analysis.asymptotics.specific_asymptotics ⟷ Mathlib.Analysis.Asymptotics.SpecificAsymptotics

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -172,7 +172,7 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
   by
   have := ((is_o_one_iff ℝ).2 h).sum_range fun i => zero_le_one
   simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this
-  exact this tendsto_nat_cast_atTop_atTop
+  exact this tendsto_natCast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -67,7 +67,7 @@ theorem Filter.tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) :
     Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
   by
   lift n to ℕ using hn.le
-  simp only [zpow_coe_nat]
+  simp only [zpow_natCast]
   exact tendsto_pow_at_top (nat.cast_pos.mp hn).ne'
 #align tendsto_zpow_at_top_at_top Filter.tendsto_zpow_atTop_atTop
 -/
@@ -115,7 +115,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α →
   rw [is_O_with] at hcuv
   convert tendsto.at_top_div_const hc (tendsto_at_top_mono' l hcuv hu)
   ext x
-  rw [mul_div_cancel_left _ hc.ne.symm]
+  rw [mul_div_cancel_left₀ _ hc.ne.symm]
 #align asymptotics.is_O.trans_tendsto_norm_at_top Asymptotics.IsBigO.trans_tendsto_norm_atTop
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -112,7 +112,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α →
     (huv : u =O[l] v) (hu : Tendsto (fun x => ‖u x‖) l atTop) : Tendsto (fun x => ‖v x‖) l atTop :=
   by
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
-  rw [is_O_with] at hcuv 
+  rw [is_O_with] at hcuv
   convert tendsto.at_top_div_const hc (tendsto_at_top_mono' l hcuv hu)
   ext x
   rw [mul_div_cancel_left _ hc.ne.symm]
@@ -171,7 +171,7 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
   by
   have := ((is_o_one_iff ℝ).2 h).sum_range fun i => zero_le_one
-  simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this 
+  simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this
   exact this tendsto_nat_cast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -67,7 +67,7 @@ theorem Filter.tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) :
     Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
   by
   lift n to ℕ using hn.le
-  simp only [zpow_ofNat]
+  simp only [zpow_coe_nat]
   exact tendsto_pow_at_top (nat.cast_pos.mp hn).ne'
 #align tendsto_zpow_at_top_at_top Filter.tendsto_zpow_atTop_atTop
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

@@ -62,13 +62,14 @@ theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
 #align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBot
 -/
 
-#print tendsto_zpow_atTop_atTop /-
-theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
+#print Filter.tendsto_zpow_atTop_atTop /-
+theorem Filter.tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) :
+    Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
   by
   lift n to ℕ using hn.le
   simp only [zpow_ofNat]
   exact tendsto_pow_at_top (nat.cast_pos.mp hn).ne'
-#align tendsto_zpow_at_top_at_top tendsto_zpow_atTop_atTop
+#align tendsto_zpow_at_top_at_top Filter.tendsto_zpow_atTop_atTop
 -/
 
 #print tendsto_pow_div_pow_atTop_atTop /-
@@ -76,7 +77,7 @@ theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop :=
   by
   rw [tendsto_congr' pow_div_pow_eventuallyEq_atTop]
-  apply tendsto_zpow_atTop_atTop
+  apply Filter.tendsto_zpow_atTop_atTop
   linarith
 #align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTop
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2021 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 -/
-import Mathbin.Analysis.Normed.Order.Basic
-import Mathbin.Analysis.Asymptotics.Asymptotics
+import Analysis.Normed.Order.Basic
+import Analysis.Asymptotics.Asymptotics
 
 #align_import analysis.asymptotics.specific_asymptotics from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.asymptotics.specific_asymptotics
-! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Order.Basic
 import Mathbin.Analysis.Asymptotics.Asymptotics
 
+#align_import analysis.asymptotics.specific_asymptotics from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
+
 /-!
 # A collection of specific asymptotic results
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -28,6 +28,7 @@ open scoped Topology
 
 section NormedField
 
+#print Filter.IsBoundedUnder.isLittleO_sub_self_inv /-
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
 theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
@@ -38,6 +39,7 @@ theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedFi
   simp only [(· ∘ ·), norm_inv]
   exact (tendsto_norm_sub_self_punctured_nhds a).inv_tendsto_zero
 #align filter.is_bounded_under.is_o_sub_self_inv Filter.IsBoundedUnder.isLittleO_sub_self_inv
+-/
 
 end NormedField
 
@@ -45,19 +47,23 @@ section LinearOrderedField
 
 variable {𝕜 : Type _} [LinearOrderedField 𝕜]
 
+#print pow_div_pow_eventuallyEq_atTop /-
 theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atTop] fun x => x ^ ((p : ℤ) - q) :=
   by
   apply (eventually_gt_at_top (0 : 𝕜)).mono fun x hx => _
   simp [zpow_sub₀ hx.ne']
 #align pow_div_pow_eventually_eq_at_top pow_div_pow_eventuallyEq_atTop
+-/
 
+#print pow_div_pow_eventuallyEq_atBot /-
 theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atBot] fun x => x ^ ((p : ℤ) - q) :=
   by
   apply (eventually_lt_at_bot (0 : 𝕜)).mono fun x hx => _
   simp [zpow_sub₀ hx.ne]
 #align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBot
+-/
 
 #print tendsto_zpow_atTop_atTop /-
 theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
@@ -68,6 +74,7 @@ theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜
 #align tendsto_zpow_at_top_at_top tendsto_zpow_atTop_atTop
 -/
 
+#print tendsto_pow_div_pow_atTop_atTop /-
 theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop :=
   by
@@ -75,7 +82,9 @@ theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
   apply tendsto_zpow_atTop_atTop
   linarith
 #align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTop
+-/
 
+#print tendsto_pow_div_pow_atTop_zero /-
 theorem tendsto_pow_div_pow_atTop_zero [TopologicalSpace 𝕜] [OrderTopology 𝕜] {p q : ℕ}
     (hpq : p < q) : Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop (𝓝 0) :=
   by
@@ -83,6 +92,7 @@ theorem tendsto_pow_div_pow_atTop_zero [TopologicalSpace 𝕜] [OrderTopology 
   apply tendsto_zpow_atTop_zero
   linarith
 #align tendsto_pow_div_pow_at_top_zero tendsto_pow_div_pow_atTop_zero
+-/
 
 end LinearOrderedField
 
@@ -90,12 +100,14 @@ section NormedLinearOrderedField
 
 variable {𝕜 : Type _} [NormedLinearOrderedField 𝕜]
 
+#print Asymptotics.isLittleO_pow_pow_atTop_of_lt /-
 theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
     (fun x : 𝕜 => x ^ p) =o[atTop] fun x => x ^ q :=
   by
   refine' (is_o_iff_tendsto' _).mpr (tendsto_pow_div_pow_atTop_zero hpq)
   exact (eventually_gt_at_top 0).mono fun x hx hxq => (pow_ne_zero q hx.ne' hxq).elim
 #align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_lt
+-/
 
 #print Asymptotics.IsBigO.trans_tendsto_norm_atTop /-
 theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 𝕜} {l : Filter α}
@@ -117,6 +129,7 @@ open scoped BigOperators
 
 open Finset
 
+#print Asymptotics.IsLittleO.sum_range /-
 theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
     (h : f =o[atTop] g) (hg : 0 ≤ g) (h'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i :=
@@ -152,7 +165,9 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
       exact add_le_add hn (mul_le_mul_of_nonneg_left le_rfl (half_pos εpos).le)
     _ = ε * ‖∑ i in range n, g i‖ := by simp [B]; ring
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
+-/
 
+#print Asymptotics.isLittleO_sum_range_of_tendsto_zero /-
 theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]
     {f : ℕ → α} (h : Tendsto f atTop (𝓝 0)) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
@@ -161,7 +176,9 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
   simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this 
   exact this tendsto_nat_cast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
+-/
 
+#print Filter.Tendsto.cesaro_smul /-
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
     {l : E} (h : Tendsto u atTop (𝓝 l)) :
@@ -178,12 +195,15 @@ theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSp
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     rw [Algebra.id.smul_eq_mul, inv_mul_cancel nposℝ.ne']
 #align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smul
+-/
 
+#print Filter.Tendsto.cesaro /-
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro {u : ℕ → ℝ} {l : ℝ} (h : Tendsto u atTop (𝓝 l)) :
     Tendsto (fun n : ℕ => (n⁻¹ : ℝ) * ∑ i in range n, u i) atTop (𝓝 l) :=
   h.cesaro_smul
 #align filter.tendsto.cesaro Filter.Tendsto.cesaro
+-/
 
 end Real
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -133,7 +133,7 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
     exact Or.inr (h'g.congr fun n => (B n).symm)
   filter_upwards [is_o_iff.1 this (half_pos εpos), Ici_mem_at_top N] with n hn Nn
   calc
-    ‖∑ i in range n, f i‖ = ‖(∑ i in range N, f i) + ∑ i in Ico N n, f i‖ := by
+    ‖∑ i in range n, f i‖ = ‖∑ i in range N, f i + ∑ i in Ico N n, f i‖ := by
       rw [sum_range_add_sum_Ico _ Nn]
     _ ≤ ‖∑ i in range N, f i‖ + ‖∑ i in Ico N n, f i‖ := (norm_add_le _ _)
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in Ico N n, ε / 2 * g i :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -151,7 +151,6 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
       rw [← mul_sum]
       exact add_le_add hn (mul_le_mul_of_nonneg_left le_rfl (half_pos εpos).le)
     _ = ε * ‖∑ i in range n, g i‖ := by simp [B]; ring
-    
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 
 theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -131,7 +131,7 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
     by
     apply is_o_const_left.2
     exact Or.inr (h'g.congr fun n => (B n).symm)
-  filter_upwards [is_o_iff.1 this (half_pos εpos), Ici_mem_at_top N]with n hn Nn
+  filter_upwards [is_o_iff.1 this (half_pos εpos), Ici_mem_at_top N] with n hn Nn
   calc
     ‖∑ i in range n, f i‖ = ‖(∑ i in range N, f i) + ∑ i in Ico N n, f i‖ := by
       rw [sum_range_add_sum_Ico _ Nn]
@@ -171,11 +171,11 @@ theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSp
   rw [← tendsto_sub_nhds_zero_iff, ← is_o_one_iff ℝ]
   have := Asymptotics.isLittleO_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 h)
   apply ((is_O_refl (fun n : ℕ => (n : ℝ)⁻¹) at_top).smul_isLittleO this).congr' _ _
-  · filter_upwards [Ici_mem_at_top 1]with n npos
+  · filter_upwards [Ici_mem_at_top 1] with n npos
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     simp only [smul_sub, sum_sub_distrib, sum_const, card_range, sub_right_inj]
     rw [nsmul_eq_smul_cast ℝ, smul_smul, inv_mul_cancel nposℝ.ne', one_smul]
-  · filter_upwards [Ici_mem_at_top 1]with n npos
+  · filter_upwards [Ici_mem_at_top 1] with n npos
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     rw [Algebra.id.smul_eq_mul, inv_mul_cancel nposℝ.ne']
 #align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smul

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -102,7 +102,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α →
     (huv : u =O[l] v) (hu : Tendsto (fun x => ‖u x‖) l atTop) : Tendsto (fun x => ‖v x‖) l atTop :=
   by
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
-  rw [is_O_with] at hcuv
+  rw [is_O_with] at hcuv 
   convert tendsto.at_top_div_const hc (tendsto_at_top_mono' l hcuv hu)
   ext x
   rw [mul_div_cancel_left _ hc.ne.symm]
@@ -159,7 +159,7 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
   by
   have := ((is_o_one_iff ℝ).2 h).sum_range fun i => zero_le_one
-  simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this
+  simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this 
   exact this tendsto_nat_cast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -24,7 +24,7 @@ theory developped in `analysis.asymptotics.asymptotics`.
 
 open Filter Asymptotics
 
-open Topology
+open scoped Topology
 
 section NormedField
 
@@ -113,7 +113,7 @@ end NormedLinearOrderedField
 
 section Real
 
-open BigOperators
+open scoped BigOperators
 
 open Finset
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -28,12 +28,6 @@ open Topology
 
 section NormedField
 
-/- warning: filter.is_bounded_under.is_o_sub_self_inv -> Filter.IsBoundedUnder.isLittleO_sub_self_inv is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.is_o_sub_self_inv Filter.IsBoundedUnder.isLittleO_sub_self_invₓ'. -/
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
 theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
@@ -51,12 +45,6 @@ section LinearOrderedField
 
 variable {𝕜 : Type _} [LinearOrderedField 𝕜]
 
-/- warning: pow_div_pow_eventually_eq_at_top -> pow_div_pow_eventuallyEq_atTop is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pow_div_pow_eventually_eq_at_top pow_div_pow_eventuallyEq_atTopₓ'. -/
 theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atTop] fun x => x ^ ((p : ℤ) - q) :=
   by
@@ -64,12 +52,6 @@ theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
   simp [zpow_sub₀ hx.ne']
 #align pow_div_pow_eventually_eq_at_top pow_div_pow_eventuallyEq_atTop
 
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-Case conversion may be inaccurate. Consider using '#align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBotₓ'. -/
 theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atBot] fun x => x ^ ((p : ℤ) - q) :=
   by
@@ -86,12 +68,6 @@ theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜
 #align tendsto_zpow_at_top_at_top tendsto_zpow_atTop_atTop
 -/
 
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-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat q p) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTopₓ'. -/
 theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop :=
   by
@@ -100,12 +76,6 @@ theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
   linarith
 #align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTop
 
-/- warning: tendsto_pow_div_pow_at_top_zero -> tendsto_pow_div_pow_atTop_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : OrderTopology.{u1} 𝕜 _inst_2 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat Nat.hasLt p q) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : OrderTopology.{u1} 𝕜 _inst_2 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat p q) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
-Case conversion may be inaccurate. Consider using '#align tendsto_pow_div_pow_at_top_zero tendsto_pow_div_pow_atTop_zeroₓ'. -/
 theorem tendsto_pow_div_pow_atTop_zero [TopologicalSpace 𝕜] [OrderTopology 𝕜] {p q : ℕ}
     (hpq : p < q) : Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop (𝓝 0) :=
   by
@@ -120,12 +90,6 @@ section NormedLinearOrderedField
 
 variable {𝕜 : Type _} [NormedLinearOrderedField 𝕜]
 
-/- warning: asymptotics.is_o_pow_pow_at_top_of_lt -> Asymptotics.isLittleO_pow_pow_atTop_of_lt is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedLinearOrderedField.{u1} 𝕜] [_inst_2 : OrderTopology.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat Nat.hasLt p q) -> (Asymptotics.IsLittleO.{u1, u1, u1} 𝕜 𝕜 𝕜 (NormedLinearOrderedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedLinearOrderedField.toHasNorm.{u1} 𝕜 _inst_1) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) x p) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) x q))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedLinearOrderedField.{u1} 𝕜] [_inst_2 : OrderTopology.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat p q) -> (Asymptotics.IsLittleO.{u1, u1, u1} 𝕜 𝕜 𝕜 (NormedLinearOrderedField.toNorm.{u1} 𝕜 _inst_1) (NormedLinearOrderedField.toNorm.{u1} 𝕜 _inst_1) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))))) x p) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))))) x q))
-Case conversion may be inaccurate. Consider using '#align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_ltₓ'. -/
 theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
     (fun x : 𝕜 => x ^ p) =o[atTop] fun x => x ^ q :=
   by
@@ -153,12 +117,6 @@ open BigOperators
 
 open Finset
 
-/- warning: asymptotics.is_o.sum_range -> Asymptotics.IsLittleO.sum_range is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α} {g : Nat -> Real}, (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f g) -> (LE.le.{0} (Nat -> Real) (Pi.hasLe.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.hasLe)) (OfNat.ofNat.{0} (Nat -> Real) 0 (OfNat.mk.{0} (Nat -> Real) 0 (Zero.zero.{0} (Nat -> Real) (Pi.instZero.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.hasZero))))) g) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => g i)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{0} Real Real.preorder)) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => g i)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α} {g : Nat -> Real}, (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toNorm.{u1} α _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f g) -> (LE.le.{0} (Nat -> Real) (Pi.hasLe.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.instLEReal)) (OfNat.ofNat.{0} (Nat -> Real) 0 (Zero.toOfNat0.{0} (Nat -> Real) (Pi.instZero.{0, 0} Nat (fun (a._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.838 : Nat) => Real) (fun (i : Nat) => Real.instZeroReal)))) g) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => g i)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{0} Real Real.instPreorderReal)) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toNorm.{u1} α _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => g i)))
-Case conversion may be inaccurate. Consider using '#align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_rangeₓ'. -/
 theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
     (h : f =o[atTop] g) (hg : 0 ≤ g) (h'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i :=
@@ -196,12 +154,6 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
     
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 
-/- warning: asymptotics.is_o_sum_range_of_tendsto_zero -> Asymptotics.isLittleO_sum_range_of_tendsto_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zeroₓ'. -/
 theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]
     {f : ℕ → α} (h : Tendsto f atTop (𝓝 0)) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
@@ -211,12 +163,6 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
   exact this tendsto_nat_cast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 
-/- warning: filter.tendsto.cesaro_smul -> Filter.Tendsto.cesaro_smul is a dubious translation:
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-  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {u : Nat -> E} {l : E}, (Filter.Tendsto.{0, u1} Nat E u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l)) -> (Filter.Tendsto.{0, u1} Nat E (fun (n : Nat) => HSMul.hSMul.{0, u1, u1} Real E E (instHSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)))))) (Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smulₓ'. -/
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
     {l : E} (h : Tendsto u atTop (𝓝 l)) :
@@ -234,12 +180,6 @@ theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSp
     rw [Algebra.id.smul_eq_mul, inv_mul_cancel nposℝ.ne']
 #align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smul
 
-/- warning: filter.tendsto.cesaro -> Filter.Tendsto.cesaro is a dubious translation:
-lean 3 declaration is
-  forall {u : Nat -> Real} {l : Real}, (Filter.Tendsto.{0, 0} Nat Real u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) (Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l))
-but is expected to have type
-  forall {u : Nat -> Real} {l : Real}, (Filter.Tendsto.{0, 0} Nat Real u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)) (Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.cesaro Filter.Tendsto.cesaroₓ'. -/
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro {u : ℕ → ℝ} {l : ℝ} (h : Tendsto u atTop (𝓝 l)) :
     Tendsto (fun n : ℕ => (n⁻¹ : ℝ) * ∑ i in range n, u i) atTop (𝓝 l) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -192,9 +192,7 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
       by
       rw [← mul_sum]
       exact add_le_add hn (mul_le_mul_of_nonneg_left le_rfl (half_pos εpos).le)
-    _ = ε * ‖∑ i in range n, g i‖ := by
-      simp [B]
-      ring
+    _ = ε * ‖∑ i in range n, g i‖ := by simp [B]; ring
     
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 
 ! This file was ported from Lean 3 source module analysis.asymptotics.specific_asymptotics
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Asymptotics.Asymptotics
 /-!
 # A collection of specific asymptotic results
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains specific lemmas about asymptotics which don't have their place in the general
 theory developped in `analysis.asymptotics.asymptotics`.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

@@ -25,6 +25,12 @@ open Topology
 
 section NormedField
 
+/- warning: filter.is_bounded_under.is_o_sub_self_inv -> Filter.IsBoundedUnder.isLittleO_sub_self_inv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : Norm.{u2} E] {a : 𝕜} {f : 𝕜 -> E}, (Filter.IsBoundedUnder.{0, u1} Real 𝕜 (LE.le.{0} Real Real.hasLe) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) a (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.booleanAlgebra.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasSingleton.{u1} 𝕜) a))) (Function.comp.{succ u1, succ u2, 1} 𝕜 E Real (Norm.norm.{u2} E _inst_2) f)) -> (Asymptotics.IsLittleO.{u1, u2, u1} 𝕜 E 𝕜 _inst_2 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) a (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.booleanAlgebra.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasSingleton.{u1} 𝕜) a))) f (fun (x : 𝕜) => Inv.inv.{u1} 𝕜 (DivInvMonoid.toHasInv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) x a)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : Norm.{u1} E] {a : 𝕜} {f : 𝕜 -> E}, (Filter.IsBoundedUnder.{0, u2} Real 𝕜 (fun (x._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.26 : Real) (x._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.28 : Real) => LE.le.{0} Real Real.instLEReal x._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.26 x._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.28) (nhdsWithin.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) a (HasCompl.compl.{u2} (Set.{u2} 𝕜) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕜) (Set.instBooleanAlgebraSet.{u2} 𝕜)) (Singleton.singleton.{u2, u2} 𝕜 (Set.{u2} 𝕜) (Set.instSingletonSet.{u2} 𝕜) a))) (Function.comp.{succ u2, succ u1, 1} 𝕜 E Real (Norm.norm.{u1} E _inst_2) f)) -> (Asymptotics.IsLittleO.{u2, u1, u2} 𝕜 E 𝕜 _inst_2 (NormedField.toNorm.{u2} 𝕜 _inst_1) (nhdsWithin.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) a (HasCompl.compl.{u2} (Set.{u2} 𝕜) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕜) (Set.instBooleanAlgebraSet.{u2} 𝕜)) (Singleton.singleton.{u2, u2} 𝕜 (Set.{u2} 𝕜) (Set.instSingletonSet.{u2} 𝕜) a))) f (fun (x : 𝕜) => Inv.inv.{u2} 𝕜 (Field.toInv.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)) (HSub.hSub.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHSub.{u2} 𝕜 (Ring.toSub.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) x a)))
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.is_o_sub_self_inv Filter.IsBoundedUnder.isLittleO_sub_self_invₓ'. -/
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
 theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
@@ -42,6 +48,12 @@ section LinearOrderedField
 
 variable {𝕜 : Type _} [LinearOrderedField 𝕜]
 
+/- warning: pow_div_pow_eventually_eq_at_top -> pow_div_pow_eventuallyEq_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, Filter.EventuallyEq.{u1, u1} 𝕜 𝕜 (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x q)) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) q)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, Filter.EventuallyEq.{u1, u1} 𝕜 𝕜 (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (Nat.cast.{0} Int instNatCastInt p) (Nat.cast.{0} Int instNatCastInt q)))
+Case conversion may be inaccurate. Consider using '#align pow_div_pow_eventually_eq_at_top pow_div_pow_eventuallyEq_atTopₓ'. -/
 theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atTop] fun x => x ^ ((p : ℤ) - q) :=
   by
@@ -49,6 +61,12 @@ theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
   simp [zpow_sub₀ hx.ne']
 #align pow_div_pow_eventually_eq_at_top pow_div_pow_eventuallyEq_atTop
 
+/- warning: pow_div_pow_eventually_eq_at_bot -> pow_div_pow_eventuallyEq_atBot is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, Filter.EventuallyEq.{u1, u1} 𝕜 𝕜 (Filter.atBot.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x q)) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) q)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, Filter.EventuallyEq.{u1, u1} 𝕜 𝕜 (Filter.atBot.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) x (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) (Nat.cast.{0} Int instNatCastInt p) (Nat.cast.{0} Int instNatCastInt q)))
+Case conversion may be inaccurate. Consider using '#align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBotₓ'. -/
 theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atBot] fun x => x ^ ((p : ℤ) - q) :=
   by
@@ -56,13 +74,21 @@ theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
   simp [zpow_sub₀ hx.ne]
 #align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBot
 
+#print tendsto_zpow_atTop_atTop /-
 theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
   by
   lift n to ℕ using hn.le
   simp only [zpow_ofNat]
   exact tendsto_pow_at_top (nat.cast_pos.mp hn).ne'
 #align tendsto_zpow_at_top_at_top tendsto_zpow_atTop_atTop
+-/
 
+/- warning: tendsto_pow_div_pow_at_top_at_top -> tendsto_pow_div_pow_atTop_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, (LT.lt.{0} Nat Nat.hasLt q p) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat q p) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTopₓ'. -/
 theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop :=
   by
@@ -71,6 +97,12 @@ theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
   linarith
 #align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTop
 
+/- warning: tendsto_pow_div_pow_at_top_zero -> tendsto_pow_div_pow_atTop_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : OrderTopology.{u1} 𝕜 _inst_2 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat Nat.hasLt p q) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : OrderTopology.{u1} 𝕜 _inst_2 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat p q) -> (Filter.Tendsto.{u1, u1} 𝕜 𝕜 (fun (x : 𝕜) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x p) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x q)) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_div_pow_at_top_zero tendsto_pow_div_pow_atTop_zeroₓ'. -/
 theorem tendsto_pow_div_pow_atTop_zero [TopologicalSpace 𝕜] [OrderTopology 𝕜] {p q : ℕ}
     (hpq : p < q) : Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop (𝓝 0) :=
   by
@@ -85,6 +117,12 @@ section NormedLinearOrderedField
 
 variable {𝕜 : Type _} [NormedLinearOrderedField 𝕜]
 
+/- warning: asymptotics.is_o_pow_pow_at_top_of_lt -> Asymptotics.isLittleO_pow_pow_atTop_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedLinearOrderedField.{u1} 𝕜] [_inst_2 : OrderTopology.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat Nat.hasLt p q) -> (Asymptotics.IsLittleO.{u1, u1, u1} 𝕜 𝕜 𝕜 (NormedLinearOrderedField.toHasNorm.{u1} 𝕜 _inst_1) (NormedLinearOrderedField.toHasNorm.{u1} 𝕜 _inst_1) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) x p) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) x q))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedLinearOrderedField.{u1} 𝕜] [_inst_2 : OrderTopology.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toNormedField.{u1} 𝕜 _inst_1))))))) (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1))))))] {p : Nat} {q : Nat}, (LT.lt.{0} Nat instLTNat p q) -> (Asymptotics.IsLittleO.{u1, u1, u1} 𝕜 𝕜 𝕜 (NormedLinearOrderedField.toNorm.{u1} 𝕜 _inst_1) (NormedLinearOrderedField.toNorm.{u1} 𝕜 _inst_1) (Filter.atTop.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))))) x p) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 (NormedLinearOrderedField.toLinearOrderedField.{u1} 𝕜 _inst_1)))))))))) x q))
+Case conversion may be inaccurate. Consider using '#align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_ltₓ'. -/
 theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
     (fun x : 𝕜 => x ^ p) =o[atTop] fun x => x ^ q :=
   by
@@ -92,6 +130,7 @@ theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : 
   exact (eventually_gt_at_top 0).mono fun x hx hxq => (pow_ne_zero q hx.ne' hxq).elim
 #align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_lt
 
+#print Asymptotics.IsBigO.trans_tendsto_norm_atTop /-
 theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 𝕜} {l : Filter α}
     (huv : u =O[l] v) (hu : Tendsto (fun x => ‖u x‖) l atTop) : Tendsto (fun x => ‖v x‖) l atTop :=
   by
@@ -101,6 +140,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α →
   ext x
   rw [mul_div_cancel_left _ hc.ne.symm]
 #align asymptotics.is_O.trans_tendsto_norm_at_top Asymptotics.IsBigO.trans_tendsto_norm_atTop
+-/
 
 end NormedLinearOrderedField
 
@@ -110,6 +150,12 @@ open BigOperators
 
 open Finset
 
+/- warning: asymptotics.is_o.sum_range -> Asymptotics.IsLittleO.sum_range is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α} {g : Nat -> Real}, (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f g) -> (LE.le.{0} (Nat -> Real) (Pi.hasLe.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.hasLe)) (OfNat.ofNat.{0} (Nat -> Real) 0 (OfNat.mk.{0} (Nat -> Real) 0 (Zero.zero.{0} (Nat -> Real) (Pi.instZero.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.hasZero))))) g) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => g i)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{0} Real Real.preorder)) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => g i)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α} {g : Nat -> Real}, (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toNorm.{u1} α _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f g) -> (LE.le.{0} (Nat -> Real) (Pi.hasLe.{0, 0} Nat (fun (ᾰ : Nat) => Real) (fun (i : Nat) => Real.instLEReal)) (OfNat.ofNat.{0} (Nat -> Real) 0 (Zero.toOfNat0.{0} (Nat -> Real) (Pi.instZero.{0, 0} Nat (fun (a._@.Mathlib.Analysis.Asymptotics.SpecificAsymptotics._hyg.838 : Nat) => Real) (fun (i : Nat) => Real.instZeroReal)))) g) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => g i)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{0} Real Real.instPreorderReal)) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toNorm.{u1} α _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => g i)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_rangeₓ'. -/
 theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
     (h : f =o[atTop] g) (hg : 0 ≤ g) (h'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i :=
@@ -149,6 +195,12 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
     
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 
+/- warning: asymptotics.is_o_sum_range_of_tendsto_zero -> Asymptotics.isLittleO_sum_range_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (NormedAddGroup.toAddGroup.{u1} α (NormedAddCommGroup.toNormedAddGroup.{u1} α _inst_1))))))))))) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] {f : Nat -> α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)))))))))) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat α Real (NormedAddCommGroup.toNorm.{u1} α _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (fun (n : Nat) => Nat.cast.{0} Real Real.natCast n))
+Case conversion may be inaccurate. Consider using '#align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zeroₓ'. -/
 theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]
     {f : ℕ → α} (h : Tendsto f atTop (𝓝 0)) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
@@ -158,6 +210,12 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
   exact this tendsto_nat_cast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 
+/- warning: filter.tendsto.cesaro_smul -> Filter.Tendsto.cesaro_smul is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {u : Nat -> E} {l : E}, (Filter.Tendsto.{0, u1} Nat E u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l)) -> (Filter.Tendsto.{0, u1} Nat E (fun (n : Nat) => SMul.smul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {u : Nat -> E} {l : E}, (Filter.Tendsto.{0, u1} Nat E u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l)) -> (Filter.Tendsto.{0, u1} Nat E (fun (n : Nat) => HSMul.hSMul.{0, u1, u1} Real E E (instHSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)))))) (Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))) l))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smulₓ'. -/
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
     {l : E} (h : Tendsto u atTop (𝓝 l)) :
@@ -175,6 +233,12 @@ theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSp
     rw [Algebra.id.smul_eq_mul, inv_mul_cancel nposℝ.ne']
 #align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smul
 
+/- warning: filter.tendsto.cesaro -> Filter.Tendsto.cesaro is a dubious translation:
+lean 3 declaration is
+  forall {u : Nat -> Real} {l : Real}, (Filter.Tendsto.{0, 0} Nat Real u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) (Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l))
+but is expected to have type
+  forall {u : Nat -> Real} {l : Real}, (Filter.Tendsto.{0, 0} Nat Real u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)) (Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => u i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.cesaro Filter.Tendsto.cesaroₓ'. -/
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro {u : ℕ → ℝ} {l : ℝ} (h : Tendsto u atTop (𝓝 l)) :
     Tendsto (fun n : ℕ => (n⁻¹ : ℝ) * ∑ i in range n, u i) atTop (𝓝 l) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -27,14 +27,14 @@ section NormedField
 
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
-theorem Filter.IsBoundedUnder.isOCat_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
+theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
     {f : 𝕜 → E} (h : IsBoundedUnder (· ≤ ·) (𝓝[≠] a) (norm ∘ f)) :
     f =o[𝓝[≠] a] fun x => (x - a)⁻¹ :=
   by
-  refine' (h.is_O_const (one_ne_zero' ℝ)).trans_isOCat (is_o_const_left.2 <| Or.inr _)
+  refine' (h.is_O_const (one_ne_zero' ℝ)).trans_isLittleO (is_o_const_left.2 <| Or.inr _)
   simp only [(· ∘ ·), norm_inv]
   exact (tendsto_norm_sub_self_punctured_nhds a).inv_tendsto_zero
-#align filter.is_bounded_under.is_o_sub_self_inv Filter.IsBoundedUnder.isOCat_sub_self_inv
+#align filter.is_bounded_under.is_o_sub_self_inv Filter.IsBoundedUnder.isLittleO_sub_self_inv
 
 end NormedField
 
@@ -85,14 +85,14 @@ section NormedLinearOrderedField
 
 variable {𝕜 : Type _} [NormedLinearOrderedField 𝕜]
 
-theorem Asymptotics.isOCat_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
+theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
     (fun x : 𝕜 => x ^ p) =o[atTop] fun x => x ^ q :=
   by
   refine' (is_o_iff_tendsto' _).mpr (tendsto_pow_div_pow_atTop_zero hpq)
   exact (eventually_gt_at_top 0).mono fun x hx hxq => (pow_ne_zero q hx.ne' hxq).elim
-#align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isOCat_pow_pow_atTop_of_lt
+#align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_lt
 
-theorem Asymptotics.IsO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 𝕜} {l : Filter α}
+theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 𝕜} {l : Filter α}
     (huv : u =O[l] v) (hu : Tendsto (fun x => ‖u x‖) l atTop) : Tendsto (fun x => ‖v x‖) l atTop :=
   by
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
@@ -100,7 +100,7 @@ theorem Asymptotics.IsO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 
   convert tendsto.at_top_div_const hc (tendsto_at_top_mono' l hcuv hu)
   ext x
   rw [mul_div_cancel_left _ hc.ne.symm]
-#align asymptotics.is_O.trans_tendsto_norm_at_top Asymptotics.IsO.trans_tendsto_norm_atTop
+#align asymptotics.is_O.trans_tendsto_norm_at_top Asymptotics.IsBigO.trans_tendsto_norm_atTop
 
 end NormedLinearOrderedField
 
@@ -110,7 +110,7 @@ open BigOperators
 
 open Finset
 
-theorem Asymptotics.IsOCat.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
+theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
     (h : f =o[atTop] g) (hg : 0 ≤ g) (h'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i :=
   by
@@ -147,15 +147,16 @@ theorem Asymptotics.IsOCat.sum_range {α : Type _} [NormedAddCommGroup α] {f :
       simp [B]
       ring
     
-#align asymptotics.is_o.sum_range Asymptotics.IsOCat.sum_range
+#align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 
-theorem Asymptotics.isOCat_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α] {f : ℕ → α}
-    (h : Tendsto f atTop (𝓝 0)) : (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
+theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]
+    {f : ℕ → α} (h : Tendsto f atTop (𝓝 0)) :
+    (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) :=
   by
   have := ((is_o_one_iff ℝ).2 h).sum_range fun i => zero_le_one
   simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this
   exact this tendsto_nat_cast_atTop_atTop
-#align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isOCat_sum_range_of_tendsto_zero
+#align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
 theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
@@ -163,8 +164,8 @@ theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSp
     Tendsto (fun n : ℕ => (n⁻¹ : ℝ) • ∑ i in range n, u i) atTop (𝓝 l) :=
   by
   rw [← tendsto_sub_nhds_zero_iff, ← is_o_one_iff ℝ]
-  have := Asymptotics.isOCat_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 h)
-  apply ((is_O_refl (fun n : ℕ => (n : ℝ)⁻¹) at_top).smul_isOCat this).congr' _ _
+  have := Asymptotics.isLittleO_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 h)
+  apply ((is_O_refl (fun n : ℕ => (n : ℝ)⁻¹) at_top).smul_isLittleO this).congr' _ _
   · filter_upwards [Ici_mem_at_top 1]with n npos
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     simp only [smul_sub, sum_sub_distrib, sum_const, card_range, sub_right_inj]

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -27,7 +27,7 @@ section NormedField
 
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
-theorem Filter.IsBoundedUnder.isOCat_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [HasNorm E] {a : 𝕜}
+theorem Filter.IsBoundedUnder.isOCat_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
     {f : 𝕜 → E} (h : IsBoundedUnder (· ≤ ·) (𝓝[≠] a) (norm ∘ f)) :
     f =o[𝓝[≠] a] fun x => (x - a)⁻¹ :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -128,9 +128,9 @@ theorem Asymptotics.IsOCat.sum_range {α : Type _} [NormedAddCommGroup α] {f :
   calc
     ‖∑ i in range n, f i‖ = ‖(∑ i in range N, f i) + ∑ i in Ico N n, f i‖ := by
       rw [sum_range_add_sum_Ico _ Nn]
-    _ ≤ ‖∑ i in range N, f i‖ + ‖∑ i in Ico N n, f i‖ := norm_add_le _ _
+    _ ≤ ‖∑ i in range N, f i‖ + ‖∑ i in Ico N n, f i‖ := (norm_add_le _ _)
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in Ico N n, ε / 2 * g i :=
-      add_le_add le_rfl (norm_sum_le_of_le _ fun i hi => hN _ (mem_Ico.1 hi).1)
+      (add_le_add le_rfl (norm_sum_le_of_le _ fun i hi => hN _ (mem_Ico.1 hi).1))
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in range n, ε / 2 * g i :=
       by
       refine' add_le_add le_rfl _

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

@@ -13,7 +13,7 @@ import Mathlib.Analysis.NormedSpace.Basic
 # A collection of specific asymptotic results
 
 This file contains specific lemmas about asymptotics which don't have their place in the general
-theory developed in `Analysis.Asymptotics.Asymptotics`.
+theory developed in `Mathlib.Analysis.Asymptotics.Asymptotics`.
 -/
 
 

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -135,7 +135,7 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type*} [NormedAddC
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) := by
   have := ((isLittleO_one_iff ℝ).2 h).sum_range fun i => zero_le_one
   simp only [sum_const, card_range, Nat.smul_one_eq_coe] at this
-  exact this tendsto_nat_cast_atTop_atTop
+  exact this tendsto_natCast_atTop_atTop
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 
 /-- The Cesaro average of a converging sequence converges to the same limit. -/

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -114,7 +114,7 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type*} [NormedAddCommGroup α] {f
   calc
     ‖∑ i in range n, f i‖ = ‖(∑ i in range N, f i) + ∑ i in Ico N n, f i‖ := by
       rw [sum_range_add_sum_Ico _ Nn]
-    _ ≤ ‖∑ i in range N, f i‖ + ‖∑ i in Ico N n, f i‖ := (norm_add_le _ _)
+    _ ≤ ‖∑ i in range N, f i‖ + ‖∑ i in Ico N n, f i‖ := norm_add_le _ _
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in Ico N n, ε / 2 * g i :=
       (add_le_add le_rfl (norm_sum_le_of_le _ fun i hi => hN _ (mem_Ico.1 hi).1))
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in range n, ε / 2 * g i := by

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -85,7 +85,7 @@ theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type*} {u v : α → 
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
   rw [IsBigOWith] at hcuv
   convert Tendsto.atTop_div_const hc (tendsto_atTop_mono' l hcuv hu)
-  rw [mul_div_cancel_left _ hc.ne.symm]
+  rw [mul_div_cancel_left₀ _ hc.ne.symm]
 set_option linter.uppercaseLean3 false in
 #align asymptotics.is_O.trans_tendsto_norm_at_top Asymptotics.IsBigO.trans_tendsto_norm_atTop
 

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -57,14 +57,14 @@ theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop := by
   rw [tendsto_congr' pow_div_pow_eventuallyEq_atTop]
   apply tendsto_zpow_atTop_atTop
-  linarith
+  omega
 #align tendsto_pow_div_pow_at_top_at_top tendsto_pow_div_pow_atTop_atTop
 
 theorem tendsto_pow_div_pow_atTop_zero [TopologicalSpace 𝕜] [OrderTopology 𝕜] {p q : ℕ}
     (hpq : p < q) : Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop (𝓝 0) := by
   rw [tendsto_congr' pow_div_pow_eventuallyEq_atTop]
   apply tendsto_zpow_atTop_zero
-  linarith
+  omega
 #align tendsto_pow_div_pow_at_top_zero tendsto_pow_div_pow_atTop_zero
 
 end LinearOrderedField

Using BoundedSMul instead of NormedSpace makes these true more generally. The old proofs do not generalize, so are replaced with copies of the mul proofs.

The const_smul_self lemmas match the existing const_mul_self ones.

shake then reports that the imports can be reduced.

@@ -5,6 +5,7 @@ Authors: Anatole Dedecker
 -/
 import Mathlib.Analysis.Normed.Order.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
+import Mathlib.Analysis.NormedSpace.Basic
 
 #align_import analysis.asymptotics.specific_asymptotics from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

@@ -12,7 +12,7 @@ import Mathlib.Analysis.Asymptotics.Asymptotics
 # A collection of specific asymptotic results
 
 This file contains specific lemmas about asymptotics which don't have their place in the general
-theory developped in `Analysis.Asymptotics.Asymptotics`.
+theory developed in `Analysis.Asymptotics.Asymptotics`.
 -/
 
 

Also move it to the Filter namespace and drop Strict from some TC assumptions.

@@ -52,13 +52,6 @@ theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
   simp [zpow_sub₀ hx.ne]
 #align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBot
 
-theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) :
-    Tendsto (fun x : 𝕜 => x ^ n) atTop atTop := by
-  lift n to ℕ using hn.le
-  simp only [zpow_ofNat]
-  exact tendsto_pow_atTop (Nat.cast_pos.mp hn).ne'
-#align tendsto_zpow_at_top_at_top tendsto_zpow_atTop_atTop
-
 theorem tendsto_pow_div_pow_atTop_atTop {p q : ℕ} (hpq : q < p) :
     Tendsto (fun x : 𝕜 => x ^ p / x ^ q) atTop atTop := by
   rw [tendsto_congr' pow_div_pow_eventuallyEq_atTop]

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -151,11 +151,11 @@ theorem Filter.Tendsto.cesaro_smul {E : Type*} [NormedAddCommGroup E] [NormedSpa
   rw [← tendsto_sub_nhds_zero_iff, ← isLittleO_one_iff ℝ]
   have := Asymptotics.isLittleO_sum_range_of_tendsto_zero (tendsto_sub_nhds_zero_iff.2 h)
   apply ((isBigO_refl (fun n : ℕ => (n : ℝ)⁻¹) atTop).smul_isLittleO this).congr' _ _
-  · filter_upwards [Ici_mem_atTop 1]with n npos
+  · filter_upwards [Ici_mem_atTop 1] with n npos
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     simp only [smul_sub, sum_sub_distrib, sum_const, card_range, sub_right_inj]
     rw [nsmul_eq_smul_cast ℝ, smul_smul, inv_mul_cancel nposℝ.ne', one_smul]
-  · filter_upwards [Ici_mem_atTop 1]with n npos
+  · filter_upwards [Ici_mem_atTop 1] with n npos
     have nposℝ : (0 : ℝ) < n := Nat.cast_pos.2 npos
     rw [Algebra.id.smul_eq_mul, inv_mul_cancel nposℝ.ne']
 #align filter.tendsto.cesaro_smul Filter.Tendsto.cesaro_smul

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -24,7 +24,7 @@ section NormedField
 
 /-- If `f : 𝕜 → E` is bounded in a punctured neighborhood of `a`, then `f(x) = o((x - a)⁻¹)` as
 `x → a`, `x ≠ a`. -/
-theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type _} [NormedField 𝕜] [Norm E] {a : 𝕜}
+theorem Filter.IsBoundedUnder.isLittleO_sub_self_inv {𝕜 E : Type*} [NormedField 𝕜] [Norm E] {a : 𝕜}
     {f : 𝕜 → E} (h : IsBoundedUnder (· ≤ ·) (𝓝[≠] a) (norm ∘ f)) :
     f =o[𝓝[≠] a] fun x => (x - a)⁻¹ := by
   refine' (h.isBigO_const (one_ne_zero' ℝ)).trans_isLittleO (isLittleO_const_left.2 <| Or.inr _)
@@ -36,7 +36,7 @@ end NormedField
 
 section LinearOrderedField
 
-variable {𝕜 : Type _} [LinearOrderedField 𝕜]
+variable {𝕜 : Type*} [LinearOrderedField 𝕜]
 
 theorem pow_div_pow_eventuallyEq_atTop {p q : ℕ} :
     (fun x : 𝕜 => x ^ p / x ^ q) =ᶠ[atTop] fun x => x ^ ((p : ℤ) - q) := by
@@ -77,7 +77,7 @@ end LinearOrderedField
 
 section NormedLinearOrderedField
 
-variable {𝕜 : Type _} [NormedLinearOrderedField 𝕜]
+variable {𝕜 : Type*} [NormedLinearOrderedField 𝕜]
 
 theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : ℕ} (hpq : p < q) :
     (fun x : 𝕜 => x ^ p) =o[atTop] fun x => x ^ q := by
@@ -85,7 +85,7 @@ theorem Asymptotics.isLittleO_pow_pow_atTop_of_lt [OrderTopology 𝕜] {p q : 
   exact (eventually_gt_atTop 0).mono fun x hx hxq => (pow_ne_zero q hx.ne' hxq).elim
 #align asymptotics.is_o_pow_pow_at_top_of_lt Asymptotics.isLittleO_pow_pow_atTop_of_lt
 
-theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type _} {u v : α → 𝕜} {l : Filter α}
+theorem Asymptotics.IsBigO.trans_tendsto_norm_atTop {α : Type*} {u v : α → 𝕜} {l : Filter α}
     (huv : u =O[l] v) (hu : Tendsto (fun x => ‖u x‖) l atTop) :
     Tendsto (fun x => ‖v x‖) l atTop := by
   rcases huv.exists_pos with ⟨c, hc, hcuv⟩
@@ -103,7 +103,7 @@ open BigOperators
 
 open Finset
 
-theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
+theorem Asymptotics.IsLittleO.sum_range {α : Type*} [NormedAddCommGroup α] {f : ℕ → α} {g : ℕ → ℝ}
     (h : f =o[atTop] g) (hg : 0 ≤ g) (h'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i := by
   have A : ∀ i, ‖g i‖ = g i := fun i => Real.norm_of_nonneg (hg i)
@@ -136,7 +136,7 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
       ring
 #align asymptotics.is_o.sum_range Asymptotics.IsLittleO.sum_range
 
-theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAddCommGroup α]
+theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type*} [NormedAddCommGroup α]
     {f : ℕ → α} (h : Tendsto f atTop (𝓝 0)) :
     (fun n => ∑ i in range n, f i) =o[atTop] fun n => (n : ℝ) := by
   have := ((isLittleO_one_iff ℝ).2 h).sum_range fun i => zero_le_one
@@ -145,7 +145,7 @@ theorem Asymptotics.isLittleO_sum_range_of_tendsto_zero {α : Type _} [NormedAdd
 #align asymptotics.is_o_sum_range_of_tendsto_zero Asymptotics.isLittleO_sum_range_of_tendsto_zero
 
 /-- The Cesaro average of a converging sequence converges to the same limit. -/
-theorem Filter.Tendsto.cesaro_smul {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
+theorem Filter.Tendsto.cesaro_smul {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {u : ℕ → E}
     {l : E} (h : Tendsto u atTop (𝓝 l)) :
     Tendsto (fun n : ℕ => (n⁻¹ : ℝ) • ∑ i in range n, u i) atTop (𝓝 l) := by
   rw [← tendsto_sub_nhds_zero_iff, ← isLittleO_one_iff ℝ]

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module analysis.asymptotics.specific_asymptotics
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Order.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 
+#align_import analysis.asymptotics.specific_asymptotics from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # A collection of specific asymptotic results
 

100 sample uses of the new tactic gcongr, added in #3965.

@@ -127,15 +127,13 @@ theorem Asymptotics.IsLittleO.sum_range {α : Type _} [NormedAddCommGroup α] {f
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in Ico N n, ε / 2 * g i :=
       (add_le_add le_rfl (norm_sum_le_of_le _ fun i hi => hN _ (mem_Ico.1 hi).1))
     _ ≤ ‖∑ i in range N, f i‖ + ∑ i in range n, ε / 2 * g i := by
-      refine' add_le_add le_rfl _
+      gcongr
       apply sum_le_sum_of_subset_of_nonneg
       · rw [range_eq_Ico]
         exact Ico_subset_Ico (zero_le _) le_rfl
       · intro i _ _
         exact mul_nonneg (half_pos εpos).le (hg i)
-    _ ≤ ε / 2 * ‖∑ i in range n, g i‖ + ε / 2 * ∑ i in range n, g i := by
-      rw [← mul_sum]
-      exact add_le_add hn (mul_le_mul_of_nonneg_left le_rfl (half_pos εpos).le)
+    _ ≤ ε / 2 * ‖∑ i in range n, g i‖ + ε / 2 * ∑ i in range n, g i := by rw [← mul_sum]; gcongr
     _ = ε * ‖∑ i in range n, g i‖ := by
       simp only [B]
       ring

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -55,8 +55,8 @@ theorem pow_div_pow_eventuallyEq_atBot {p q : ℕ} :
   simp [zpow_sub₀ hx.ne]
 #align pow_div_pow_eventually_eq_at_bot pow_div_pow_eventuallyEq_atBot
 
-theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : 𝕜 => x ^ n) atTop atTop :=
-  by
+theorem tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) :
+    Tendsto (fun x : 𝕜 => x ^ n) atTop atTop := by
   lift n to ℕ using hn.le
   simp only [zpow_ofNat]
   exact tendsto_pow_atTop (Nat.cast_pos.mp hn).ne'

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>