theorem
proved
tactic proof
anomalous_nu_correction_small
show as:
view Lean formalization →
formal statement (Lean)
147theorem anomalous_nu_correction_small (D η : ℝ) (hD : 0 < D) (hη : 0 ≤ η) :
148 anomalous_nu_correction D η ≤ η / D := by
proof body
Tactic-mode proof.
149 unfold anomalous_nu_correction
150 have hDη : 0 < D + η := by linarith
151 have hDη_ne : D + η ≠ 0 := ne_of_gt hDη
152 have hD_ne : D ≠ 0 := ne_of_gt hD
153 rcases eq_or_lt_of_le hη with rfl | hη_pos
154 · simp
155 · rw [div_le_div_iff₀ hDη hD]
156 nlinarith
157
158/-- The corrected ν₀ + η/(D + η). -/