14143
70 have hden :
71 Real.sqrt 2 * vev_canonical ^ 2 < (1.4143 : ℝ) * (246 : ℝ) ^ 2 := by
72 have hv : vev_canonical = (246 : ℝ) := rfl
73 have hvpos : 0 < vev_canonical ^ 2 := sq_pos_of_ne_zero (ne_of_gt vev_canonical_pos)
74 rw [hv]
75 nlinarith
76 have hnum : (1.16e-5 : ℝ) * ((1.4143 : ℝ) * (246 : ℝ) ^ 2) < 1 := by
77 norm_num
78 nlinarith
79