case pos
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : 0 ≤ leadingCoeff P / leadingCoeff Q
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop

case neg
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : ¬0 ≤ leadingCoeff P / leadingCoeff Q
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
by_cases h : 0 ≤ P.leadingCoeff / Q.leadingCoeff
no goals
case pos
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : 0 ≤ leadingCoeff P / leadingCoeff Q
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
exact tendsto_abs_atTop_atTop.comp (P.div_tendsto_atTop_of_degree_gt Q hdeg hQ h)
case neg
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : leadingCoeff P / leadingCoeff Q < 0
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
case neg
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : ¬0 ≤ leadingCoeff P / leadingCoeff Q
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
push_neg at h
no goals
case neg
𝕜 : Type u_1
inst✝¹ : NormedLinearOrderedField 𝕜
P Q : 𝕜[X]
inst✝ : OrderTopology 𝕜
hdeg : degree Q < degree P
hQ : Q ≠ 0
h : leadingCoeff P / leadingCoeff Q < 0
⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop
exact tendsto_abs_atBot_atTop.comp (P.div_tendsto_atBot_of_degree_gt Q hdeg hQ h.le)