analysis.asymptotics.superpolynomial_decay ⟷ Mathlib.Analysis.Asymptotics.SuperpolynomialDecay

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

@@ -5,7 +5,7 @@ Authors: Devon Tuma
 -/
 import Analysis.Asymptotics.Asymptotics
 import Analysis.Normed.Order.Basic
-import Data.Polynomial.Eval
+import Algebra.Polynomial.Eval
 import Topology.Algebra.Order.LiminfLimsup
 
 #align_import analysis.asymptotics.superpolynomial_decay from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"

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

@@ -125,7 +125,7 @@ theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (k * f) := fun z =>
   tendsto_nhds.2 fun s hs hs0 =>
     l.sets_of_superset ((tendsto_nhds.1 (hf <| z + 1)) s hs hs0) fun x hx => by
-      simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx
+      simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ] using hx
 #align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mul
 -/
 
@@ -142,7 +142,7 @@ theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n
   by
   induction' n with n hn
   · simpa only [one_mul, pow_zero] using hf
-  · simpa only [pow_succ, mul_assoc] using hn.param_mul
+  · simpa only [pow_succ', mul_assoc] using hn.param_mul
 #align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mul
 -/
 
@@ -283,7 +283,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
       ((eventually_map.1 hm).mp _)
   refine' (hk.eventually_ne_at_top 0).mono fun x hk0 hx => _
   refine' Eq.trans_le _ (mul_le_mul_of_nonneg_left hx <| abs_nonneg (k x)⁻¹)
-  rw [← abs_mul, ← mul_assoc, pow_succ, ← mul_assoc, inv_mul_cancel hk0, one_mul]
+  rw [← abs_mul, ← mul_assoc, pow_succ', ← mul_assoc, inv_mul_cancel hk0, one_mul]
 #align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder
 -/
 
@@ -291,7 +291,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) :=
   by
-  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_coe_nat] using h (n : ℤ)⟩
+  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_natCast] using h (n : ℤ)⟩
   by_cases hz : 0 ≤ z
   · lift z to ℕ using hz
     simpa using h z
@@ -361,7 +361,7 @@ theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ
   induction' n with n hn
   · simp
   ·
-    simpa [pow_succ, ← mul_comm k, mul_assoc,
+    simpa [pow_succ', ← mul_comm k, mul_assoc,
       superpolynomial_decay_param_mul_iff (k ^ n * f) hk] using hn
 #align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iff
 -/

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

@@ -291,7 +291,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) :=
   by
-  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_ofNat] using h (n : ℤ)⟩
+  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_coe_nat] using h (n : ℤ)⟩
   by_cases hz : 0 ≤ z
   · lift z to ℕ using hz
     simpa using h z

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
 -/
-import Mathbin.Analysis.Asymptotics.Asymptotics
-import Mathbin.Analysis.Normed.Order.Basic
-import Mathbin.Data.Polynomial.Eval
-import Mathbin.Topology.Algebra.Order.LiminfLimsup
+import Analysis.Asymptotics.Asymptotics
+import Analysis.Normed.Order.Basic
+import Data.Polynomial.Eval
+import Topology.Algebra.Order.LiminfLimsup
 
 #align_import analysis.asymptotics.superpolynomial_decay from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
-
-! This file was ported from Lean 3 source module analysis.asymptotics.superpolynomial_decay
-! 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.Asymptotics.Asymptotics
 import Mathbin.Analysis.Normed.Order.Basic
 import Mathbin.Data.Polynomial.Eval
 import Mathbin.Topology.Algebra.Order.LiminfLimsup
 
+#align_import analysis.asymptotics.superpolynomial_decay from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
+
 /-!
 # Super-Polynomial Function Decay
 

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

@@ -74,53 +74,72 @@ section CommSemiring
 
 variable [TopologicalSpace β] [CommSemiring β]
 
+#print Asymptotics.SuperpolynomialDecay.congr' /-
 theorem SuperpolynomialDecay.congr' (hf : SuperpolynomialDecay l k f) (hfg : f =ᶠ[l] g) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr' (EventuallyEq.mul (EventuallyEq.refl l _) hfg)
 #align asymptotics.superpolynomial_decay.congr' Asymptotics.SuperpolynomialDecay.congr'
+-/
 
+#print Asymptotics.SuperpolynomialDecay.congr /-
 theorem SuperpolynomialDecay.congr (hf : SuperpolynomialDecay l k f) (hfg : ∀ x, f x = g x) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr fun x => (congr_arg fun a => k x ^ z * a) <| hfg x
 #align asymptotics.superpolynomial_decay.congr Asymptotics.SuperpolynomialDecay.congr
+-/
 
+#print Asymptotics.superpolynomialDecay_zero /-
 @[simp]
 theorem superpolynomialDecay_zero (l : Filter α) (k : α → β) : SuperpolynomialDecay l k 0 :=
   fun z => by simpa only [Pi.zero_apply, MulZeroClass.mul_zero] using tendsto_const_nhds
 #align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zero
+-/
 
+#print Asymptotics.SuperpolynomialDecay.add /-
 theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f + g) := fun z => by
   simpa only [mul_add, add_zero, Pi.add_apply] using (hf z).add (hg z)
 #align asymptotics.superpolynomial_decay.add Asymptotics.SuperpolynomialDecay.add
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul /-
 theorem SuperpolynomialDecay.mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f * g) := fun z => by
   simpa only [mul_assoc, one_mul, MulZeroClass.mul_zero, pow_zero] using (hf z).mul (hg 0)
 #align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul_const /-
 theorem SuperpolynomialDecay.mul_const [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => f n * c := fun z => by
   simpa only [← mul_assoc, MulZeroClass.zero_mul] using tendsto.mul_const c (hf z)
 #align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_const
+-/
 
+#print Asymptotics.SuperpolynomialDecay.const_mul /-
 theorem SuperpolynomialDecay.const_mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => c * f n :=
   (hf.mul_const c).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.const_mul Asymptotics.SuperpolynomialDecay.const_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.param_mul /-
 theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (k * f) := fun z =>
   tendsto_nhds.2 fun s hs hs0 =>
     l.sets_of_superset ((tendsto_nhds.1 (hf <| z + 1)) s hs hs0) fun x hx => by
       simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx
 #align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul_param /-
 theorem SuperpolynomialDecay.mul_param (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (f * k) :=
   hf.param_mul.congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param Asymptotics.SuperpolynomialDecay.mul_param
+-/
 
+#print Asymptotics.SuperpolynomialDecay.param_pow_mul /-
 theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) :=
   by
@@ -128,24 +147,31 @@ theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n
   · simpa only [one_mul, pow_zero] using hf
   · simpa only [pow_succ, mul_assoc] using hn.param_mul
 #align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul_param_pow /-
 theorem SuperpolynomialDecay.mul_param_pow (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) :=
   (hf.param_pow_mul n).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_pow Asymptotics.SuperpolynomialDecay.mul_param_pow
+-/
 
+#print Asymptotics.SuperpolynomialDecay.polynomial_mul /-
 theorem SuperpolynomialDecay.polynomial_mul [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => (p.eval <| k x) * f x :=
   Polynomial.induction_on' p (fun p q hp hq => by simpa [add_mul] using hp.add hq) fun n c => by
     simpa [mul_assoc] using (hf.param_pow_mul n).const_mul c
 #align asymptotics.superpolynomial_decay.polynomial_mul Asymptotics.SuperpolynomialDecay.polynomial_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul_polynomial /-
 theorem SuperpolynomialDecay.mul_polynomial [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => f x * (p.eval <| k x) :=
   (hf.polynomial_mul p).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_polynomial Asymptotics.SuperpolynomialDecay.mul_polynomial
+-/
 
 end CommSemiring
 
@@ -153,6 +179,7 @@ section OrderedCommSemiring
 
 variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 
+#print Asymptotics.SuperpolynomialDecay.trans_eventuallyLE /-
 theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :
     SuperpolynomialDecay l k f := fun z =>
@@ -160,6 +187,7 @@ theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : Super
     (hfg.mp (hk.mono fun x hx hx' => mul_le_mul_of_nonneg_left hx' (pow_nonneg hx z)))
     (hfg'.mp (hk.mono fun x hx hx' => mul_le_mul_of_nonneg_left hx' (pow_nonneg hx z)))
 #align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLE
+-/
 
 end OrderedCommSemiring
 
@@ -169,20 +197,25 @@ variable [TopologicalSpace β] [LinearOrderedCommRing β] [OrderTopology β]
 
 variable (l k f)
 
+#print Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero /-
 theorem superpolynomialDecay_iff_abs_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => |k a ^ n * f a|) l (𝓝 0) :=
   ⟨fun h z => (tendsto_zero_iff_abs_tendsto_zero _).1 (h z), fun h z =>
     (tendsto_zero_iff_abs_tendsto_zero _).2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_abs_tendsto_zero Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero
+-/
 
+#print Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs /-
 theorem superpolynomialDecay_iff_superpolynomialDecay_abs :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => |k a|) fun a => |f a| :=
   (superpolynomialDecay_iff_abs_tendsto_zero l k f).trans
     (by simp_rw [superpolynomial_decay, abs_mul, abs_pow])
 #align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_abs Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs
+-/
 
 variable {l k f}
 
+#print Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le /-
 theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : abs ∘ g ≤ᶠ[l] abs ∘ f) : SuperpolynomialDecay l k g :=
   by
@@ -195,11 +228,14 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
     _ ≤ |k x ^ z| * |f x| := (mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _))
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
+-/
 
+#print Asymptotics.SuperpolynomialDecay.trans_abs_le /-
 theorem SuperpolynomialDecay.trans_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : ∀ x, |g x| ≤ |f x|) : SuperpolynomialDecay l k g :=
   hf.trans_eventually_abs_le (eventually_of_forall hfg)
 #align asymptotics.superpolynomial_decay.trans_abs_le Asymptotics.SuperpolynomialDecay.trans_abs_le
+-/
 
 end LinearOrderedCommRing
 
@@ -207,17 +243,21 @@ section Field
 
 variable [TopologicalSpace β] [Field β] (l k f)
 
+#print Asymptotics.superpolynomialDecay_mul_const_iff /-
 theorem superpolynomialDecay_mul_const_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => f n * c) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.mul_const c⁻¹).congr fun x => by simp [mul_assoc, mul_inv_cancel hc0], fun h =>
     h.mul_const c⟩
 #align asymptotics.superpolynomial_decay_mul_const_iff Asymptotics.superpolynomialDecay_mul_const_iff
+-/
 
+#print Asymptotics.superpolynomialDecay_const_mul_iff /-
 theorem superpolynomialDecay_const_mul_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => c * f n) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.const_mul c⁻¹).congr fun x => by simp [← mul_assoc, inv_mul_cancel hc0], fun h =>
     h.const_mul c⟩
 #align asymptotics.superpolynomial_decay_const_mul_iff Asymptotics.superpolynomialDecay_const_mul_iff
+-/
 
 variable {l k f}
 
@@ -229,6 +269,7 @@ variable [TopologicalSpace β] [LinearOrderedField β] [OrderTopology β]
 
 variable (f)
 
+#print Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder /-
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| :=
   by
@@ -247,7 +288,9 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
   refine' Eq.trans_le _ (mul_le_mul_of_nonneg_left hx <| abs_nonneg (k x)⁻¹)
   rw [← abs_mul, ← mul_assoc, pow_succ, ← mul_assoc, inv_mul_cancel hk0, one_mul]
 #align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder
+-/
 
+#print Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero /-
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) :=
   by
@@ -260,9 +303,11 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     have h : tendsto f l (𝓝 0) := by simpa using h 0
     exact MulZeroClass.zero_mul (0 : β) ▸ this.mul h
 #align asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero
+-/
 
 variable {f}
 
+#print Asymptotics.SuperpolynomialDecay.param_zpow_mul /-
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => k a ^ z * f a :=
   by
@@ -270,24 +315,32 @@ theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
   refine' fun z' => (hf <| z' + z).congr' ((hk.eventually_ne_at_top 0).mono fun x hx => _)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]
 #align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.mul_param_zpow /-
 theorem SuperpolynomialDecay.mul_param_zpow (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => f a * k a ^ z :=
   (hf.param_zpow_mul hk z).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_zpow Asymptotics.SuperpolynomialDecay.mul_param_zpow
+-/
 
+#print Asymptotics.SuperpolynomialDecay.inv_param_mul /-
 theorem SuperpolynomialDecay.inv_param_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (k⁻¹ * f) := by
   simpa using hf.param_zpow_mul hk (-1)
 #align asymptotics.superpolynomial_decay.inv_param_mul Asymptotics.SuperpolynomialDecay.inv_param_mul
+-/
 
+#print Asymptotics.SuperpolynomialDecay.param_inv_mul /-
 theorem SuperpolynomialDecay.param_inv_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (f * k⁻¹) :=
   (hf.inv_param_mul hk).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.param_inv_mul Asymptotics.SuperpolynomialDecay.param_inv_mul
+-/
 
 variable (f)
 
+#print Asymptotics.superpolynomialDecay_param_mul_iff /-
 theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (k * f) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h =>
@@ -295,12 +348,16 @@ theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
       ((hk.eventually_ne_atTop 0).mono fun x hx => by simp [← mul_assoc, inv_mul_cancel hx]),
     fun h => h.param_mul⟩
 #align asymptotics.superpolynomial_decay_param_mul_iff Asymptotics.superpolynomialDecay_param_mul_iff
+-/
 
+#print Asymptotics.superpolynomialDecay_mul_param_iff /-
 theorem superpolynomialDecay_mul_param_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm k] using superpolynomial_decay_param_mul_iff f hk
 #align asymptotics.superpolynomial_decay_mul_param_iff Asymptotics.superpolynomialDecay_mul_param_iff
+-/
 
+#print Asymptotics.superpolynomialDecay_param_pow_mul_iff /-
 theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f :=
   by
@@ -310,11 +367,14 @@ theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ
     simpa [pow_succ, ← mul_comm k, mul_assoc,
       superpolynomial_decay_param_mul_iff (k ^ n * f) hk] using hn
 #align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iff
+-/
 
+#print Asymptotics.superpolynomialDecay_mul_param_pow_iff /-
 theorem superpolynomialDecay_mul_param_pow_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm f] using superpolynomial_decay_param_pow_mul_iff f hk n
 #align asymptotics.superpolynomial_decay_mul_param_pow_iff Asymptotics.superpolynomialDecay_mul_param_pow_iff
+-/
 
 variable {f}
 
@@ -326,21 +386,26 @@ variable [NormedLinearOrderedField β]
 
 variable (l k f)
 
+#print Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero /-
 theorem superpolynomialDecay_iff_norm_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => ‖k a ^ n * f a‖) l (𝓝 0) :=
   ⟨fun h z => tendsto_zero_iff_norm_tendsto_zero.1 (h z), fun h z =>
     tendsto_zero_iff_norm_tendsto_zero.2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_norm_tendsto_zero Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero
+-/
 
+#print Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm /-
 theorem superpolynomialDecay_iff_superpolynomialDecay_norm :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => ‖k a‖) fun a => ‖f a‖ :=
   (superpolynomialDecay_iff_norm_tendsto_zero l k f).trans (by simp [superpolynomial_decay])
 #align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm
+-/
 
 variable {l k}
 
 variable [OrderTopology β]
 
+#print Asymptotics.superpolynomialDecay_iff_isBigO /-
 theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =O[l] fun a : α => k a ^ z :=
   by
@@ -359,7 +424,9 @@ theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     simp only [one_mul, neg_add z 1, zpow_add₀ ha0, ← mul_assoc, zpow_neg,
       mul_inv_cancel (zpow_ne_zero z ha0), zpow_one]
 #align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigO
+-/
 
+#print Asymptotics.superpolynomialDecay_iff_isLittleO /-
 theorem superpolynomialDecay_iff_isLittleO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =o[l] fun a : α => k a ^ z :=
   by
@@ -373,6 +440,7 @@ theorem superpolynomialDecay_iff_isLittleO (hk : Tendsto k l atTop) :
   refine' this.trans_is_O (is_O.of_bound 1 (hk0.mono fun x hkx => le_of_eq _))
   rw [one_mul, zpow_sub_one₀ hkx, mul_comm (k x), mul_assoc, inv_mul_cancel hkx, mul_one]
 #align asymptotics.superpolynomial_decay_iff_is_o Asymptotics.superpolynomialDecay_iff_isLittleO
+-/
 
 end NormedLinearOrderedField
 

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

@@ -194,7 +194,6 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
     |k x ^ z * g x| = |k x ^ z| * |g x| := abs_mul (k x ^ z) (g x)
     _ ≤ |k x ^ z| * |f x| := (mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _))
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
-    
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 
 theorem SuperpolynomialDecay.trans_abs_le (hf : SuperpolynomialDecay l k f)

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

@@ -186,7 +186,7 @@ variable {l k f}
 theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : abs ∘ g ≤ᶠ[l] abs ∘ f) : SuperpolynomialDecay l k g :=
   by
-  rw [superpolynomial_decay_iff_abs_tendsto_zero] at hf⊢
+  rw [superpolynomial_decay_iff_abs_tendsto_zero] at hf ⊢
   refine' fun z =>
     tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds (hf z)
       (eventually_of_forall fun x => abs_nonneg _) (hfg.mono fun x hx => _)
@@ -267,7 +267,7 @@ variable {f}
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => k a ^ z * f a :=
   by
-  rw [superpolynomial_decay_iff_zpow_tendsto_zero _ hk] at hf⊢
+  rw [superpolynomial_decay_iff_zpow_tendsto_zero _ hk] at hf ⊢
   refine' fun z' => (hf <| z' + z).congr' ((hk.eventually_ne_at_top 0).mono fun x hx => _)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]
 #align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mul

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

@@ -55,7 +55,7 @@ https://ncatlab.org/nlab/show/rapidly+decreasing+function
 
 namespace Asymptotics
 
-open Topology Polynomial
+open scoped Topology Polynomial
 
 open Filter
 

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

@@ -74,89 +74,41 @@ section CommSemiring
 
 variable [TopologicalSpace β] [CommSemiring β]
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.congr' Asymptotics.SuperpolynomialDecay.congr'ₓ'. -/
 theorem SuperpolynomialDecay.congr' (hf : SuperpolynomialDecay l k f) (hfg : f =ᶠ[l] g) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr' (EventuallyEq.mul (EventuallyEq.refl l _) hfg)
 #align asymptotics.superpolynomial_decay.congr' Asymptotics.SuperpolynomialDecay.congr'
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.congr Asymptotics.SuperpolynomialDecay.congrₓ'. -/
 theorem SuperpolynomialDecay.congr (hf : SuperpolynomialDecay l k f) (hfg : ∀ x, f x = g x) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr fun x => (congr_arg fun a => k x ^ z * a) <| hfg x
 #align asymptotics.superpolynomial_decay.congr Asymptotics.SuperpolynomialDecay.congr
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zeroₓ'. -/
 @[simp]
 theorem superpolynomialDecay_zero (l : Filter α) (k : α → β) : SuperpolynomialDecay l k 0 :=
   fun z => by simpa only [Pi.zero_apply, MulZeroClass.mul_zero] using tendsto_const_nhds
 #align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zero
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.add Asymptotics.SuperpolynomialDecay.addₓ'. -/
 theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f + g) := fun z => by
   simpa only [mul_add, add_zero, Pi.add_apply] using (hf z).add (hg z)
 #align asymptotics.superpolynomial_decay.add Asymptotics.SuperpolynomialDecay.add
 
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 theorem SuperpolynomialDecay.mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f * g) := fun z => by
   simpa only [mul_assoc, one_mul, MulZeroClass.mul_zero, pow_zero] using (hf z).mul (hg 0)
 #align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_constₓ'. -/
 theorem SuperpolynomialDecay.mul_const [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => f n * c := fun z => by
   simpa only [← mul_assoc, MulZeroClass.zero_mul] using tendsto.mul_const c (hf z)
 #align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_const
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.const_mul Asymptotics.SuperpolynomialDecay.const_mulₓ'. -/
 theorem SuperpolynomialDecay.const_mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => c * f n :=
   (hf.mul_const c).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.const_mul Asymptotics.SuperpolynomialDecay.const_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mulₓ'. -/
 theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (k * f) := fun z =>
   tendsto_nhds.2 fun s hs hs0 =>
@@ -164,23 +116,11 @@ theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
       simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx
 #align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param Asymptotics.SuperpolynomialDecay.mul_paramₓ'. -/
 theorem SuperpolynomialDecay.mul_param (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (f * k) :=
   hf.param_mul.congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param Asymptotics.SuperpolynomialDecay.mul_param
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mulₓ'. -/
 theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) :=
   by
@@ -189,23 +129,11 @@ theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n
   · simpa only [pow_succ, mul_assoc] using hn.param_mul
 #align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param_pow Asymptotics.SuperpolynomialDecay.mul_param_powₓ'. -/
 theorem SuperpolynomialDecay.mul_param_pow (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) :=
   (hf.param_pow_mul n).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_pow Asymptotics.SuperpolynomialDecay.mul_param_pow
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.polynomial_mul Asymptotics.SuperpolynomialDecay.polynomial_mulₓ'. -/
 theorem SuperpolynomialDecay.polynomial_mul [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => (p.eval <| k x) * f x :=
@@ -213,12 +141,6 @@ theorem SuperpolynomialDecay.polynomial_mul [ContinuousAdd β] [ContinuousMul β
     simpa [mul_assoc] using (hf.param_pow_mul n).const_mul c
 #align asymptotics.superpolynomial_decay.polynomial_mul Asymptotics.SuperpolynomialDecay.polynomial_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_polynomial Asymptotics.SuperpolynomialDecay.mul_polynomialₓ'. -/
 theorem SuperpolynomialDecay.mul_polynomial [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => f x * (p.eval <| k x) :=
@@ -231,12 +153,6 @@ section OrderedCommSemiring
 
 variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLEₓ'. -/
 theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :
     SuperpolynomialDecay l k f := fun z =>
@@ -253,24 +169,12 @@ variable [TopologicalSpace β] [LinearOrderedCommRing β] [OrderTopology β]
 
 variable (l k f)
 
-/- warning: asymptotics.superpolynomial_decay_iff_abs_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_tendsto_zero Asymptotics.superpolynomialDecay_iff_abs_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_abs_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => |k a ^ n * f a|) l (𝓝 0) :=
   ⟨fun h z => (tendsto_zero_iff_abs_tendsto_zero _).1 (h z), fun h z =>
     (tendsto_zero_iff_abs_tendsto_zero _).2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_abs_tendsto_zero Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_abs Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_absₓ'. -/
 theorem superpolynomialDecay_iff_superpolynomialDecay_abs :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => |k a|) fun a => |f a| :=
   (superpolynomialDecay_iff_abs_tendsto_zero l k f).trans
@@ -279,12 +183,6 @@ theorem superpolynomialDecay_iff_superpolynomialDecay_abs :
 
 variable {l k f}
 
-/- warning: asymptotics.superpolynomial_decay.trans_eventually_abs_le -> Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) l (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) g) (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_leₓ'. -/
 theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : abs ∘ g ≤ᶠ[l] abs ∘ f) : SuperpolynomialDecay l k g :=
   by
@@ -299,12 +197,6 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
     
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 
-/- warning: asymptotics.superpolynomial_decay.trans_abs_le -> Asymptotics.SuperpolynomialDecay.trans_abs_le is a dubious translation:
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-  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (g x)) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k g)
-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_abs_le Asymptotics.SuperpolynomialDecay.trans_abs_leₓ'. -/
 theorem SuperpolynomialDecay.trans_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : ∀ x, |g x| ≤ |f x|) : SuperpolynomialDecay l k g :=
   hf.trans_eventually_abs_le (eventually_of_forall hfg)
@@ -316,24 +208,12 @@ section Field
 
 variable [TopologicalSpace β] [Field β] (l k f)
 
-/- warning: asymptotics.superpolynomial_decay_mul_const_iff -> Asymptotics.superpolynomialDecay_mul_const_iff is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Field.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))] {c : β}, (Ne.{succ u2} β c (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))) (f n) c)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k f))
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_const_iff Asymptotics.superpolynomialDecay_mul_const_iffₓ'. -/
 theorem superpolynomialDecay_mul_const_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => f n * c) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.mul_const c⁻¹).congr fun x => by simp [mul_assoc, mul_inv_cancel hc0], fun h =>
     h.mul_const c⟩
 #align asymptotics.superpolynomial_decay_mul_const_iff Asymptotics.superpolynomialDecay_mul_const_iff
 
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 theorem superpolynomialDecay_const_mul_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => c * f n) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.const_mul c⁻¹).congr fun x => by simp [← mul_assoc, inv_mul_cancel hc0], fun h =>
@@ -350,12 +230,6 @@ variable [TopologicalSpace β] [LinearOrderedField β] [OrderTopology β]
 
 variable (f)
 
-/- warning: asymptotics.superpolynomial_decay_iff_abs_is_bounded_under -> Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnderₓ'. -/
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| :=
   by
@@ -375,12 +249,6 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
   rw [← abs_mul, ← mul_assoc, pow_succ, ← mul_assoc, inv_mul_cancel hk0, one_mul]
 #align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder
 
-/- warning: asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) :=
   by
@@ -396,12 +264,6 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
 
 variable {f}
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mulₓ'. -/
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => k a ^ z * f a :=
   by
@@ -410,34 +272,16 @@ theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]
 #align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param_zpow Asymptotics.SuperpolynomialDecay.mul_param_zpowₓ'. -/
 theorem SuperpolynomialDecay.mul_param_zpow (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => f a * k a ^ z :=
   (hf.param_zpow_mul hk z).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_zpow Asymptotics.SuperpolynomialDecay.mul_param_zpow
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.inv_param_mul Asymptotics.SuperpolynomialDecay.inv_param_mulₓ'. -/
 theorem SuperpolynomialDecay.inv_param_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (k⁻¹ * f) := by
   simpa using hf.param_zpow_mul hk (-1)
 #align asymptotics.superpolynomial_decay.inv_param_mul Asymptotics.SuperpolynomialDecay.inv_param_mul
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_inv_mul Asymptotics.SuperpolynomialDecay.param_inv_mulₓ'. -/
 theorem SuperpolynomialDecay.param_inv_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (f * k⁻¹) :=
   (hf.inv_param_mul hk).congr fun _ => mul_comm _ _
@@ -445,12 +289,6 @@ theorem SuperpolynomialDecay.param_inv_mul (hk : Tendsto k l atTop)
 
 variable (f)
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_param_mul_iff Asymptotics.superpolynomialDecay_param_mul_iffₓ'. -/
 theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (k * f) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h =>
@@ -459,23 +297,11 @@ theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
     fun h => h.param_mul⟩
 #align asymptotics.superpolynomial_decay_param_mul_iff Asymptotics.superpolynomialDecay_param_mul_iff
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_param_iff Asymptotics.superpolynomialDecay_mul_param_iffₓ'. -/
 theorem superpolynomialDecay_mul_param_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm k] using superpolynomial_decay_param_mul_iff f hk
 #align asymptotics.superpolynomial_decay_mul_param_iff Asymptotics.superpolynomialDecay_mul_param_iff
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iffₓ'. -/
 theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f :=
   by
@@ -486,12 +312,6 @@ theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ
       superpolynomial_decay_param_mul_iff (k ^ n * f) hk] using hn
 #align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iff
 
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_param_pow_iff Asymptotics.superpolynomialDecay_mul_param_pow_iffₓ'. -/
 theorem superpolynomialDecay_mul_param_pow_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm f] using superpolynomial_decay_param_pow_mul_iff f hk n
@@ -507,24 +327,12 @@ variable [NormedLinearOrderedField β]
 
 variable (l k f)
 
-/- warning: asymptotics.superpolynomial_decay_iff_norm_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_norm_tendsto_zero Asymptotics.superpolynomialDecay_iff_norm_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_norm_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => ‖k a ^ n * f a‖) l (𝓝 0) :=
   ⟨fun h z => tendsto_zero_iff_norm_tendsto_zero.1 (h z), fun h z =>
     tendsto_zero_iff_norm_tendsto_zero.2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_norm_tendsto_zero Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero
 
-/- warning: asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm -> Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β], Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (Asymptotics.SuperpolynomialDecay.{u1, 0} α Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.commSemiring l (fun (a : α) => Norm.norm.{u2} β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (k a)) (fun (a : α) => Norm.norm.{u2} β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (f a)))
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_normₓ'. -/
 theorem superpolynomialDecay_iff_superpolynomialDecay_norm :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => ‖k a‖) fun a => ‖f a‖ :=
   (superpolynomialDecay_iff_norm_tendsto_zero l k f).trans (by simp [superpolynomial_decay])
@@ -534,12 +342,6 @@ variable {l k}
 
 variable [OrderTopology β]
 
-/- warning: asymptotics.superpolynomial_decay_iff_is_O -> Asymptotics.superpolynomialDecay_iff_isBigO is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β] [_inst_2 : OrderTopology.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsBigO.{u1, u2, u2} α β β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) l f (fun (a : α) => HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (NormedDivisionRing.toDivisionRing.{u2} β (NormedField.toNormedDivisionRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1)))))) (k a) z)))
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-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigOₓ'. -/
 theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =O[l] fun a : α => k a ^ z :=
   by
@@ -559,12 +361,6 @@ theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
       mul_inv_cancel (zpow_ne_zero z ha0), zpow_one]
 #align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigO
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β] [_inst_2 : OrderTopology.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsLittleO.{u1, u2, u2} α β β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) l f (fun (a : α) => HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (NormedDivisionRing.toDivisionRing.{u2} β (NormedField.toNormedDivisionRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1)))))) (k a) z)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u1} β] [_inst_2 : OrderTopology.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1))))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsLittleO.{u2, u1, u1} α β β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (NormedLinearOrderedField.toNorm.{u1} β _inst_1) l f (fun (a : α) => HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (NormedDivisionRing.toDivisionRing.{u1} β (NormedField.toNormedDivisionRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1)))))) (k a) z)))
-Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_is_o Asymptotics.superpolynomialDecay_iff_isLittleOₓ'. -/
 theorem superpolynomialDecay_iff_isLittleO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =o[l] fun a : α => k a ^ z :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -233,7 +233,7 @@ variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 
 /- warning: asymptotics.superpolynomial_decay.trans_eventually_le -> Asymptotics.SuperpolynomialDecay.trans_eventuallyLE is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : OrderedCommSemiring.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))], (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (OrderedSemiring.toSemiring.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2)))))))))) k) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g') -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l g f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k f)
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : OrderedCommSemiring.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))], (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (OrderedSemiring.toSemiring.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2)))))))))) k) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g') -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l g f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k f)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21854 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLEₓ'. -/
@@ -281,7 +281,7 @@ variable {l k f}
 
 /- warning: asymptotics.superpolynomial_decay.trans_eventually_abs_le -> Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) l (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) g) (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) l (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) g) (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))) l (Function.comp.{succ u2, succ u1, succ u1} α β β (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))))))) g) (Function.comp.{succ u2, succ u1, succ u1} α β β (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k g)
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_leₓ'. -/
@@ -301,7 +301,7 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
 
 /- warning: asymptotics.superpolynomial_decay.trans_abs_le -> Asymptotics.SuperpolynomialDecay.trans_abs_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (g x)) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (g x)) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (g x)) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k g)
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_abs_le Asymptotics.SuperpolynomialDecay.trans_abs_leₓ'. -/
@@ -352,7 +352,7 @@ variable (f)
 
 /- warning: asymptotics.superpolynomial_decay_iff_abs_is_bounded_under -> Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) l (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (k a) z) (f a)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) l (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (k a) z) (f a)))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1979 : β) (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))) x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1979 x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981) l (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))))) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2)))))))) (k a) z) (f a)))))
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnderₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -235,7 +235,7 @@ variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : OrderedCommSemiring.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))], (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (OrderedSemiring.toSemiring.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2)))))))))) k) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g') -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l g f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k f)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21851 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21854 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLEₓ'. -/
 theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -235,7 +235,7 @@ variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : OrderedCommSemiring.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))], (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (OrderedSemiring.toSemiring.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2)))))))))) k) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g') -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l g f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k f)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21857 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21851 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLEₓ'. -/
 theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :
@@ -354,7 +354,7 @@ variable (f)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) l (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (k a) z) (f a)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 : β) (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1983 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))) x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1983) l (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))))) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2)))))))) (k a) z) (f a)))))
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1979 : β) (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))) x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1979 x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981) l (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))))) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2)))))))) (k a) z) (f a)))))
 Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnderₓ'. -/
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| :=

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: Devon Tuma
 
 ! This file was ported from Lean 3 source module analysis.asymptotics.superpolynomial_decay
-! 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.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Order.LiminfLimsup
 /-!
 # Super-Polynomial Function Decay
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines a predicate `asymptotics.superpolynomial_decay f` for a function satisfying
   one of following equivalent definitions (The definition is in terms of the first condition):
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

@@ -56,12 +56,14 @@ open Topology Polynomial
 
 open Filter
 
+#print Asymptotics.SuperpolynomialDecay /-
 /-- `f` has superpolynomial decay in parameter `k` along filter `l` if
   `k ^ n * f` tends to zero at `l` for all naturals `n` -/
 def SuperpolynomialDecay {α β : Type _} [TopologicalSpace β] [CommSemiring β] (l : Filter α)
     (k : α → β) (f : α → β) :=
   ∀ n : ℕ, Tendsto (fun a : α => k a ^ n * f a) l (𝓝 0)
 #align asymptotics.superpolynomial_decay Asymptotics.SuperpolynomialDecay
+-/
 
 variable {α β : Type _} {l : Filter α} {k : α → β} {f g g' : α → β}
 
@@ -69,41 +71,89 @@ section CommSemiring
 
 variable [TopologicalSpace β] [CommSemiring β]
 
+/- warning: asymptotics.superpolynomial_decay.congr' -> Asymptotics.SuperpolynomialDecay.congr' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Filter.EventuallyEq.{u1, u2} α β l f g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (Filter.EventuallyEq.{u2, u1} α β l f g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k g)
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.congr' Asymptotics.SuperpolynomialDecay.congr'ₓ'. -/
 theorem SuperpolynomialDecay.congr' (hf : SuperpolynomialDecay l k f) (hfg : f =ᶠ[l] g) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr' (EventuallyEq.mul (EventuallyEq.refl l _) hfg)
 #align asymptotics.superpolynomial_decay.congr' Asymptotics.SuperpolynomialDecay.congr'
 
+/- warning: asymptotics.superpolynomial_decay.congr -> Asymptotics.SuperpolynomialDecay.congr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (x : α), Eq.{succ u2} β (f x) (g x)) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (forall (x : α), Eq.{succ u1} β (f x) (g x)) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k g)
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.congr Asymptotics.SuperpolynomialDecay.congrₓ'. -/
 theorem SuperpolynomialDecay.congr (hf : SuperpolynomialDecay l k f) (hfg : ∀ x, f x = g x) :
     SuperpolynomialDecay l k g := fun z =>
   (hf z).congr fun x => (congr_arg fun a => k x ^ z * a) <| hfg x
 #align asymptotics.superpolynomial_decay.congr Asymptotics.SuperpolynomialDecay.congr
 
+/- warning: asymptotics.superpolynomial_decay_zero -> Asymptotics.superpolynomialDecay_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] (l : Filter.{u1} α) (k : α -> β), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β] (l : Filter.{u2} α) (k : α -> β), Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.20 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zeroₓ'. -/
 @[simp]
 theorem superpolynomialDecay_zero (l : Filter α) (k : α → β) : SuperpolynomialDecay l k 0 :=
   fun z => by simpa only [Pi.zero_apply, MulZeroClass.mul_zero] using tendsto_const_nhds
 #align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zero
 
+/- warning: asymptotics.superpolynomial_decay.add -> Asymptotics.SuperpolynomialDecay.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toHasAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHAdd.{max u1 u2} (α -> β) (Pi.instAdd.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) f g))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHAdd.{max u1 u2} (α -> β) (Pi.instAdd.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) f g))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.add Asymptotics.SuperpolynomialDecay.addₓ'. -/
 theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f + g) := fun z => by
   simpa only [mul_add, add_zero, Pi.add_apply] using (hf z).add (hg z)
 #align asymptotics.superpolynomial_decay.add Asymptotics.SuperpolynomialDecay.add
 
+/- warning: asymptotics.superpolynomial_decay.mul -> Asymptotics.SuperpolynomialDecay.mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) f g))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) f g))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mulₓ'. -/
 theorem SuperpolynomialDecay.mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f * g) := fun z => by
   simpa only [mul_assoc, one_mul, MulZeroClass.mul_zero, pow_zero] using (hf z).mul (hg 0)
 #align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mul
 
+/- warning: asymptotics.superpolynomial_decay.mul_const -> Asymptotics.SuperpolynomialDecay.mul_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (c : β), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) (f n) c))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (c : β), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))) (f n) c))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_constₓ'. -/
 theorem SuperpolynomialDecay.mul_const [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => f n * c := fun z => by
   simpa only [← mul_assoc, MulZeroClass.zero_mul] using tendsto.mul_const c (hf z)
 #align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_const
 
+/- warning: asymptotics.superpolynomial_decay.const_mul -> Asymptotics.SuperpolynomialDecay.const_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (c : β), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) c (f n)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (c : β), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))) c (f n)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.const_mul Asymptotics.SuperpolynomialDecay.const_mulₓ'. -/
 theorem SuperpolynomialDecay.const_mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => c * f n :=
   (hf.mul_const c).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.const_mul Asymptotics.SuperpolynomialDecay.const_mul
 
+/- warning: asymptotics.superpolynomial_decay.param_mul -> Asymptotics.SuperpolynomialDecay.param_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) k f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocSemiring.toMul.{u1} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} β (Semiring.toNonAssocSemiring.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mulₓ'. -/
 theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (k * f) := fun z =>
   tendsto_nhds.2 fun s hs hs0 =>
@@ -111,11 +161,23 @@ theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
       simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx
 #align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mul
 
+/- warning: asymptotics.superpolynomial_decay.mul_param -> Asymptotics.SuperpolynomialDecay.mul_param is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) f k))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocSemiring.toMul.{u1} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} β (Semiring.toNonAssocSemiring.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) f k))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param Asymptotics.SuperpolynomialDecay.mul_paramₓ'. -/
 theorem SuperpolynomialDecay.mul_param (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (f * k) :=
   hf.param_mul.congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param Asymptotics.SuperpolynomialDecay.mul_param
 
+/- warning: asymptotics.superpolynomial_decay.param_pow_mul -> Asymptotics.SuperpolynomialDecay.param_pow_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (n : Nat), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (α -> β) Nat (α -> β) (instHPow.{max u1 u2, 0} (α -> β) Nat (Pi.hasPow.{u1, u2, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u2} β (MonoidWithZero.toMonoid.{u2} β (Semiring.toMonoidWithZero.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) k n) f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (forall (n : Nat), Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocSemiring.toMul.{u1} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} β (Semiring.toNonAssocSemiring.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (α -> β) Nat (α -> β) (instHPow.{max u2 u1, 0} (α -> β) Nat (Pi.instPow.{u2, u1, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) k n) f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mulₓ'. -/
 theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) :=
   by
@@ -124,11 +186,23 @@ theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n
   · simpa only [pow_succ, mul_assoc] using hn.param_mul
 #align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mul
 
+/- warning: asymptotics.superpolynomial_decay.mul_param_pow -> Asymptotics.SuperpolynomialDecay.mul_param_pow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (n : Nat), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))))) f (HPow.hPow.{max u1 u2, 0, max u1 u2} (α -> β) Nat (α -> β) (instHPow.{max u1 u2, 0} (α -> β) Nat (Pi.hasPow.{u1, u2, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u2} β (MonoidWithZero.toMonoid.{u2} β (Semiring.toMonoidWithZero.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) k n)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : CommSemiring.{u1} β], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k f) -> (forall (n : Nat), Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 _inst_2 l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocSemiring.toMul.{u1} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} β (Semiring.toNonAssocSemiring.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) f (HPow.hPow.{max u2 u1, 0, max u2 u1} (α -> β) Nat (α -> β) (instHPow.{max u2 u1, 0} (α -> β) Nat (Pi.instPow.{u2, u1, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (CommSemiring.toSemiring.{u1} β _inst_2)))))) k n)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param_pow Asymptotics.SuperpolynomialDecay.mul_param_powₓ'. -/
 theorem SuperpolynomialDecay.mul_param_pow (hf : SuperpolynomialDecay l k f) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) :=
   (hf.param_pow_mul n).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_pow Asymptotics.SuperpolynomialDecay.mul_param_pow
 
+/- warning: asymptotics.superpolynomial_decay.polynomial_mul -> Asymptotics.SuperpolynomialDecay.polynomial_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toHasAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))] [_inst_4 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (p : Polynomial.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (x : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) (Polynomial.eval.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2) (k x) p) (f x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))] [_inst_4 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (p : Polynomial.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (x : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))) (Polynomial.eval.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2) (k x) p) (f x)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.polynomial_mul Asymptotics.SuperpolynomialDecay.polynomial_mulₓ'. -/
 theorem SuperpolynomialDecay.polynomial_mul [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => (p.eval <| k x) * f x :=
@@ -136,6 +210,12 @@ theorem SuperpolynomialDecay.polynomial_mul [ContinuousAdd β] [ContinuousMul β
     simpa [mul_assoc] using (hf.param_pow_mul n).const_mul c
 #align asymptotics.superpolynomial_decay.polynomial_mul Asymptotics.SuperpolynomialDecay.polynomial_mul
 
+/- warning: asymptotics.superpolynomial_decay.mul_polynomial -> Asymptotics.SuperpolynomialDecay.mul_polynomial is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toHasAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))] [_inst_4 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (p : Polynomial.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (x : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))) (f x) (Polynomial.eval.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2) (k x) p)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : CommSemiring.{u2} β] [_inst_3 : ContinuousAdd.{u2} β _inst_1 (Distrib.toAdd.{u2} β (NonUnitalNonAssocSemiring.toDistrib.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)))))] [_inst_4 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k f) -> (forall (p : Polynomial.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2)), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 _inst_2 l k (fun (x : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocSemiring.toMul.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2))))) (f x) (Polynomial.eval.{u2} β (CommSemiring.toSemiring.{u2} β _inst_2) (k x) p)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_polynomial Asymptotics.SuperpolynomialDecay.mul_polynomialₓ'. -/
 theorem SuperpolynomialDecay.mul_polynomial [ContinuousAdd β] [ContinuousMul β]
     (hf : SuperpolynomialDecay l k f) (p : β[X]) :
     SuperpolynomialDecay l k fun x => f x * (p.eval <| k x) :=
@@ -148,6 +228,12 @@ section OrderedCommSemiring
 
 variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 
+/- warning: asymptotics.superpolynomial_decay.trans_eventually_le -> Asymptotics.SuperpolynomialDecay.trans_eventuallyLE is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : OrderedCommSemiring.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))], (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l (OfNat.ofNat.{max u1 u2} (α -> β) 0 (OfNat.mk.{max u1 u2} (α -> β) 0 (Zero.zero.{max u1 u2} (α -> β) (Pi.instZero.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} β (Semiring.toNonAssocSemiring.{u2} β (OrderedSemiring.toSemiring.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2)))))))))) k) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k g') -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l g f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommMonoid.toPartialOrder.{u2} β (OrderedSemiring.toOrderedAddCommMonoid.{u2} β (OrderedCommSemiring.toOrderedSemiring.{u2} β _inst_2))))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u2} β _inst_2) l k f)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} {g' : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : OrderedCommSemiring.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))], (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l (OfNat.ofNat.{max u2 u1} (α -> β) 0 (Zero.toOfNat0.{max u2 u1} (α -> β) (Pi.instZero.{u2, u1} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.21857 : α) => β) (fun (i : α) => CommMonoidWithZero.toZero.{u1} β (CommSemiring.toCommMonoidWithZero.{u1} β (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2)))))) k) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k g') -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l g f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedSemiring.toPartialOrder.{u1} β (OrderedCommSemiring.toOrderedSemiring.{u1} β _inst_2)))) l f g') -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (OrderedCommSemiring.toCommSemiring.{u1} β _inst_2) l k f)
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLEₓ'. -/
 theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :
     SuperpolynomialDecay l k f := fun z =>
@@ -164,12 +250,24 @@ variable [TopologicalSpace β] [LinearOrderedCommRing β] [OrderTopology β]
 
 variable (l k f)
 
+/- warning: asymptotics.superpolynomial_decay_iff_abs_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) (forall (n : Nat), Filter.Tendsto.{u1, u2} α β (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (k a) n) (f a))) l (nhds.{u2} β _inst_1 (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (l : Filter.{u2} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) (forall (n : Nat), Filter.Tendsto.{u2, u1} α β (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (StrictOrderedSemiring.toSemiring.{u1} β (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} β (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2)))))))) (k a) n) (f a))) l (nhds.{u1} β _inst_1 (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β (CommMonoidWithZero.toZero.{u1} β (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} β (IsDomain.toCancelCommMonoidWithZero.{u1} β (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) (LinearOrderedRing.isDomain.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))))))))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_tendsto_zero Asymptotics.superpolynomialDecay_iff_abs_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_abs_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => |k a ^ n * f a|) l (𝓝 0) :=
   ⟨fun h z => (tendsto_zero_iff_abs_tendsto_zero _).1 (h z), fun h z =>
     (tendsto_zero_iff_abs_tendsto_zero _).2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_abs_tendsto_zero Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero
 
+/- warning: asymptotics.superpolynomial_decay_iff_superpolynomial_decay_abs -> Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (k a)) (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (f a)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (l : Filter.{u2} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (k a)) (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (f a)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_abs Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_absₓ'. -/
 theorem superpolynomialDecay_iff_superpolynomialDecay_abs :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => |k a|) fun a => |f a| :=
   (superpolynomialDecay_iff_abs_tendsto_zero l k f).trans
@@ -178,6 +276,12 @@ theorem superpolynomialDecay_iff_superpolynomialDecay_abs :
 
 variable {l k f}
 
+/- warning: asymptotics.superpolynomial_decay.trans_eventually_abs_le -> Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) l (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) g) (Function.comp.{succ u1, succ u2, succ u2} α β β (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) -> (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))) l (Function.comp.{succ u2, succ u1, succ u1} α β β (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))))))) g) (Function.comp.{succ u2, succ u1, succ u1} α β β (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))))))) f)) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k g)
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_leₓ'. -/
 theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : abs ∘ g ≤ᶠ[l] abs ∘ f) : SuperpolynomialDecay l k g :=
   by
@@ -192,6 +296,12 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
     
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 
+/- warning: asymptotics.superpolynomial_decay.trans_abs_le -> Asymptotics.SuperpolynomialDecay.trans_abs_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedCommRing.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))], (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (g x)) (Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (StrictOrderedRing.toRing.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β _inst_2)))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u2} β (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} β (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} β _inst_2))) l k g)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} {g : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedCommRing.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))], (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k f) -> (forall (x : α), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (g x)) (Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (StrictOrderedRing.toRing.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β _inst_2))))))) (f x))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (StrictOrderedCommSemiring.toCommSemiring.{u1} β (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} β (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} β _inst_2))) l k g)
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.trans_abs_le Asymptotics.SuperpolynomialDecay.trans_abs_leₓ'. -/
 theorem SuperpolynomialDecay.trans_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : ∀ x, |g x| ≤ |f x|) : SuperpolynomialDecay l k g :=
   hf.trans_eventually_abs_le (eventually_of_forall hfg)
@@ -203,12 +313,24 @@ section Field
 
 variable [TopologicalSpace β] [Field β] (l k f)
 
+/- warning: asymptotics.superpolynomial_decay_mul_const_iff -> Asymptotics.superpolynomialDecay_mul_const_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Field.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))] {c : β}, (Ne.{succ u2} β c (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))) (f n) c)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Field.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocRing.toMul.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2)))))] {c : β}, (Ne.{succ u2} β c (OfNat.ofNat.{u2} β 0 (Zero.toOfNat0.{u2} β (CommMonoidWithZero.toZero.{u2} β (CommGroupWithZero.toCommMonoidWithZero.{u2} β (Semifield.toCommGroupWithZero.{u2} β (Field.toSemifield.{u2} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocRing.toMul.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2)))))) (f n) c)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_const_iff Asymptotics.superpolynomialDecay_mul_const_iffₓ'. -/
 theorem superpolynomialDecay_mul_const_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => f n * c) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.mul_const c⁻¹).congr fun x => by simp [mul_assoc, mul_inv_cancel hc0], fun h =>
     h.mul_const c⟩
 #align asymptotics.superpolynomial_decay_mul_const_iff Asymptotics.superpolynomialDecay_mul_const_iff
 
+/- warning: asymptotics.superpolynomial_decay_const_mul_iff -> Asymptotics.superpolynomialDecay_const_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Field.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))] {c : β}, (Ne.{succ u2} β c (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2))))) c (f n))) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Field.{u2} β] [_inst_3 : ContinuousMul.{u2} β _inst_1 (NonUnitalNonAssocRing.toMul.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2)))))] {c : β}, (Ne.{succ u2} β c (OfNat.ofNat.{u2} β 0 (Zero.toOfNat0.{u2} β (CommMonoidWithZero.toZero.{u2} β (CommGroupWithZero.toCommMonoidWithZero.{u2} β (Semifield.toCommGroupWithZero.{u2} β (Field.toSemifield.{u2} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k (fun (n : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (NonUnitalNonAssocRing.toMul.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β _inst_2)))))) c (f n))) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (Field.toSemifield.{u2} β _inst_2)) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_const_mul_iff Asymptotics.superpolynomialDecay_const_mul_iffₓ'. -/
 theorem superpolynomialDecay_const_mul_iff [ContinuousMul β] {c : β} (hc0 : c ≠ 0) :
     (SuperpolynomialDecay l k fun n => c * f n) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h => (h.const_mul c⁻¹).congr fun x => by simp [← mul_assoc, inv_mul_cancel hc0], fun h =>
@@ -225,6 +347,12 @@ variable [TopologicalSpace β] [LinearOrderedField β] [OrderTopology β]
 
 variable (f)
 
+/- warning: asymptotics.superpolynomial_decay_iff_abs_is_bounded_under -> Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) l (fun (a : α) => Abs.abs.{u2} β (Neg.toHasAbs.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))))) (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β (LinearOrderedRing.toLinearOrder.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (k a) z) (f a)))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) (forall (z : Nat), Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 : β) (x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1983 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))) x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1981 x._@.Mathlib.Analysis.Asymptotics.SuperpolynomialDecay._hyg.1983) l (fun (a : α) => Abs.abs.{u1} β (Neg.toHasAbs.{u1} β (Ring.toNeg.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))) (SemilatticeSup.toSup.{u1} β (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedRing.toLinearOrder.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))))) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2)))))))) (k a) z) (f a)))))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnderₓ'. -/
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| :=
   by
@@ -244,6 +372,12 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
   rw [← abs_mul, ← mul_assoc, pow_succ, ← mul_assoc, inv_mul_cancel hk0, one_mul]
 #align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder
 
+/- warning: asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) (forall (z : Int), Filter.Tendsto.{u1, u2} α β (fun (a : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))) (k a) z) (f a)) l (nhds.{u2} β _inst_1 (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) (forall (z : Int), Filter.Tendsto.{u2, u1} α β (fun (a : α) => HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))) (k a) z) (f a)) l (nhds.{u1} β _inst_1 (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β (CommMonoidWithZero.toZero.{u1} β (CommGroupWithZero.toCommMonoidWithZero.{u1} β (Semifield.toCommGroupWithZero.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))))))))))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) :=
   by
@@ -259,6 +393,12 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
 
 variable {f}
 
+/- warning: asymptotics.superpolynomial_decay.param_zpow_mul -> Asymptotics.SuperpolynomialDecay.param_zpow_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) -> (forall (z : Int), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (fun (a : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))) (k a) z) (f a)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) -> (forall (z : Int), Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (fun (a : α) => HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))) (k a) z) (f a)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mulₓ'. -/
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => k a ^ z * f a :=
   by
@@ -267,16 +407,34 @@ theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]
 #align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mul
 
+/- warning: asymptotics.superpolynomial_decay.mul_param_zpow -> Asymptotics.SuperpolynomialDecay.mul_param_zpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) -> (forall (z : Int), Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (fun (a : α) => HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2)))))) (f a) (HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))) (k a) z)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) -> (forall (z : Int), Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (fun (a : α) => HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))))) (f a) (HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2))))) (k a) z)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.mul_param_zpow Asymptotics.SuperpolynomialDecay.mul_param_zpowₓ'. -/
 theorem SuperpolynomialDecay.mul_param_zpow (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => f a * k a ^ z :=
   (hf.param_zpow_mul hk z).congr fun _ => mul_comm _ _
 #align asymptotics.superpolynomial_decay.mul_param_zpow Asymptotics.SuperpolynomialDecay.mul_param_zpow
 
+/- warning: asymptotics.superpolynomial_decay.inv_param_mul -> Asymptotics.SuperpolynomialDecay.inv_param_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) (Inv.inv.{max u1 u2} (α -> β) (Pi.instInv.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => DivInvMonoid.toHasInv.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))) k) f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) (Inv.inv.{max u2 u1} (α -> β) (Pi.instInv.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => LinearOrderedField.toInv.{u1} β _inst_2)) k) f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.inv_param_mul Asymptotics.SuperpolynomialDecay.inv_param_mulₓ'. -/
 theorem SuperpolynomialDecay.inv_param_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (k⁻¹ * f) := by
   simpa using hf.param_zpow_mul hk (-1)
 #align asymptotics.superpolynomial_decay.inv_param_mul Asymptotics.SuperpolynomialDecay.inv_param_mul
 
+/- warning: asymptotics.superpolynomial_decay.param_inv_mul -> Asymptotics.SuperpolynomialDecay.param_inv_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f) -> (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) f (Inv.inv.{max u1 u2} (α -> β) (Pi.instInv.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => DivInvMonoid.toHasInv.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))) k)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} {f : α -> β} [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f) -> (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) f (Inv.inv.{max u2 u1} (α -> β) (Pi.instInv.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => LinearOrderedField.toInv.{u1} β _inst_2)) k)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay.param_inv_mul Asymptotics.SuperpolynomialDecay.param_inv_mulₓ'. -/
 theorem SuperpolynomialDecay.param_inv_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) : SuperpolynomialDecay l k (f * k⁻¹) :=
   (hf.inv_param_mul hk).congr fun _ => mul_comm _ _
@@ -284,6 +442,12 @@ theorem SuperpolynomialDecay.param_inv_mul (hk : Tendsto k l atTop)
 
 variable (f)
 
+/- warning: asymptotics.superpolynomial_decay_param_mul_iff -> Asymptotics.superpolynomialDecay_param_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) k f)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) k f)) (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_param_mul_iff Asymptotics.superpolynomialDecay_param_mul_iffₓ'. -/
 theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (k * f) ↔ SuperpolynomialDecay l k f :=
   ⟨fun h =>
@@ -292,11 +456,23 @@ theorem superpolynomialDecay_param_mul_iff (hk : Tendsto k l atTop) :
     fun h => h.param_mul⟩
 #align asymptotics.superpolynomial_decay_param_mul_iff Asymptotics.superpolynomialDecay_param_mul_iff
 
+/- warning: asymptotics.superpolynomial_decay_mul_param_iff -> Asymptotics.superpolynomialDecay_mul_param_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) f k)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) f k)) (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_param_iff Asymptotics.superpolynomialDecay_mul_param_iffₓ'. -/
 theorem superpolynomialDecay_mul_param_iff (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm k] using superpolynomial_decay_param_mul_iff f hk
 #align asymptotics.superpolynomial_decay_mul_param_iff Asymptotics.superpolynomialDecay_mul_param_iff
 
+/- warning: asymptotics.superpolynomial_decay_param_pow_mul_iff -> Asymptotics.superpolynomialDecay_param_pow_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (forall (n : Nat), Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (α -> β) Nat (α -> β) (instHPow.{max u1 u2, 0} (α -> β) Nat (Pi.hasPow.{u1, u2, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) k n) f)) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (forall (n : Nat), Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (α -> β) Nat (α -> β) (instHPow.{max u2 u1, 0} (α -> β) Nat (Pi.instPow.{u2, u1, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))))))))) k n) f)) (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iffₓ'. -/
 theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f :=
   by
@@ -307,6 +483,12 @@ theorem superpolynomialDecay_param_pow_mul_iff (hk : Tendsto k l atTop) (n : ℕ
       superpolynomial_decay_param_mul_iff (k ^ n * f) hk] using hn
 #align asymptotics.superpolynomial_decay_param_pow_mul_iff Asymptotics.superpolynomialDecay_param_pow_mul_iff
 
+/- warning: asymptotics.superpolynomial_decay_mul_param_pow_iff -> Asymptotics.superpolynomialDecay_mul_param_pow_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : LinearOrderedField.{u2} β] [_inst_3 : OrderTopology.{u2} β _inst_1 (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β _inst_2)))))))) -> (forall (n : Nat), Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (α -> β) (α -> β) (α -> β) (instHMul.{max u1 u2} (α -> β) (Pi.instMul.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) f (HPow.hPow.{max u1 u2, 0, max u1 u2} (α -> β) Nat (α -> β) (instHPow.{max u1 u2, 0} (α -> β) Nat (Pi.hasPow.{u1, u2, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (DivisionRing.toRing.{u2} β (Field.toDivisionRing.{u2} β (LinearOrderedField.toField.{u2} β _inst_2))))))) k n))) (Asymptotics.SuperpolynomialDecay.{u1, u2} α β _inst_1 (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β _inst_2))) l k f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : TopologicalSpace.{u1} β] [_inst_2 : LinearOrderedField.{u1} β] [_inst_3 : OrderTopology.{u1} β _inst_1 (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2)))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β _inst_2))))))) -> (forall (n : Nat), Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (α -> β) (α -> β) (α -> β) (instHMul.{max u2 u1} (α -> β) (Pi.instMul.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (DivisionRing.toRing.{u1} β (Field.toDivisionRing.{u1} β (LinearOrderedField.toField.{u1} β _inst_2)))))))) f (HPow.hPow.{max u2 u1, 0, max u2 u1} (α -> β) Nat (α -> β) (instHPow.{max u2 u1, 0} (α -> β) Nat (Pi.instPow.{u2, u1, 0} α Nat (fun (ᾰ : α) => β) (fun (i : α) => Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))))))))) k n))) (Asymptotics.SuperpolynomialDecay.{u2, u1} α β _inst_1 (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β _inst_2))) l k f))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_mul_param_pow_iff Asymptotics.superpolynomialDecay_mul_param_pow_iffₓ'. -/
 theorem superpolynomialDecay_mul_param_pow_iff (hk : Tendsto k l atTop) (n : ℕ) :
     SuperpolynomialDecay l k (f * k ^ n) ↔ SuperpolynomialDecay l k f := by
   simpa [mul_comm f] using superpolynomial_decay_param_pow_mul_iff f hk n
@@ -322,12 +504,24 @@ variable [NormedLinearOrderedField β]
 
 variable (l k f)
 
+/- warning: asymptotics.superpolynomial_decay_iff_norm_tendsto_zero -> Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β], Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (forall (n : Nat), Filter.Tendsto.{u1, 0} α Real (fun (a : α) => Norm.norm.{u2} β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (HMul.hMul.{u2, u2, u2} β β β (instHMul.{u2} β (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (NormedRing.toRing.{u2} β (NormedCommRing.toNormedRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (HPow.hPow.{u2, 0, u2} β Nat β (instHPow.{u2, 0} β Nat (Monoid.Pow.{u2} β (Ring.toMonoid.{u2} β (NormedRing.toRing.{u2} β (NormedCommRing.toNormedRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (k a) n) (f a))) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (l : Filter.{u2} α) (k : α -> β) (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u1} β], Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))) l k f) (forall (n : Nat), Filter.Tendsto.{u2, 0} α Real (fun (a : α) => Norm.norm.{u1} β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (HMul.hMul.{u1, u1, u1} β β β (instHMul.{u1} β (NonUnitalNonAssocRing.toMul.{u1} β (NonAssocRing.toNonUnitalNonAssocRing.{u1} β (Ring.toNonAssocRing.{u1} β (NormedRing.toRing.{u1} β (NormedCommRing.toNormedRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1)))))))) (HPow.hPow.{u1, 0, u1} β Nat β (instHPow.{u1, 0} β Nat (Monoid.Pow.{u1} β (MonoidWithZero.toMonoid.{u1} β (Semiring.toMonoidWithZero.{u1} β (DivisionSemiring.toSemiring.{u1} β (Semifield.toDivisionSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1))))))))) (k a) n) (f a))) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_norm_tendsto_zero Asymptotics.superpolynomialDecay_iff_norm_tendsto_zeroₓ'. -/
 theorem superpolynomialDecay_iff_norm_tendsto_zero :
     SuperpolynomialDecay l k f ↔ ∀ n : ℕ, Tendsto (fun a : α => ‖k a ^ n * f a‖) l (𝓝 0) :=
   ⟨fun h z => tendsto_zero_iff_norm_tendsto_zero.1 (h z), fun h z =>
     tendsto_zero_iff_norm_tendsto_zero.2 (h z)⟩
 #align asymptotics.superpolynomial_decay_iff_norm_tendsto_zero Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero
 
+/- warning: asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm -> Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (l : Filter.{u1} α) (k : α -> β) (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β], Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (Asymptotics.SuperpolynomialDecay.{u1, 0} α Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.commSemiring l (fun (a : α) => Norm.norm.{u2} β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (k a)) (fun (a : α) => Norm.norm.{u2} β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (f a)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (l : Filter.{u2} α) (k : α -> β) (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u1} β], Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))) l k f) (Asymptotics.SuperpolynomialDecay.{u2, 0} α Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instCommSemiringReal l (fun (a : α) => Norm.norm.{u1} β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (k a)) (fun (a : α) => Norm.norm.{u1} β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (f a)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_normₓ'. -/
 theorem superpolynomialDecay_iff_superpolynomialDecay_norm :
     SuperpolynomialDecay l k f ↔ SuperpolynomialDecay l (fun a => ‖k a‖) fun a => ‖f a‖ :=
   (superpolynomialDecay_iff_norm_tendsto_zero l k f).trans (by simp [superpolynomial_decay])
@@ -337,6 +531,12 @@ variable {l k}
 
 variable [OrderTopology β]
 
+/- warning: asymptotics.superpolynomial_decay_iff_is_O -> Asymptotics.superpolynomialDecay_iff_isBigO is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β] [_inst_2 : OrderTopology.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsBigO.{u1, u2, u2} α β β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) l f (fun (a : α) => HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (NormedDivisionRing.toDivisionRing.{u2} β (NormedField.toNormedDivisionRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1)))))) (k a) z)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u1} β] [_inst_2 : OrderTopology.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1))))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsBigO.{u2, u1, u1} α β β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (NormedLinearOrderedField.toNorm.{u1} β _inst_1) l f (fun (a : α) => HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (NormedDivisionRing.toDivisionRing.{u1} β (NormedField.toNormedDivisionRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1)))))) (k a) z)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigOₓ'. -/
 theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =O[l] fun a : α => k a ^ z :=
   by
@@ -356,6 +556,12 @@ theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
       mul_inv_cancel (zpow_ne_zero z ha0), zpow_one]
 #align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigO
 
+/- warning: asymptotics.superpolynomial_decay_iff_is_o -> Asymptotics.superpolynomialDecay_iff_isLittleO is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {l : Filter.{u1} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u2} β] [_inst_2 : OrderTopology.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))))))], (Filter.Tendsto.{u1, u2} α β k l (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (StrictOrderedRing.toOrderedAddCommGroup.{u2} β (LinearOrderedRing.toStrictOrderedRing.{u2} β (LinearOrderedCommRing.toLinearOrderedRing.{u2} β (LinearOrderedField.toLinearOrderedCommRing.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1))))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedRing.toPseudoMetricSpace.{u2} β (SeminormedCommRing.toSemiNormedRing.{u2} β (NormedCommRing.toSeminormedCommRing.{u2} β (NormedField.toNormedCommRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1))))))) (Semifield.toCommSemiring.{u2} β (LinearOrderedSemifield.toSemifield.{u2} β (LinearOrderedField.toLinearOrderedSemifield.{u2} β (NormedLinearOrderedField.toLinearOrderedField.{u2} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsLittleO.{u1, u2, u2} α β β (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) (NormedLinearOrderedField.toHasNorm.{u2} β _inst_1) l f (fun (a : α) => HPow.hPow.{u2, 0, u2} β Int β (instHPow.{u2, 0} β Int (DivInvMonoid.Pow.{u2} β (DivisionRing.toDivInvMonoid.{u2} β (NormedDivisionRing.toDivisionRing.{u2} β (NormedField.toNormedDivisionRing.{u2} β (NormedLinearOrderedField.toNormedField.{u2} β _inst_1)))))) (k a) z)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {l : Filter.{u2} α} {k : α -> β} (f : α -> β) [_inst_1 : NormedLinearOrderedField.{u1} β] [_inst_2 : OrderTopology.{u1} β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1))))))], (Filter.Tendsto.{u2, u1} α β k l (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (StrictOrderedRing.toPartialOrder.{u1} β (LinearOrderedRing.toStrictOrderedRing.{u1} β (LinearOrderedCommRing.toLinearOrderedRing.{u1} β (LinearOrderedField.toLinearOrderedCommRing.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))))))) -> (Iff (Asymptotics.SuperpolynomialDecay.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u1} β (PseudoMetricSpace.toUniformSpace.{u1} β (SeminormedRing.toPseudoMetricSpace.{u1} β (SeminormedCommRing.toSeminormedRing.{u1} β (NormedCommRing.toSeminormedCommRing.{u1} β (NormedField.toNormedCommRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1))))))) (Semifield.toCommSemiring.{u1} β (LinearOrderedSemifield.toSemifield.{u1} β (LinearOrderedField.toLinearOrderedSemifield.{u1} β (NormedLinearOrderedField.toLinearOrderedField.{u1} β _inst_1)))) l k f) (forall (z : Int), Asymptotics.IsLittleO.{u2, u1, u1} α β β (NormedLinearOrderedField.toNorm.{u1} β _inst_1) (NormedLinearOrderedField.toNorm.{u1} β _inst_1) l f (fun (a : α) => HPow.hPow.{u1, 0, u1} β Int β (instHPow.{u1, 0} β Int (DivInvMonoid.Pow.{u1} β (DivisionRing.toDivInvMonoid.{u1} β (NormedDivisionRing.toDivisionRing.{u1} β (NormedField.toNormedDivisionRing.{u1} β (NormedLinearOrderedField.toNormedField.{u1} β _inst_1)))))) (k a) z)))
+Case conversion may be inaccurate. Consider using '#align asymptotics.superpolynomial_decay_iff_is_o Asymptotics.superpolynomialDecay_iff_isLittleOₓ'. -/
 theorem superpolynomialDecay_iff_isLittleO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =o[l] fun a : α => k a ^ z :=
   by

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

@@ -337,7 +337,7 @@ variable {l k}
 
 variable [OrderTopology β]
 
-theorem superpolynomialDecay_iff_isO (hk : Tendsto k l atTop) :
+theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =O[l] fun a : α => k a ^ z :=
   by
   refine' (superpolynomial_decay_iff_zpow_tendsto_zero f hk).trans _
@@ -354,12 +354,12 @@ theorem superpolynomialDecay_iff_isO (hk : Tendsto k l atTop) :
         (is_O.of_bound 1 <| hk0.mono fun a ha0 => _)
     simp only [one_mul, neg_add z 1, zpow_add₀ ha0, ← mul_assoc, zpow_neg,
       mul_inv_cancel (zpow_ne_zero z ha0), zpow_one]
-#align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isO
+#align asymptotics.superpolynomial_decay_iff_is_O Asymptotics.superpolynomialDecay_iff_isBigO
 
-theorem superpolynomialDecay_iff_isOCat (hk : Tendsto k l atTop) :
+theorem superpolynomialDecay_iff_isLittleO (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, f =o[l] fun a : α => k a ^ z :=
   by
-  refine' ⟨fun h z => _, fun h => (superpolynomial_decay_iff_is_O f hk).2 fun z => (h z).IsO⟩
+  refine' ⟨fun h z => _, fun h => (superpolynomial_decay_iff_is_O f hk).2 fun z => (h z).IsBigO⟩
   have hk0 : ∀ᶠ x in l, k x ≠ 0 := hk.eventually_ne_at_top 0
   have : (fun x : α => (1 : β)) =o[l] k :=
     is_o_of_tendsto' (hk0.mono fun x hkx hkx' => absurd hkx' hkx)
@@ -368,7 +368,7 @@ theorem superpolynomialDecay_iff_isOCat (hk : Tendsto k l atTop) :
     simpa using this.mul_is_O ((superpolynomial_decay_iff_is_O f hk).1 h <| z - 1)
   refine' this.trans_is_O (is_O.of_bound 1 (hk0.mono fun x hkx => le_of_eq _))
   rw [one_mul, zpow_sub_one₀ hkx, mul_comm (k x), mul_assoc, inv_mul_cancel hkx, mul_one]
-#align asymptotics.superpolynomial_decay_iff_is_o Asymptotics.superpolynomialDecay_iff_isOCat
+#align asymptotics.superpolynomial_decay_iff_is_o Asymptotics.superpolynomialDecay_iff_isLittleO
 
 end NormedLinearOrderedField
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -81,7 +81,7 @@ theorem SuperpolynomialDecay.congr (hf : SuperpolynomialDecay l k f) (hfg : ∀
 
 @[simp]
 theorem superpolynomialDecay_zero (l : Filter α) (k : α → β) : SuperpolynomialDecay l k 0 :=
-  fun z => by simpa only [Pi.zero_apply, mul_zero] using tendsto_const_nhds
+  fun z => by simpa only [Pi.zero_apply, MulZeroClass.mul_zero] using tendsto_const_nhds
 #align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zero
 
 theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l k f)
@@ -91,12 +91,12 @@ theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l
 
 theorem SuperpolynomialDecay.mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f * g) := fun z => by
-  simpa only [mul_assoc, one_mul, mul_zero, pow_zero] using (hf z).mul (hg 0)
+  simpa only [mul_assoc, one_mul, MulZeroClass.mul_zero, pow_zero] using (hf z).mul (hg 0)
 #align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mul
 
 theorem SuperpolynomialDecay.mul_const [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => f n * c := fun z => by
-  simpa only [← mul_assoc, zero_mul] using tendsto.mul_const c (hf z)
+  simpa only [← mul_assoc, MulZeroClass.zero_mul] using tendsto.mul_const c (hf z)
 #align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_const
 
 theorem SuperpolynomialDecay.const_mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
@@ -234,7 +234,8 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
   obtain ⟨m, hm⟩ := h (z + 1)
   have h1 : tendsto (fun a : α => (0 : β)) l (𝓝 0) := tendsto_const_nhds
   have h2 : tendsto (fun a : α => |(k a)⁻¹| * m) l (𝓝 0) :=
-    zero_mul m ▸ tendsto.mul_const m ((tendsto_zero_iff_abs_tendsto_zero _).1 hk.inv_tendsto_at_top)
+    MulZeroClass.zero_mul m ▸
+      tendsto.mul_const m ((tendsto_zero_iff_abs_tendsto_zero _).1 hk.inv_tendsto_at_top)
   refine'
     tendsto_of_tendsto_of_tendsto_of_le_of_le' h1 h2 (eventually_of_forall fun x => abs_nonneg _)
       ((eventually_map.1 hm).mp _)
@@ -253,7 +254,7 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
   · have : tendsto (fun a => k a ^ z) l (𝓝 0) :=
       tendsto.comp (tendsto_zpow_atTop_zero (not_le.1 hz)) hk
     have h : tendsto f l (𝓝 0) := by simpa using h 0
-    exact zero_mul (0 : β) ▸ this.mul h
+    exact MulZeroClass.zero_mul (0 : β) ▸ this.mul h
 #align asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero
 
 variable {f}

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -148,13 +148,13 @@ section OrderedCommSemiring
 
 variable [TopologicalSpace β] [OrderedCommSemiring β] [OrderTopology β]
 
-theorem SuperpolynomialDecay.trans_eventuallyLe (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
+theorem SuperpolynomialDecay.trans_eventuallyLE (hk : 0 ≤ᶠ[l] k) (hg : SuperpolynomialDecay l k g)
     (hg' : SuperpolynomialDecay l k g') (hfg : g ≤ᶠ[l] f) (hfg' : f ≤ᶠ[l] g') :
     SuperpolynomialDecay l k f := fun z =>
   tendsto_of_tendsto_of_tendsto_of_le_of_le' (hg z) (hg' z)
     (hfg.mp (hk.mono fun x hx hx' => mul_le_mul_of_nonneg_left hx' (pow_nonneg hx z)))
     (hfg'.mp (hk.mono fun x hx hx' => mul_le_mul_of_nonneg_left hx' (pow_nonneg hx z)))
-#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLe
+#align asymptotics.superpolynomial_decay.trans_eventually_le Asymptotics.SuperpolynomialDecay.trans_eventuallyLE
 
 end OrderedCommSemiring
 

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

@@ -187,7 +187,7 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
       (eventually_of_forall fun x => abs_nonneg _) (hfg.mono fun x hx => _)
   calc
     |k x ^ z * g x| = |k x ^ z| * |g x| := abs_mul (k x ^ z) (g x)
-    _ ≤ |k x ^ z| * |f x| := mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _)
+    _ ≤ |k x ^ z| * |f x| := (mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _))
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
     
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le

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

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,9 +3,9 @@ Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
 -/
+import Mathlib.Algebra.Polynomial.Eval
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.Normed.Order.Basic
-import Mathlib.Data.Polynomial.Eval
 import Mathlib.Topology.Algebra.Order.LiminfLimsup
 
 #align_import analysis.asymptotics.superpolynomial_decay from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -105,7 +105,7 @@ theorem SuperpolynomialDecay.param_mul (hf : SuperpolynomialDecay l k f) :
     SuperpolynomialDecay l k (k * f) := fun z =>
   tendsto_nhds.2 fun s hs hs0 =>
     l.sets_of_superset ((tendsto_nhds.1 (hf <| z + 1)) s hs hs0) fun x hx => by
-      simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ'] using hx
+      simpa only [Set.mem_preimage, Pi.mul_apply, ← mul_assoc, ← pow_succ] using hx
 #align asymptotics.superpolynomial_decay.param_mul Asymptotics.SuperpolynomialDecay.param_mul
 
 theorem SuperpolynomialDecay.mul_param (hf : SuperpolynomialDecay l k f) :
@@ -117,7 +117,7 @@ theorem SuperpolynomialDecay.param_pow_mul (hf : SuperpolynomialDecay l k f) (n
     SuperpolynomialDecay l k (k ^ n * f) := by
   induction' n with n hn
   · simpa only [Nat.zero_eq, one_mul, pow_zero] using hf
-  · simpa only [pow_succ, mul_assoc] using hn.param_mul
+  · simpa only [pow_succ', mul_assoc] using hn.param_mul
 #align asymptotics.superpolynomial_decay.param_pow_mul Asymptotics.SuperpolynomialDecay.param_pow_mul
 
 theorem SuperpolynomialDecay.mul_param_pow (hf : SuperpolynomialDecay l k f) (n : ℕ) :
@@ -233,7 +233,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
       ((eventually_map.1 hm).mp _)
   refine' (hk.eventually_ne_atTop 0).mono fun x hk0 hx => _
   refine' Eq.trans_le _ (mul_le_mul_of_nonneg_left hx <| abs_nonneg (k x)⁻¹)
-  rw [← abs_mul, ← mul_assoc, pow_succ, ← mul_assoc, inv_mul_cancel hk0, one_mul]
+  rw [← abs_mul, ← mul_assoc, pow_succ', ← mul_assoc, inv_mul_cancel hk0, one_mul]
 #align asymptotics.superpolynomial_decay_iff_abs_is_bounded_under Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder
 
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

@@ -238,7 +238,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
 
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) := by
-  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_coe_nat] using h (n : ℤ)⟩
+  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_natCast] using h (n : ℤ)⟩
   by_cases hz : 0 ≤ z
   · unfold Tendsto
     lift z to ℕ using hz

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -157,7 +157,6 @@ end OrderedCommSemiring
 section LinearOrderedCommRing
 
 variable [TopologicalSpace β] [LinearOrderedCommRing β] [OrderTopology β]
-
 variable (l k f)
 
 theorem superpolynomialDecay_iff_abs_tendsto_zero :
@@ -216,7 +215,6 @@ end Field
 section LinearOrderedField
 
 variable [TopologicalSpace β] [LinearOrderedField β] [OrderTopology β]
-
 variable (f)
 
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
@@ -311,7 +309,6 @@ end LinearOrderedField
 section NormedLinearOrderedField
 
 variable [NormedLinearOrderedField β]
-
 variable (l k f)
 
 theorem superpolynomialDecay_iff_norm_tendsto_zero :
@@ -326,7 +323,6 @@ theorem superpolynomialDecay_iff_superpolynomialDecay_norm :
 #align asymptotics.superpolynomial_decay_iff_superpolynomial_decay_norm Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm
 
 variable {l k}
-
 variable [OrderTopology β]
 
 theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :

Previously these were syntactically identical to the corresponding zpow_coe_nat and coe_nat_zsmul lemmas, now they are about OfNat.ofNat.

Unfortunately, almost every call site uses the ofNat name to refer to Nat.cast, so the downstream proofs had to be adjusted too.

@@ -240,7 +240,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
 
 theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
     SuperpolynomialDecay l k f ↔ ∀ z : ℤ, Tendsto (fun a : α => k a ^ z * f a) l (𝓝 0) := by
-  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_ofNat] using h (n : ℤ)⟩
+  refine' ⟨fun h z => _, fun h n => by simpa only [zpow_coe_nat] using h (n : ℤ)⟩
   by_cases hz : 0 ≤ z
   · unfold Tendsto
     lift z to ℕ using hz

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -338,8 +338,8 @@ theorem superpolynomialDecay_iff_isBigO (hk : Tendsto k l atTop) :
     have : (fun a : α => k a ^ z)⁻¹ = fun a : α => k a ^ (-z) := funext fun x => by simp
     rw [div_eq_mul_inv, mul_comm f, this]
     exact h (-z)
-  · suffices : (fun a : α => k a ^ z * f a) =O[l] fun a : α => (k a)⁻¹
-    exact IsBigO.trans_tendsto this hk.inv_tendsto_atTop
+  · suffices (fun a : α => k a ^ z * f a) =O[l] fun a : α => (k a)⁻¹ from
+      IsBigO.trans_tendsto this hk.inv_tendsto_atTop
     refine'
       ((isBigO_refl (fun a => k a ^ z) l).mul (h (-(z + 1)))).trans
         (IsBigO.of_bound 1 <| hk0.mono fun a ha0 => _)

From LeanAPAP

@@ -182,7 +182,7 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
       (eventually_of_forall fun x => abs_nonneg _) (hfg.mono fun x hx => _)
   calc
     |k x ^ z * g x| = |k x ^ z| * |g x| := abs_mul (k x ^ z) (g x)
-    _ ≤ |k x ^ z| * |f x| := by gcongr; exact hx
+    _ ≤ |k x ^ z| * |f x| := by gcongr _ * ?_; exact hx
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -78,7 +78,7 @@ theorem SuperpolynomialDecay.congr (hf : SuperpolynomialDecay l k f) (hfg : ∀
 
 @[simp]
 theorem superpolynomialDecay_zero (l : Filter α) (k : α → β) : SuperpolynomialDecay l k 0 :=
-  fun z => by simpa only [Pi.zero_apply, MulZeroClass.mul_zero] using tendsto_const_nhds
+  fun z => by simpa only [Pi.zero_apply, mul_zero] using tendsto_const_nhds
 #align asymptotics.superpolynomial_decay_zero Asymptotics.superpolynomialDecay_zero
 
 theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l k f)
@@ -88,12 +88,12 @@ theorem SuperpolynomialDecay.add [ContinuousAdd β] (hf : SuperpolynomialDecay l
 
 theorem SuperpolynomialDecay.mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f)
     (hg : SuperpolynomialDecay l k g) : SuperpolynomialDecay l k (f * g) := fun z => by
-  simpa only [mul_assoc, one_mul, MulZeroClass.mul_zero, pow_zero] using (hf z).mul (hg 0)
+  simpa only [mul_assoc, one_mul, mul_zero, pow_zero] using (hf z).mul (hg 0)
 #align asymptotics.superpolynomial_decay.mul Asymptotics.SuperpolynomialDecay.mul
 
 theorem SuperpolynomialDecay.mul_const [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
     SuperpolynomialDecay l k fun n => f n * c := fun z => by
-  simpa only [← mul_assoc, MulZeroClass.zero_mul] using Tendsto.mul_const c (hf z)
+  simpa only [← mul_assoc, zero_mul] using Tendsto.mul_const c (hf z)
 #align asymptotics.superpolynomial_decay.mul_const Asymptotics.SuperpolynomialDecay.mul_const
 
 theorem SuperpolynomialDecay.const_mul [ContinuousMul β] (hf : SuperpolynomialDecay l k f) (c : β) :
@@ -228,7 +228,7 @@ theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
   obtain ⟨m, hm⟩ := h (z + 1)
   have h1 : Tendsto (fun _ : α => (0 : β)) l (𝓝 0) := tendsto_const_nhds
   have h2 : Tendsto (fun a : α => |(k a)⁻¹| * m) l (𝓝 0) :=
-    MulZeroClass.zero_mul m ▸
+    zero_mul m ▸
       Tendsto.mul_const m ((tendsto_zero_iff_abs_tendsto_zero _).1 hk.inv_tendsto_atTop)
   refine'
     tendsto_of_tendsto_of_tendsto_of_le_of_le' h1 h2 (eventually_of_forall fun x => abs_nonneg _)
@@ -248,7 +248,7 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
   · have : Tendsto (fun a => k a ^ z) l (𝓝 0) :=
       Tendsto.comp (tendsto_zpow_atTop_zero (not_le.1 hz)) hk
     have h : Tendsto f l (𝓝 0) := by simpa using h 0
-    exact MulZeroClass.zero_mul (0 : β) ▸ this.mul h
+    exact zero_mul (0 : β) ▸ this.mul h
 #align asymptotics.superpolynomial_decay_iff_zpow_tendsto_zero Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero
 
 variable {f}

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

This has nice performance benefits.

@@ -55,12 +55,12 @@ open Filter
 
 /-- `f` has superpolynomial decay in parameter `k` along filter `l` if
   `k ^ n * f` tends to zero at `l` for all naturals `n` -/
-def SuperpolynomialDecay {α β : Type _} [TopologicalSpace β] [CommSemiring β] (l : Filter α)
+def SuperpolynomialDecay {α β : Type*} [TopologicalSpace β] [CommSemiring β] (l : Filter α)
     (k : α → β) (f : α → β) :=
   ∀ n : ℕ, Tendsto (fun a : α => k a ^ n * f a) l (𝓝 0)
 #align asymptotics.superpolynomial_decay Asymptotics.SuperpolynomialDecay
 
-variable {α β : Type _} {l : Filter α} {k : α → β} {f g g' : α → β}
+variable {α β : Type*} {l : Filter α} {k : α → β} {f g g' : α → β}
 
 section CommSemiring
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
-
-! This file was ported from Lean 3 source module analysis.asymptotics.superpolynomial_decay
-! 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.Asymptotics.Asymptotics
 import Mathlib.Analysis.Normed.Order.Basic
 import Mathlib.Data.Polynomial.Eval
 import Mathlib.Topology.Algebra.Order.LiminfLimsup
 
+#align_import analysis.asymptotics.superpolynomial_decay from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Super-Polynomial Function Decay
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -179,7 +179,7 @@ variable {l k f}
 
 theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay l k f)
     (hfg : abs ∘ g ≤ᶠ[l] abs ∘ f) : SuperpolynomialDecay l k g := by
-  rw [superpolynomialDecay_iff_abs_tendsto_zero] at hf⊢
+  rw [superpolynomialDecay_iff_abs_tendsto_zero] at hf ⊢
   refine' fun z =>
     tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds (hf z)
       (eventually_of_forall fun x => abs_nonneg _) (hfg.mono fun x hx => _)
@@ -259,7 +259,7 @@ variable {f}
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
     (hf : SuperpolynomialDecay l k f) (z : ℤ) :
     SuperpolynomialDecay l k fun a => k a ^ z * f a := by
-  rw [superpolynomialDecay_iff_zpow_tendsto_zero _ hk] at hf⊢
+  rw [superpolynomialDecay_iff_zpow_tendsto_zero _ hk] at hf ⊢
   refine' fun z' => (hf <| z' + z).congr' ((hk.eventually_ne_atTop 0).mono fun x hx => _)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]
 #align asymptotics.superpolynomial_decay.param_zpow_mul Asymptotics.SuperpolynomialDecay.param_zpow_mul

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

@@ -185,7 +185,7 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
       (eventually_of_forall fun x => abs_nonneg _) (hfg.mono fun x hx => _)
   calc
     |k x ^ z * g x| = |k x ^ z| * |g x| := abs_mul (k x ^ z) (g x)
-    _ ≤ |k x ^ z| * |f x| := (mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _))
+    _ ≤ |k x ^ z| * |f x| := by gcongr; exact hx
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 

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".

@@ -223,8 +223,8 @@ variable [TopologicalSpace β] [LinearOrderedField β] [OrderTopology β]
 variable (f)
 
 theorem superpolynomialDecay_iff_abs_isBoundedUnder (hk : Tendsto k l atTop) :
-    SuperpolynomialDecay l k f ↔ ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| :=
-  by
+    SuperpolynomialDecay l k f ↔
+    ∀ z : ℕ, IsBoundedUnder (· ≤ ·) l fun a : α => |k a ^ z * f a| := by
   refine'
     ⟨fun h z => Tendsto.isBoundedUnder_le (Tendsto.abs (h z)), fun h =>
       (superpolynomialDecay_iff_abs_tendsto_zero l k f).2 fun z => _⟩
@@ -257,8 +257,8 @@ theorem superpolynomialDecay_iff_zpow_tendsto_zero (hk : Tendsto k l atTop) :
 variable {f}
 
 theorem SuperpolynomialDecay.param_zpow_mul (hk : Tendsto k l atTop)
-    (hf : SuperpolynomialDecay l k f) (z : ℤ) : SuperpolynomialDecay l k fun a => k a ^ z * f a :=
-  by
+    (hf : SuperpolynomialDecay l k f) (z : ℤ) :
+    SuperpolynomialDecay l k fun a => k a ^ z * f a := by
   rw [superpolynomialDecay_iff_zpow_tendsto_zero _ hk] at hf⊢
   refine' fun z' => (hf <| z' + z).congr' ((hk.eventually_ne_atTop 0).mono fun x hx => _)
   simp [zpow_add₀ hx, mul_assoc, Pi.mul_apply]

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -187,7 +187,6 @@ theorem SuperpolynomialDecay.trans_eventually_abs_le (hf : SuperpolynomialDecay
     |k x ^ z * g x| = |k x ^ z| * |g x| := abs_mul (k x ^ z) (g x)
     _ ≤ |k x ^ z| * |f x| := (mul_le_mul le_rfl hx (abs_nonneg _) (abs_nonneg _))
     _ = |k x ^ z * f x| := (abs_mul (k x ^ z) (f x)).symm
-
 #align asymptotics.superpolynomial_decay.trans_eventually_abs_le Asymptotics.SuperpolynomialDecay.trans_eventually_abs_le
 
 theorem SuperpolynomialDecay.trans_abs_le (hf : SuperpolynomialDecay l k f)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>