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

@@ -535,7 +535,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
   rw [tsub_add_cancel_of_le hy.le] at hm
   refine' eventually_at_top.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
-    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
+    NNReal.rpow_natCast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
 #align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_le
 -/
 

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

@@ -94,7 +94,7 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) p :=
   by
   have hp_fst_ne_zero : p.fst ≠ 0 := by intro h;
-    cases hp_fst <;> · rw [h] at hp_fst ; simpa using hp_fst
+    cases hp_fst <;> · rw [h] at hp_fst; simpa using hp_fst
   rw [continuousAt_congr (cpow_eq_nhds' hp_fst_ne_zero)]
   refine' continuous_exp.continuous_at.comp _
   refine'
@@ -251,7 +251,7 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
 theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
-  rw [ne_iff_lt_or_gt] at hp 
+  rw [ne_iff_lt_or_gt] at hp
   cases hp
   · rw [continuousAt_congr (rpow_eq_nhds_of_neg hp)]
     refine' ContinuousAt.mul _ (continuous_cos.continuous_at.comp _)
@@ -432,7 +432,7 @@ theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.
   by
   cases' p with z w
   rw [← not_lt_zero_iff, lt_iff_le_and_ne, not_and_or, Ne.def, Classical.not_not,
-    not_le_zero_iff] at h₁ 
+    not_le_zero_iff] at h₁
   rcases h₁ with (h₁ | (rfl : z = 0))
   exacts [continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
 #align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_pos
@@ -520,8 +520,8 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   rw [this]
   refine' continuous_real_to_nnreal.continuous_at.comp (ContinuousAt.comp _ _)
   · apply Real.continuousAt_rpow
-    simp only [Ne.def] at h 
-    rw [← NNReal.coe_eq_zero x] at h 
+    simp only [Ne.def] at h
+    rw [← NNReal.coe_eq_zero x] at h
     exact h
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
@@ -532,7 +532,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
   obtain ⟨m, hm⟩ := add_one_pow_unbounded_of_pos x (tsub_pos_of_lt hy)
-  rw [tsub_add_cancel_of_le hy.le] at hm 
+  rw [tsub_add_cancel_of_le hy.le] at hm
   refine' eventually_at_top.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
     NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))

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

@@ -416,7 +416,7 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
     refine' ⟨Real.exp (π * C), eventually_map.2 _⟩
     refine'
       (((continuous_im.comp continuous_snd).abs.Tendsto (_, z)).Eventually (gt_mem_nhds hC)).mono
-        fun z hz => Real.exp_le_exp.2 <| (neg_le_abs_self _).trans _
+        fun z hz => Real.exp_le_exp.2 <| (neg_le_abs _).trans _
     rw [_root_.abs_mul]
     exact
       mul_le_mul (abs_le.2 ⟨(neg_pi_lt_arg _).le, arg_le_pi _⟩) hz.le (_root_.abs_nonneg _)

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

@@ -515,7 +515,7 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
       Real.toNNReal ∘ (fun p : ℝ × ℝ => p.1 ^ p.2) ∘ fun p : ℝ≥0 × ℝ => (p.1.1, p.2) :=
     by
     ext p
-    rw [coe_rpow, Real.coe_toNNReal _ (Real.rpow_nonneg_of_nonneg p.1.2 _)]
+    rw [coe_rpow, Real.coe_toNNReal _ (Real.rpow_nonneg p.1.2 _)]
     rfl
   rw [this]
   refine' continuous_real_to_nnreal.continuous_at.comp (ContinuousAt.comp _ _)

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

@@ -535,7 +535,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
   rw [tsub_add_cancel_of_le hy.le] at hm 
   refine' eventually_at_top.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
-    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow hy.le (m.le_succ.trans hn))
+    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
 #align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_le
 -/
 

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

@@ -70,7 +70,7 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
 -- Continuity of `λ x, a ^ x`: union of these two lemmas is optimal.
 theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
-  have cpow_eq : (fun x : ℂ => a ^ x) = fun x => exp (log a * x) := by ext1 b;
+  have cpow_eq : (fun x : ℂ => a ^ x) = fun x => NormedSpace.exp (log a * x) := by ext1 b;
     rw [cpow_def_of_ne_zero ha]
   rw [cpow_eq]
   exact continuous_exp.continuous_at.comp (ContinuousAt.mul continuousAt_const continuousAt_id)
@@ -273,7 +273,7 @@ theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
   cases' p with x y
   obtain hx | rfl := ne_or_eq x 0
   · exact continuous_at_rpow_of_ne (x, y) hx
-  have A : tendsto (fun p : ℝ × ℝ => exp (log p.1 * p.2)) (𝓝[≠] 0 ×ᶠ 𝓝 y) (𝓝 0) :=
+  have A : tendsto (fun p : ℝ × ℝ => NormedSpace.exp (log p.1 * p.2)) (𝓝[≠] 0 ×ᶠ 𝓝 y) (𝓝 0) :=
     tendsto_exp_at_bot.comp
       ((tendsto_log_nhds_within_zero.comp tendsto_fst).atBot_mul hp tendsto_snd)
   have B : tendsto (fun p : ℝ × ℝ => p.1 ^ p.2) (𝓝[≠] 0 ×ᶠ 𝓝 y) (𝓝 0) :=
@@ -468,7 +468,8 @@ theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
       continuous_of_real.continuous_at.prod_map continuousAt_id
     exact @ContinuousAt.comp (ℝ × ℂ) (ℂ × ℂ) ℂ _ _ _ _ (fun p => ⟨↑p.1, p.2⟩) ⟨0, y⟩ A B
   · -- x < 0 : difficult case
-    suffices ContinuousAt (fun p => (-↑p.1) ^ p.2 * exp (π * I * p.2) : ℝ × ℂ → ℂ) (x, y)
+    suffices
+      ContinuousAt (fun p => (-↑p.1) ^ p.2 * NormedSpace.exp (π * I * p.2) : ℝ × ℂ → ℂ) (x, y)
       by
       refine' this.congr (eventually_of_mem (prod_mem_nhds (Iio_mem_nhds hx) univ_mem) _)
       exact fun p hp => (of_real_cpow_of_nonpos (le_of_lt hp.1) p.2).symm

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
   Rémy Degenne, David Loeffler
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow.Asymptotics
+import Analysis.SpecialFunctions.Pow.Asymptotics
 
 #align_import analysis.special_functions.pow.continuity from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -3,14 +3,11 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
   Rémy Degenne, David Loeffler
-
-! This file was ported from Lean 3 source module analysis.special_functions.pow.continuity
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Pow.Asymptotics
 
+#align_import analysis.special_functions.pow.continuity from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Continuity of power functions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -415,7 +415,7 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
         (continuous_fst.norm.tendsto _).rpow ((continuous_re.comp continuous_snd).Tendsto _) _ <;>
       simp [hz, Real.zero_rpow hz.ne']
   · simp only [(· ∘ ·), Real.norm_eq_abs, abs_of_pos (Real.exp_pos _)]
-    rcases exists_gt (|im z|) with ⟨C, hC⟩
+    rcases exists_gt |im z| with ⟨C, hC⟩
     refine' ⟨Real.exp (π * C), eventually_map.2 _⟩
     refine'
       (((continuous_im.comp continuous_snd).abs.Tendsto (_, z)).Eventually (gt_mem_nhds hC)).mono

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

@@ -38,20 +38,25 @@ open Complex
 
 variable {α : Type _}
 
+#print zero_cpow_eq_nhds /-
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
   exact this.mono fun x hx => by dsimp only; rw [zero_cpow hx, Pi.zero_apply]
   exact IsOpen.eventually_mem isOpen_ne hb
 #align zero_cpow_eq_nhds zero_cpow_eq_nhds
+-/
 
+#print cpow_eq_nhds /-
 theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a] fun x => exp (log x * b) :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0
   exact this.mono fun x hx => by dsimp only; rw [cpow_def_of_ne_zero hx]
   exact IsOpen.eventually_mem isOpen_ne ha
 #align cpow_eq_nhds cpow_eq_nhds
+-/
 
+#print cpow_eq_nhds' /-
 theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
     (fun x => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -62,7 +67,9 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
   rw [isOpen_compl_iff]
   exact isClosed_eq continuous_fst continuous_const
 #align cpow_eq_nhds' cpow_eq_nhds'
+-/
 
+#print continuousAt_const_cpow /-
 -- Continuity of `λ x, a ^ x`: union of these two lemmas is optimal.
 theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
@@ -71,14 +78,18 @@ theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x
   rw [cpow_eq]
   exact continuous_exp.continuous_at.comp (ContinuousAt.mul continuousAt_const continuousAt_id)
 #align continuous_at_const_cpow continuousAt_const_cpow
+-/
 
+#print continuousAt_const_cpow' /-
 theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
   by_cases ha : a = 0
   · rw [ha, continuousAt_congr (zero_cpow_eq_nhds h)]; exact continuousAt_const
   · exact continuousAt_const_cpow ha
 #align continuous_at_const_cpow' continuousAt_const_cpow'
+-/
 
+#print continuousAt_cpow /-
 /-- The function `z ^ w` is continuous in `(z, w)` provided that `z` does not belong to the interval
 `(-∞, 0]` on the real line. See also `complex.continuous_at_cpow_zero_of_re_pos` for a version that
 works for `z = 0` but assumes `0 < re w`. -/
@@ -93,18 +104,24 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
     ContinuousAt.mul (ContinuousAt.comp _ continuous_fst.continuous_at) continuous_snd.continuous_at
   exact continuousAt_clog hp_fst
 #align continuous_at_cpow continuousAt_cpow
+-/
 
+#print continuousAt_cpow_const /-
 theorem continuousAt_cpow_const {a b : ℂ} (ha : 0 < a.re ∨ a.im ≠ 0) :
     ContinuousAt (fun x => cpow x b) a :=
   Tendsto.comp (@continuousAt_cpow (a, b) ha) (continuousAt_id.Prod continuousAt_const)
 #align continuous_at_cpow_const continuousAt_cpow_const
+-/
 
+#print Filter.Tendsto.cpow /-
 theorem Filter.Tendsto.cpow {l : Filter α} {f g : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 a))
     (hg : Tendsto g l (𝓝 b)) (ha : 0 < a.re ∨ a.im ≠ 0) :
     Tendsto (fun x => f x ^ g x) l (𝓝 (a ^ b)) :=
   (@continuousAt_cpow (a, b) ha).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.cpow Filter.Tendsto.cpow
+-/
 
+#print Filter.Tendsto.const_cpow /-
 theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 b))
     (h : a ≠ 0 ∨ b ≠ 0) : Tendsto (fun x => a ^ f x) l (𝓝 (a ^ b)) :=
   by
@@ -112,52 +129,71 @@ theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (
   · exact (continuousAt_const_cpow h).Tendsto.comp hf
   · exact (continuousAt_const_cpow' h).Tendsto.comp hf
 #align filter.tendsto.const_cpow Filter.Tendsto.const_cpow
+-/
 
 variable [TopologicalSpace α] {f g : α → ℂ} {s : Set α} {a : α}
 
+#print ContinuousWithinAt.cpow /-
 theorem ContinuousWithinAt.cpow (hf : ContinuousWithinAt f s a) (hg : ContinuousWithinAt g s a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousWithinAt (fun x => f x ^ g x) s a :=
   hf.cpow hg h0
 #align continuous_within_at.cpow ContinuousWithinAt.cpow
+-/
 
+#print ContinuousWithinAt.const_cpow /-
 theorem ContinuousWithinAt.const_cpow {b : ℂ} (hf : ContinuousWithinAt f s a)
     (h : b ≠ 0 ∨ f a ≠ 0) : ContinuousWithinAt (fun x => b ^ f x) s a :=
   hf.const_cpow h
 #align continuous_within_at.const_cpow ContinuousWithinAt.const_cpow
+-/
 
+#print ContinuousAt.cpow /-
 theorem ContinuousAt.cpow (hf : ContinuousAt f a) (hg : ContinuousAt g a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousAt (fun x => f x ^ g x) a :=
   hf.cpow hg h0
 #align continuous_at.cpow ContinuousAt.cpow
+-/
 
+#print ContinuousAt.const_cpow /-
 theorem ContinuousAt.const_cpow {b : ℂ} (hf : ContinuousAt f a) (h : b ≠ 0 ∨ f a ≠ 0) :
     ContinuousAt (fun x => b ^ f x) a :=
   hf.const_cpow h
 #align continuous_at.const_cpow ContinuousAt.const_cpow
+-/
 
+#print ContinuousOn.cpow /-
 theorem ContinuousOn.cpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h0 : ∀ a ∈ s, 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ g x) s := fun a ha =>
   (hf a ha).cpow (hg a ha) (h0 a ha)
 #align continuous_on.cpow ContinuousOn.cpow
+-/
 
+#print ContinuousOn.const_cpow /-
 theorem ContinuousOn.const_cpow {b : ℂ} (hf : ContinuousOn f s) (h : b ≠ 0 ∨ ∀ a ∈ s, f a ≠ 0) :
     ContinuousOn (fun x => b ^ f x) s := fun a ha => (hf a ha).const_cpow (h.imp id fun h => h a ha)
 #align continuous_on.const_cpow ContinuousOn.const_cpow
+-/
 
+#print Continuous.cpow /-
 theorem Continuous.cpow (hf : Continuous f) (hg : Continuous g)
     (h0 : ∀ a, 0 < (f a).re ∨ (f a).im ≠ 0) : Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.cpow hg.ContinuousAt (h0 a)
 #align continuous.cpow Continuous.cpow
+-/
 
+#print Continuous.const_cpow /-
 theorem Continuous.const_cpow {b : ℂ} (hf : Continuous f) (h : b ≠ 0 ∨ ∀ a, f a ≠ 0) :
     Continuous fun x => b ^ f x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.const_cpow <| h.imp id fun h => h a
 #align continuous.const_cpow Continuous.const_cpow
+-/
 
+#print ContinuousOn.cpow_const /-
 theorem ContinuousOn.cpow_const {b : ℂ} (hf : ContinuousOn f s)
     (h : ∀ a : α, a ∈ s → 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ b) s :=
   hf.cpow continuousOn_const h
 #align continuous_on.cpow_const ContinuousOn.cpow_const
+-/
 
 end CpowLimits
 
@@ -170,6 +206,7 @@ section RpowLimits
 
 namespace Real
 
+#print Real.continuousAt_const_rpow /-
 theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
@@ -179,7 +216,9 @@ theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a
   norm_cast
   exact h
 #align real.continuous_at_const_rpow Real.continuousAt_const_rpow
+-/
 
+#print Real.continuousAt_const_rpow' /-
 theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
@@ -189,7 +228,9 @@ theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow
   norm_cast
   exact h
 #align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'
+-/
 
+#print Real.rpow_eq_nhds_of_neg /-
 theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) :=
   by
@@ -197,7 +238,9 @@ theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
   exact this.mono fun x hx => by dsimp only; rw [rpow_def_of_neg hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_fst continuous_const) hp_fst
 #align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_neg
+-/
 
+#print Real.rpow_eq_nhds_of_pos /-
 theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -205,7 +248,9 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
   exact this.mono fun x hx => by dsimp only; rw [rpow_def_of_pos hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_const continuous_fst) hp_fst
 #align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_pos
+-/
 
+#print Real.continuousAt_rpow_of_ne /-
 theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -222,7 +267,9 @@ theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     refine' (continuous_at_log _).comp continuous_fst.continuous_at
     exact hp.lt.ne.symm
 #align real.continuous_at_rpow_of_ne Real.continuousAt_rpow_of_ne
+-/
 
+#print Real.continuousAt_rpow_of_pos /-
 theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -241,12 +288,16 @@ theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
   simpa only [← sup_prod, ← nhdsWithin_union, compl_union_self, nhdsWithin_univ, nhds_prod_eq,
     ContinuousAt, zero_rpow hp.ne'] using B.sup (C.mono_right (pure_le_nhds _))
 #align real.continuous_at_rpow_of_pos Real.continuousAt_rpow_of_pos
+-/
 
+#print Real.continuousAt_rpow /-
 theorem continuousAt_rpow (p : ℝ × ℝ) (h : p.1 ≠ 0 ∨ 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   h.elim (fun h => continuousAt_rpow_of_ne p h) fun h => continuousAt_rpow_of_pos p h
 #align real.continuous_at_rpow Real.continuousAt_rpow
+-/
 
+#print Real.continuousAt_rpow_const /-
 theorem continuousAt_rpow_const (x : ℝ) (q : ℝ) (h : x ≠ 0 ∨ 0 < q) :
     ContinuousAt (fun x : ℝ => x ^ q) x :=
   by
@@ -255,6 +306,7 @@ theorem continuousAt_rpow_const (x : ℝ) (q : ℝ) (h : x ≠ 0 ∨ 0 < q) :
   · exact continuous_at_rpow (x, q) h
   · exact (continuous_id'.prod_mk continuous_const).ContinuousAt
 #align real.continuous_at_rpow_const Real.continuousAt_rpow_const
+-/
 
 end Real
 
@@ -262,57 +314,77 @@ section
 
 variable {α : Type _}
 
+#print Filter.Tendsto.rpow /-
 theorem Filter.Tendsto.rpow {l : Filter α} {f g : α → ℝ} {x y : ℝ} (hf : Tendsto f l (𝓝 x))
     (hg : Tendsto g l (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) : Tendsto (fun t => f t ^ g t) l (𝓝 (x ^ y)) :=
   (Real.continuousAt_rpow (x, y) h).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.rpow Filter.Tendsto.rpow
+-/
 
+#print Filter.Tendsto.rpow_const /-
 theorem Filter.Tendsto.rpow_const {l : Filter α} {f : α → ℝ} {x p : ℝ} (hf : Tendsto f l (𝓝 x))
     (h : x ≠ 0 ∨ 0 ≤ p) : Tendsto (fun a => f a ^ p) l (𝓝 (x ^ p)) :=
   if h0 : 0 = p then h0 ▸ by simp [tendsto_const_nhds]
   else hf.rpow tendsto_const_nhds (h.imp id fun h' => h'.lt_of_ne h0)
 #align filter.tendsto.rpow_const Filter.Tendsto.rpow_const
+-/
 
 variable [TopologicalSpace α] {f g : α → ℝ} {s : Set α} {x : α} {p : ℝ}
 
+#print ContinuousAt.rpow /-
 theorem ContinuousAt.rpow (hf : ContinuousAt f x) (hg : ContinuousAt g x) (h : f x ≠ 0 ∨ 0 < g x) :
     ContinuousAt (fun t => f t ^ g t) x :=
   hf.rpow hg h
 #align continuous_at.rpow ContinuousAt.rpow
+-/
 
+#print ContinuousWithinAt.rpow /-
 theorem ContinuousWithinAt.rpow (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : f x ≠ 0 ∨ 0 < g x) : ContinuousWithinAt (fun t => f t ^ g t) s x :=
   hf.rpow hg h
 #align continuous_within_at.rpow ContinuousWithinAt.rpow
+-/
 
+#print ContinuousOn.rpow /-
 theorem ContinuousOn.rpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 < g x) : ContinuousOn (fun t => f t ^ g t) s := fun t ht =>
   (hf t ht).rpow (hg t ht) (h t ht)
 #align continuous_on.rpow ContinuousOn.rpow
+-/
 
+#print Continuous.rpow /-
 theorem Continuous.rpow (hf : Continuous f) (hg : Continuous g) (h : ∀ x, f x ≠ 0 ∨ 0 < g x) :
     Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow hg.ContinuousAt (h x)
 #align continuous.rpow Continuous.rpow
+-/
 
+#print ContinuousWithinAt.rpow_const /-
 theorem ContinuousWithinAt.rpow_const (hf : ContinuousWithinAt f s x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousWithinAt (fun x => f x ^ p) s x :=
   hf.rpow_const h
 #align continuous_within_at.rpow_const ContinuousWithinAt.rpow_const
+-/
 
+#print ContinuousAt.rpow_const /-
 theorem ContinuousAt.rpow_const (hf : ContinuousAt f x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousAt (fun x => f x ^ p) x :=
   hf.rpow_const h
 #align continuous_at.rpow_const ContinuousAt.rpow_const
+-/
 
+#print ContinuousOn.rpow_const /-
 theorem ContinuousOn.rpow_const (hf : ContinuousOn f s) (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousOn (fun x => f x ^ p) s := fun x hx => (hf x hx).rpow_const (h x hx)
 #align continuous_on.rpow_const ContinuousOn.rpow_const
+-/
 
+#print Continuous.rpow_const /-
 theorem Continuous.rpow_const (hf : Continuous f) (h : ∀ x, f x ≠ 0 ∨ 0 ≤ p) :
     Continuous fun x => f x ^ p :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow_const (h x)
 #align continuous.rpow_const Continuous.rpow_const
+-/
 
 end
 
@@ -328,6 +400,7 @@ section CpowLimits2
 
 namespace Complex
 
+#print Complex.continuousAt_cpow_zero_of_re_pos /-
 /-- See also `continuous_at_cpow` and `complex.continuous_at_cpow_of_re_pos`. -/
 theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) (0, z) :=
@@ -352,7 +425,9 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
       mul_le_mul (abs_le.2 ⟨(neg_pi_lt_arg _).le, arg_le_pi _⟩) hz.le (_root_.abs_nonneg _)
         real.pi_pos.le
 #align complex.continuous_at_cpow_zero_of_re_pos Complex.continuousAt_cpow_zero_of_re_pos
+-/
 
+#print Complex.continuousAt_cpow_of_re_pos /-
 /-- See also `continuous_at_cpow` for a version that assumes `p.1 ≠ 0` but makes no
 assumptions about `p.2`. -/
 theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.1.im ≠ 0) (h₂ : 0 < p.2.re) :
@@ -364,14 +439,18 @@ theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.
   rcases h₁ with (h₁ | (rfl : z = 0))
   exacts [continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
 #align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_pos
+-/
 
+#print Complex.continuousAt_cpow_const_of_re_pos /-
 /-- See also `continuous_at_cpow_const` for a version that assumes `z ≠ 0` but makes no
 assumptions about `w`. -/
 theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z ≠ 0) (hw : 0 < re w) :
     ContinuousAt (fun x => x ^ w) z :=
   Tendsto.comp (@continuousAt_cpow_of_re_pos (z, w) hz hw) (continuousAt_id.Prod continuousAt_const)
 #align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_pos
+-/
 
+#print Complex.continuousAt_ofReal_cpow /-
 /-- Continuity of `(x, y) ↦ x ^ y` as a function on `ℝ × ℂ`. -/
 theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun p => ↑p.1 ^ p.2 : ℝ × ℂ → ℂ) (x, y) :=
@@ -403,17 +482,22 @@ theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
       rwa [neg_re, of_real_re, neg_pos]
     · exact (continuous_exp.comp (continuous_const.mul continuous_snd)).ContinuousAt
 #align complex.continuous_at_of_real_cpow Complex.continuousAt_ofReal_cpow
+-/
 
+#print Complex.continuousAt_ofReal_cpow_const /-
 theorem continuousAt_ofReal_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => a ^ y : ℝ → ℂ) x :=
   @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_ofReal_cpow x y h)
     (continuous_id.prod_mk continuous_const).ContinuousAt
 #align complex.continuous_at_of_real_cpow_const Complex.continuousAt_ofReal_cpow_const
+-/
 
+#print Complex.continuous_ofReal_cpow_const /-
 theorem continuous_ofReal_cpow_const {y : ℂ} (hs : 0 < y.re) :
     Continuous (fun x => x ^ y : ℝ → ℂ) :=
   continuous_iff_continuousAt.mpr fun x => continuousAt_ofReal_cpow_const x y (Or.inl hs)
 #align complex.continuous_of_real_cpow_const Complex.continuous_ofReal_cpow_const
+-/
 
 end Complex
 
@@ -424,6 +508,7 @@ end CpowLimits2
 
 namespace NNReal
 
+#print NNReal.continuousAt_rpow /-
 theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
     ContinuousAt (fun p : ℝ≥0 × ℝ => p.1 ^ p.2) (x, y) :=
   by
@@ -442,6 +527,7 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
     exact h
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
+-/
 
 #print NNReal.eventually_pow_one_div_le /-
 theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
@@ -459,24 +545,30 @@ end NNReal
 
 open Filter
 
+#print Filter.Tendsto.nnrpow /-
 theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0} {v : α → ℝ} {x : ℝ≥0}
     {y : ℝ} (hx : Tendsto u f (𝓝 x)) (hy : Tendsto v f (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) :
     Tendsto (fun a => u a ^ v a) f (𝓝 (x ^ y)) :=
   Tendsto.comp (NNReal.continuousAt_rpow h) (hx.prod_mk_nhds hy)
 #align filter.tendsto.nnrpow Filter.Tendsto.nnrpow
+-/
 
 namespace NNReal
 
+#print NNReal.continuousAt_rpow_const /-
 theorem continuousAt_rpow_const {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 ≤ y) :
     ContinuousAt (fun z => z ^ y) x :=
   h.elim (fun h => tendsto_id.nnrpow tendsto_const_nhds (Or.inl h)) fun h =>
     h.eq_or_lt.elim (fun h => h ▸ by simp only [rpow_zero, continuousAt_const]) fun h =>
       tendsto_id.nnrpow tendsto_const_nhds (Or.inr h)
 #align nnreal.continuous_at_rpow_const NNReal.continuousAt_rpow_const
+-/
 
+#print NNReal.continuous_rpow_const /-
 theorem continuous_rpow_const {y : ℝ} (h : 0 ≤ y) : Continuous fun x : ℝ≥0 => x ^ y :=
   continuous_iff_continuousAt.2 fun x => continuousAt_rpow_const (Or.inr h)
 #align nnreal.continuous_rpow_const NNReal.continuous_rpow_const
+-/
 
 end NNReal
 
@@ -485,6 +577,7 @@ end NNReal
 
 namespace ENNReal
 
+#print ENNReal.eventually_pow_one_div_le /-
 theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0∞} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -496,6 +589,7 @@ theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0
     refine' this.congr (eventually_of_forall fun n => _)
     rw [coe_rpow_of_nonneg x (by positivity : 0 ≤ (1 / n : ℝ)), coe_le_coe]
 #align ennreal.eventually_pow_one_div_le ENNReal.eventually_pow_one_div_le
+-/
 
 private theorem continuous_at_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h : 0 < y) :
     ContinuousAt (fun a : ℝ≥0∞ => a ^ y) x :=
@@ -510,6 +604,7 @@ private theorem continuous_at_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h :
   ext1 x
   simp [coe_rpow_of_nonneg _ h.le]
 
+#print ENNReal.continuous_rpow_const /-
 @[continuity]
 theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y :=
   by
@@ -522,7 +617,9 @@ theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y
     simp_rw [hz, rpow_neg]
     exact continuous_inv.continuous_at.comp (continuous_at_rpow_const_of_pos z_pos)
 #align ennreal.continuous_rpow_const ENNReal.continuous_rpow_const
+-/
 
+#print ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos /-
 theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞) {y : ℝ} (hy : 0 < y) :
     Tendsto (fun x : ℝ≥0∞ => c * x ^ y) (𝓝 0) (𝓝 0) :=
   by
@@ -530,11 +627,14 @@ theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞
   · simp [hy]
   · exact Or.inr hc
 #align ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos
+-/
 
 end ENNReal
 
+#print Filter.Tendsto.ennrpow_const /-
 theorem Filter.Tendsto.ennrpow_const {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} (r : ℝ)
     (hm : Tendsto m f (𝓝 a)) : Tendsto (fun x => m x ^ r) f (𝓝 (a ^ r)) :=
   (ENNReal.continuous_rpow_const.Tendsto a).comp hm
 #align filter.tendsto.ennrpow_const Filter.Tendsto.ennrpow_const
+-/
 

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

@@ -373,7 +373,7 @@ theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z
 #align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_pos
 
 /-- Continuity of `(x, y) ↦ x ^ y` as a function on `ℝ × ℂ`. -/
-theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
+theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun p => ↑p.1 ^ p.2 : ℝ × ℂ → ℂ) (x, y) :=
   by
   rcases lt_trichotomy 0 x with (hx | rfl | hx)
@@ -402,18 +402,18 @@ theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
     · refine' (continuousAt_cpow (Or.inl _)).comp A
       rwa [neg_re, of_real_re, neg_pos]
     · exact (continuous_exp.comp (continuous_const.mul continuous_snd)).ContinuousAt
-#align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpow
+#align complex.continuous_at_of_real_cpow Complex.continuousAt_ofReal_cpow
 
-theorem continuousAt_of_real_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
+theorem continuousAt_ofReal_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => a ^ y : ℝ → ℂ) x :=
-  @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_of_real_cpow x y h)
+  @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_ofReal_cpow x y h)
     (continuous_id.prod_mk continuous_const).ContinuousAt
-#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_const
+#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_ofReal_cpow_const
 
-theorem continuous_of_real_cpow_const {y : ℂ} (hs : 0 < y.re) :
+theorem continuous_ofReal_cpow_const {y : ℂ} (hs : 0 < y.re) :
     Continuous (fun x => x ^ y : ℝ → ℂ) :=
-  continuous_iff_continuousAt.mpr fun x => continuousAt_of_real_cpow_const x y (Or.inl hs)
-#align complex.continuous_of_real_cpow_const Complex.continuous_of_real_cpow_const
+  continuous_iff_continuousAt.mpr fun x => continuousAt_ofReal_cpow_const x y (Or.inl hs)
+#align complex.continuous_of_real_cpow_const Complex.continuous_ofReal_cpow_const
 
 end Complex
 

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

@@ -58,7 +58,7 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
   suffices : ∀ᶠ x : ℂ × ℂ in 𝓝 p, x.1 ≠ 0
   exact this.mono fun x hx => by dsimp only; rw [cpow_def_of_ne_zero hx]
   refine' IsOpen.eventually_mem _ hp_fst
-  change IsOpen ({ x : ℂ × ℂ | x.1 = 0 }ᶜ)
+  change IsOpen ({x : ℂ × ℂ | x.1 = 0}ᶜ)
   rw [isOpen_compl_iff]
   exact isClosed_eq continuous_fst continuous_const
 #align cpow_eq_nhds' cpow_eq_nhds'
@@ -338,8 +338,8 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
   simp only [div_eq_mul_inv, ← Real.exp_neg]
   refine' tendsto.zero_mul_is_bounded_under_le _ _
   ·
-    convert(continuous_fst.norm.tendsto _).rpow ((continuous_re.comp continuous_snd).Tendsto _)
-          _ <;>
+    convert
+        (continuous_fst.norm.tendsto _).rpow ((continuous_re.comp continuous_snd).Tendsto _) _ <;>
       simp [hz, Real.zero_rpow hz.ne']
   · simp only [(· ∘ ·), Real.norm_eq_abs, abs_of_pos (Real.exp_pos _)]
     rcases exists_gt (|im z|) with ⟨C, hC⟩

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

@@ -86,7 +86,7 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) p :=
   by
   have hp_fst_ne_zero : p.fst ≠ 0 := by intro h;
-    cases hp_fst <;> · rw [h] at hp_fst; simpa using hp_fst
+    cases hp_fst <;> · rw [h] at hp_fst ; simpa using hp_fst
   rw [continuousAt_congr (cpow_eq_nhds' hp_fst_ne_zero)]
   refine' continuous_exp.continuous_at.comp _
   refine'
@@ -209,7 +209,7 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
 theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
-  rw [ne_iff_lt_or_gt] at hp
+  rw [ne_iff_lt_or_gt] at hp 
   cases hp
   · rw [continuousAt_congr (rpow_eq_nhds_of_neg hp)]
     refine' ContinuousAt.mul _ (continuous_cos.continuous_at.comp _)
@@ -360,9 +360,9 @@ theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.
   by
   cases' p with z w
   rw [← not_lt_zero_iff, lt_iff_le_and_ne, not_and_or, Ne.def, Classical.not_not,
-    not_le_zero_iff] at h₁
+    not_le_zero_iff] at h₁ 
   rcases h₁ with (h₁ | (rfl : z = 0))
-  exacts[continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
+  exacts [continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
 #align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_pos
 
 /-- See also `continuous_at_cpow_const` for a version that assumes `z ≠ 0` but makes no
@@ -437,8 +437,8 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   rw [this]
   refine' continuous_real_to_nnreal.continuous_at.comp (ContinuousAt.comp _ _)
   · apply Real.continuousAt_rpow
-    simp only [Ne.def] at h
-    rw [← NNReal.coe_eq_zero x] at h
+    simp only [Ne.def] at h 
+    rw [← NNReal.coe_eq_zero x] at h 
     exact h
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
@@ -448,7 +448,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
   obtain ⟨m, hm⟩ := add_one_pow_unbounded_of_pos x (tsub_pos_of_lt hy)
-  rw [tsub_add_cancel_of_le hy.le] at hm
+  rw [tsub_add_cancel_of_le hy.le] at hm 
   refine' eventually_at_top.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
     NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow hy.le (m.le_succ.trans hn))

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

@@ -23,7 +23,7 @@ This file contains lemmas about continuity of the power functions on `ℂ`, `ℝ
 
 noncomputable section
 
-open Classical Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
+open scoped Classical Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
 
 open Filter Finset Set
 
@@ -443,6 +443,7 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
 
+#print NNReal.eventually_pow_one_div_le /-
 theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -452,6 +453,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
     NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow hy.le (m.le_succ.trans hn))
 #align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_le
+-/
 
 end NNReal
 

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

@@ -38,12 +38,6 @@ open Complex
 
 variable {α : Type _}
 
-/- warning: zero_cpow_eq_nhds -> zero_cpow_eq_nhds is a dubious translation:
-lean 3 declaration is
-  forall {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) b) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) x) (OfNat.ofNat.{0} (Complex -> Complex) 0 (OfNat.mk.{0} (Complex -> Complex) 0 (Zero.zero.{0} (Complex -> Complex) (Pi.instZero.{0, 0} Complex (fun (ᾰ : Complex) => Complex) (fun (i : Complex) => Complex.hasZero))))))
-but is expected to have type
-  forall {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) b) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) x) (OfNat.ofNat.{0} (Complex -> Complex) 0 (Zero.toOfNat0.{0} (Complex -> Complex) (Pi.instZero.{0, 0} Complex (fun (a._@.Mathlib.Order.Filter.Basic._hyg.19136 : Complex) => Complex) (fun (i : Complex) => Complex.instZeroComplex)))))
-Case conversion may be inaccurate. Consider using '#align zero_cpow_eq_nhds zero_cpow_eq_nhdsₓ'. -/
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
@@ -51,12 +45,6 @@ theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^
   exact IsOpen.eventually_mem isOpen_ne hb
 #align zero_cpow_eq_nhds zero_cpow_eq_nhds
 
-/- warning: cpow_eq_nhds -> cpow_eq_nhds is a dubious translation:
-lean 3 declaration is
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) a) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) x b) (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.log x) b)))
-but is expected to have type
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) a) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) x b) (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.log x) b)))
-Case conversion may be inaccurate. Consider using '#align cpow_eq_nhds cpow_eq_nhdsₓ'. -/
 theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a] fun x => exp (log x * b) :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0
@@ -64,12 +52,6 @@ theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a]
   exact IsOpen.eventually_mem isOpen_ne ha
 #align cpow_eq_nhds cpow_eq_nhds
 
-/- warning: cpow_eq_nhds' -> cpow_eq_nhds' is a dubious translation:
-lean 3 declaration is
-  forall {p : Prod.{0, 0} Complex Complex}, (Ne.{1} Complex (Prod.fst.{0, 0} Complex Complex p) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Complex Complex) Complex (nhds.{0} (Prod.{0, 0} Complex Complex) (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) p) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (fun (x : Prod.{0, 0} Complex Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.log (Prod.fst.{0, 0} Complex Complex x)) (Prod.snd.{0, 0} Complex Complex x))))
-but is expected to have type
-  forall {p : Prod.{0, 0} Complex Complex}, (Ne.{1} Complex (Prod.fst.{0, 0} Complex Complex p) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Complex Complex) Complex (nhds.{0} (Prod.{0, 0} Complex Complex) (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) p) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (fun (x : Prod.{0, 0} Complex Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.log (Prod.fst.{0, 0} Complex Complex x)) (Prod.snd.{0, 0} Complex Complex x))))
-Case conversion may be inaccurate. Consider using '#align cpow_eq_nhds' cpow_eq_nhds'ₓ'. -/
 theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
     (fun x => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -81,12 +63,6 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
   exact isClosed_eq continuous_fst continuous_const
 #align cpow_eq_nhds' cpow_eq_nhds'
 
-/- warning: continuous_at_const_cpow -> continuousAt_const_cpow is a dubious translation:
-lean 3 declaration is
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a x) b)
-but is expected to have type
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a x) b)
-Case conversion may be inaccurate. Consider using '#align continuous_at_const_cpow continuousAt_const_cpowₓ'. -/
 -- Continuity of `λ x, a ^ x`: union of these two lemmas is optimal.
 theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
@@ -96,12 +72,6 @@ theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x
   exact continuous_exp.continuous_at.comp (ContinuousAt.mul continuousAt_const continuousAt_id)
 #align continuous_at_const_cpow continuousAt_const_cpow
 
-/- warning: continuous_at_const_cpow' -> continuousAt_const_cpow' is a dubious translation:
-lean 3 declaration is
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a x) b)
-but is expected to have type
-  forall {a : Complex} {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a x) b)
-Case conversion may be inaccurate. Consider using '#align continuous_at_const_cpow' continuousAt_const_cpow'ₓ'. -/
 theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
   by_cases ha : a = 0
@@ -109,12 +79,6 @@ theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x
   · exact continuousAt_const_cpow ha
 #align continuous_at_const_cpow' continuousAt_const_cpow'
 
-/- warning: continuous_at_cpow -> continuousAt_cpow is a dubious translation:
-lean 3 declaration is
-  forall {p : Prod.{0, 0} Complex Complex}, (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
-but is expected to have type
-  forall {p : Prod.{0, 0} Complex Complex}, (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
-Case conversion may be inaccurate. Consider using '#align continuous_at_cpow continuousAt_cpowₓ'. -/
 /-- The function `z ^ w` is continuous in `(z, w)` provided that `z` does not belong to the interval
 `(-∞, 0]` on the real line. See also `complex.continuous_at_cpow_zero_of_re_pos` for a version that
 works for `z = 0` but assumes `0 < re w`. -/
@@ -130,35 +94,17 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
   exact continuousAt_clog hp_fst
 #align continuous_at_cpow continuousAt_cpow
 
-/- warning: continuous_at_cpow_const -> continuousAt_cpow_const is a dubious translation:
-lean 3 declaration is
-  forall {a : Complex} {b : Complex}, (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => Complex.cpow x b) a)
-but is expected to have type
-  forall {a : Complex} {b : Complex}, (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => Complex.cpow x b) a)
-Case conversion may be inaccurate. Consider using '#align continuous_at_cpow_const continuousAt_cpow_constₓ'. -/
 theorem continuousAt_cpow_const {a b : ℂ} (ha : 0 < a.re ∨ a.im ≠ 0) :
     ContinuousAt (fun x => cpow x b) a :=
   Tendsto.comp (@continuousAt_cpow (a, b) ha) (continuousAt_id.Prod continuousAt_const)
 #align continuous_at_cpow_const continuousAt_cpow_const
 
-/- warning: filter.tendsto.cpow -> Filter.Tendsto.cpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Complex} {g : α -> Complex} {a : Complex} {b : Complex}, (Filter.Tendsto.{u1, 0} α Complex f l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) a)) -> (Filter.Tendsto.{u1, 0} α Complex g l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) b)) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Filter.Tendsto.{u1, 0} α Complex (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)) l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a b)))
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.cpow Filter.Tendsto.cpowₓ'. -/
 theorem Filter.Tendsto.cpow {l : Filter α} {f g : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 a))
     (hg : Tendsto g l (𝓝 b)) (ha : 0 < a.re ∨ a.im ≠ 0) :
     Tendsto (fun x => f x ^ g x) l (𝓝 (a ^ b)) :=
   (@continuousAt_cpow (a, b) ha).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.cpow Filter.Tendsto.cpow
 
-/- warning: filter.tendsto.const_cpow -> Filter.Tendsto.const_cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.const_cpow Filter.Tendsto.const_cpowₓ'. -/
 theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 b))
     (h : a ≠ 0 ∨ b ≠ 0) : Tendsto (fun x => a ^ f x) l (𝓝 (a ^ b)) :=
   by
@@ -169,99 +115,45 @@ theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (
 
 variable [TopologicalSpace α] {f g : α → ℂ} {s : Set α} {a : α}
 
-/- warning: continuous_within_at.cpow -> ContinuousWithinAt.cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at.cpow ContinuousWithinAt.cpowₓ'. -/
 theorem ContinuousWithinAt.cpow (hf : ContinuousWithinAt f s a) (hg : ContinuousWithinAt g s a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousWithinAt (fun x => f x ^ g x) s a :=
   hf.cpow hg h0
 #align continuous_within_at.cpow ContinuousWithinAt.cpow
 
-/- warning: continuous_within_at.const_cpow -> ContinuousWithinAt.const_cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at.const_cpow ContinuousWithinAt.const_cpowₓ'. -/
 theorem ContinuousWithinAt.const_cpow {b : ℂ} (hf : ContinuousWithinAt f s a)
     (h : b ≠ 0 ∨ f a ≠ 0) : ContinuousWithinAt (fun x => b ^ f x) s a :=
   hf.const_cpow h
 #align continuous_within_at.const_cpow ContinuousWithinAt.const_cpow
 
-/- warning: continuous_at.cpow -> ContinuousAt.cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_at.cpow ContinuousAt.cpowₓ'. -/
 theorem ContinuousAt.cpow (hf : ContinuousAt f a) (hg : ContinuousAt g a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousAt (fun x => f x ^ g x) a :=
   hf.cpow hg h0
 #align continuous_at.cpow ContinuousAt.cpow
 
-/- warning: continuous_at.const_cpow -> ContinuousAt.const_cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_at.const_cpow ContinuousAt.const_cpowₓ'. -/
 theorem ContinuousAt.const_cpow {b : ℂ} (hf : ContinuousAt f a) (h : b ≠ 0 ∨ f a ≠ 0) :
     ContinuousAt (fun x => b ^ f x) a :=
   hf.const_cpow h
 #align continuous_at.const_cpow ContinuousAt.const_cpow
 
-/- warning: continuous_on.cpow -> ContinuousOn.cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_on.cpow ContinuousOn.cpowₓ'. -/
 theorem ContinuousOn.cpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h0 : ∀ a ∈ s, 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ g x) s := fun a ha =>
   (hf a ha).cpow (hg a ha) (h0 a ha)
 #align continuous_on.cpow ContinuousOn.cpow
 
-/- warning: continuous_on.const_cpow -> ContinuousOn.const_cpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_on.const_cpow ContinuousOn.const_cpowₓ'. -/
 theorem ContinuousOn.const_cpow {b : ℂ} (hf : ContinuousOn f s) (h : b ≠ 0 ∨ ∀ a ∈ s, f a ≠ 0) :
     ContinuousOn (fun x => b ^ f x) s := fun a ha => (hf a ha).const_cpow (h.imp id fun h => h a ha)
 #align continuous_on.const_cpow ContinuousOn.const_cpow
 
-/- warning: continuous.cpow -> Continuous.cpow is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex}, (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) g) -> (forall (a : α), Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)))
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-Case conversion may be inaccurate. Consider using '#align continuous.cpow Continuous.cpowₓ'. -/
 theorem Continuous.cpow (hf : Continuous f) (hg : Continuous g)
     (h0 : ∀ a, 0 < (f a).re ∨ (f a).im ≠ 0) : Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.cpow hg.ContinuousAt (h0 a)
 #align continuous.cpow Continuous.cpow
 
-/- warning: continuous.const_cpow -> Continuous.const_cpow is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align continuous.const_cpow Continuous.const_cpowₓ'. -/
 theorem Continuous.const_cpow {b : ℂ} (hf : Continuous f) (h : b ≠ 0 ∨ ∀ a, f a ≠ 0) :
     Continuous fun x => b ^ f x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.const_cpow <| h.imp id fun h => h a
 #align continuous.const_cpow Continuous.const_cpow
 
-/- warning: continuous_on.cpow_const -> ContinuousOn.cpow_const is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_on.cpow_const ContinuousOn.cpow_constₓ'. -/
 theorem ContinuousOn.cpow_const {b : ℂ} (hf : ContinuousOn f s)
     (h : ∀ a : α, a ∈ s → 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ b) s :=
   hf.cpow continuousOn_const h
@@ -278,12 +170,6 @@ section RpowLimits
 
 namespace Real
 
-/- warning: real.continuous_at_const_rpow -> Real.continuousAt_const_rpow is a dubious translation:
-lean 3 declaration is
-  forall {a : Real} {b : Real}, (Ne.{1} Real a (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
-but is expected to have type
-  forall {a : Real} {b : Real}, (Ne.{1} Real a (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow Real.continuousAt_const_rpowₓ'. -/
 theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
@@ -294,12 +180,6 @@ theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a
   exact h
 #align real.continuous_at_const_rpow Real.continuousAt_const_rpow
 
-/- warning: real.continuous_at_const_rpow' -> Real.continuousAt_const_rpow' is a dubious translation:
-lean 3 declaration is
-  forall {a : Real} {b : Real}, (Ne.{1} Real b (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
-but is expected to have type
-  forall {a : Real} {b : Real}, (Ne.{1} Real b (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'ₓ'. -/
 theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
@@ -310,12 +190,6 @@ theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow
   exact h
 #align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'
 
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-but is expected to have type
-  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.instLTReal (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))) (Real.cos (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Prod.snd.{0, 0} Real Real x) Real.pi))))
-Case conversion may be inaccurate. Consider using '#align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_negₓ'. -/
 theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) :=
   by
@@ -324,12 +198,6 @@ theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
   exact IsOpen.eventually_mem (isOpen_lt continuous_fst continuous_const) hp_fst
 #align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_neg
 
-/- warning: real.rpow_eq_nhds_of_pos -> Real.rpow_eq_nhds_of_pos is a dubious translation:
-lean 3 declaration is
-  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.fst.{0, 0} Real Real p)) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))))
-but is expected to have type
-  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.fst.{0, 0} Real Real p)) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))))
-Case conversion may be inaccurate. Consider using '#align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_posₓ'. -/
 theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -338,12 +206,6 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
   exact IsOpen.eventually_mem (isOpen_lt continuous_const continuous_fst) hp_fst
 #align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_pos
 
-/- warning: real.continuous_at_rpow_of_ne -> Real.continuousAt_rpow_of_ne is a dubious translation:
-lean 3 declaration is
-  forall (p : Prod.{0, 0} Real Real), (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-but is expected to have type
-  forall (p : Prod.{0, 0} Real Real), (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_of_ne Real.continuousAt_rpow_of_neₓ'. -/
 theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -361,12 +223,6 @@ theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     exact hp.lt.ne.symm
 #align real.continuous_at_rpow_of_ne Real.continuousAt_rpow_of_ne
 
-/- warning: real.continuous_at_rpow_of_pos -> Real.continuousAt_rpow_of_pos is a dubious translation:
-lean 3 declaration is
-  forall (p : Prod.{0, 0} Real Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{0, 0} Real Real p)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-but is expected to have type
-  forall (p : Prod.{0, 0} Real Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{0, 0} Real Real p)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_of_pos Real.continuousAt_rpow_of_posₓ'. -/
 theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -386,23 +242,11 @@ theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
     ContinuousAt, zero_rpow hp.ne'] using B.sup (C.mono_right (pure_le_nhds _))
 #align real.continuous_at_rpow_of_pos Real.continuousAt_rpow_of_pos
 
-/- warning: real.continuous_at_rpow -> Real.continuousAt_rpow is a dubious translation:
-lean 3 declaration is
-  forall (p : Prod.{0, 0} Real Real), (Or (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{0, 0} Real Real p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-but is expected to have type
-  forall (p : Prod.{0, 0} Real Real), (Or (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{0, 0} Real Real p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow Real.continuousAt_rpowₓ'. -/
 theorem continuousAt_rpow (p : ℝ × ℝ) (h : p.1 ≠ 0 ∨ 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   h.elim (fun h => continuousAt_rpow_of_ne p h) fun h => continuousAt_rpow_of_pos p h
 #align real.continuous_at_rpow Real.continuousAt_rpow
 
-/- warning: real.continuous_at_rpow_const -> Real.continuousAt_rpow_const is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (q : Real), (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) q)) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x q) x)
-but is expected to have type
-  forall (x : Real) (q : Real), (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) q)) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x q) x)
-Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_const Real.continuousAt_rpow_constₓ'. -/
 theorem continuousAt_rpow_const (x : ℝ) (q : ℝ) (h : x ≠ 0 ∨ 0 < q) :
     ContinuousAt (fun x : ℝ => x ^ q) x :=
   by
@@ -418,23 +262,11 @@ section
 
 variable {α : Type _}
 
-/- warning: filter.tendsto.rpow -> Filter.Tendsto.rpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {g : α -> Real} {x : Real} {y : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Filter.Tendsto.{u1, 0} α Real g l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (Filter.Tendsto.{u1, 0} α Real (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x y)))
-but is expected to have type
-  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {g : α -> Real} {x : Real} {y : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Filter.Tendsto.{u1, 0} α Real g l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (Filter.Tendsto.{u1, 0} α Real (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x y)))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.rpow Filter.Tendsto.rpowₓ'. -/
 theorem Filter.Tendsto.rpow {l : Filter α} {f g : α → ℝ} {x y : ℝ} (hf : Tendsto f l (𝓝 x))
     (hg : Tendsto g l (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) : Tendsto (fun t => f t ^ g t) l (𝓝 (x ^ y)) :=
   (Real.continuousAt_rpow (x, y) h).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.rpow Filter.Tendsto.rpow
 
-/- warning: filter.tendsto.rpow_const -> Filter.Tendsto.rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {x : Real} {p : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (Filter.Tendsto.{u1, 0} α Real (fun (a : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f a) p) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x p)))
-but is expected to have type
-  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {x : Real} {p : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (Filter.Tendsto.{u1, 0} α Real (fun (a : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f a) p) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x p)))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.rpow_const Filter.Tendsto.rpow_constₓ'. -/
 theorem Filter.Tendsto.rpow_const {l : Filter α} {f : α → ℝ} {x p : ℝ} (hf : Tendsto f l (𝓝 x))
     (h : x ≠ 0 ∨ 0 ≤ p) : Tendsto (fun a => f a ^ p) l (𝓝 (x ^ p)) :=
   if h0 : 0 = p then h0 ▸ by simp [tendsto_const_nhds]
@@ -443,88 +275,40 @@ theorem Filter.Tendsto.rpow_const {l : Filter α} {f : α → ℝ} {x p : ℝ} (
 
 variable [TopologicalSpace α] {f g : α → ℝ} {s : Set α} {x : α} {p : ℝ}
 
-/- warning: continuous_at.rpow -> ContinuousAt.rpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {x : α}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {x : α}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.rpow ContinuousAt.rpowₓ'. -/
 theorem ContinuousAt.rpow (hf : ContinuousAt f x) (hg : ContinuousAt g x) (h : f x ≠ 0 ∨ 0 < g x) :
     ContinuousAt (fun t => f t ^ g t) x :=
   hf.rpow hg h
 #align continuous_at.rpow ContinuousAt.rpow
 
-/- warning: continuous_within_at.rpow -> ContinuousWithinAt.rpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α} {x : α}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) s x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α} {x : α}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) s x)
-Case conversion may be inaccurate. Consider using '#align continuous_within_at.rpow ContinuousWithinAt.rpowₓ'. -/
 theorem ContinuousWithinAt.rpow (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : f x ≠ 0 ∨ 0 < g x) : ContinuousWithinAt (fun t => f t ^ g t) s x :=
   hf.rpow hg h
 #align continuous_within_at.rpow ContinuousWithinAt.rpow
 
-/- warning: continuous_on.rpow -> ContinuousOn.rpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x)))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x)))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) s)
-Case conversion may be inaccurate. Consider using '#align continuous_on.rpow ContinuousOn.rpowₓ'. -/
 theorem ContinuousOn.rpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 < g x) : ContinuousOn (fun t => f t ^ g t) s := fun t ht =>
   (hf t ht).rpow (hg t ht) (h t ht)
 #align continuous_on.rpow ContinuousOn.rpow
 
-/- warning: continuous.rpow -> Continuous.rpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) (g x)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) (g x)))
-Case conversion may be inaccurate. Consider using '#align continuous.rpow Continuous.rpowₓ'. -/
 theorem Continuous.rpow (hf : Continuous f) (hg : Continuous g) (h : ∀ x, f x ≠ 0 ∨ 0 < g x) :
     Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow hg.ContinuousAt (h x)
 #align continuous.rpow Continuous.rpow
 
-/- warning: continuous_within_at.rpow_const -> ContinuousWithinAt.rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {x : α} {p : Real}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) s x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {x : α} {p : Real}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) s x)
-Case conversion may be inaccurate. Consider using '#align continuous_within_at.rpow_const ContinuousWithinAt.rpow_constₓ'. -/
 theorem ContinuousWithinAt.rpow_const (hf : ContinuousWithinAt f s x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousWithinAt (fun x => f x ^ p) s x :=
   hf.rpow_const h
 #align continuous_within_at.rpow_const ContinuousWithinAt.rpow_const
 
-/- warning: continuous_at.rpow_const -> ContinuousAt.rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {x : α} {p : Real}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {x : α} {p : Real}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.rpow_const ContinuousAt.rpow_constₓ'. -/
 theorem ContinuousAt.rpow_const (hf : ContinuousAt f x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousAt (fun x => f x ^ p) x :=
   hf.rpow_const h
 #align continuous_at.rpow_const ContinuousAt.rpow_const
 
-/- warning: continuous_on.rpow_const -> ContinuousOn.rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {p : Real}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {p : Real}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) s)
-Case conversion may be inaccurate. Consider using '#align continuous_on.rpow_const ContinuousOn.rpow_constₓ'. -/
 theorem ContinuousOn.rpow_const (hf : ContinuousOn f s) (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousOn (fun x => f x ^ p) s := fun x hx => (hf x hx).rpow_const (h x hx)
 #align continuous_on.rpow_const ContinuousOn.rpow_const
 
-/- warning: continuous.rpow_const -> Continuous.rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {p : Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {p : Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p))
-Case conversion may be inaccurate. Consider using '#align continuous.rpow_const Continuous.rpow_constₓ'. -/
 theorem Continuous.rpow_const (hf : Continuous f) (h : ∀ x, f x ≠ 0 ∨ 0 ≤ p) :
     Continuous fun x => f x ^ p :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow_const (h x)
@@ -544,12 +328,6 @@ section CpowLimits2
 
 namespace Complex
 
-/- warning: complex.continuous_at_cpow_zero_of_re_pos -> Complex.continuousAt_cpow_zero_of_re_pos is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (Prod.mk.{0, 0} Complex Complex (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z))
-but is expected to have type
-  forall {z : Complex}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (Prod.mk.{0, 0} Complex Complex (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) z))
-Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_zero_of_re_pos Complex.continuousAt_cpow_zero_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow` and `complex.continuous_at_cpow_of_re_pos`. -/
 theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) (0, z) :=
@@ -575,12 +353,6 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
         real.pi_pos.le
 #align complex.continuous_at_cpow_zero_of_re_pos Complex.continuousAt_cpow_zero_of_re_pos
 
-/- warning: complex.continuous_at_cpow_of_re_pos -> Complex.continuousAt_cpow_of_re_pos is a dubious translation:
-lean 3 declaration is
-  forall {p : Prod.{0, 0} Complex Complex}, (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.snd.{0, 0} Complex Complex p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
-but is expected to have type
-  forall {p : Prod.{0, 0} Complex Complex}, (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.snd.{0, 0} Complex Complex p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
-Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow` for a version that assumes `p.1 ≠ 0` but makes no
 assumptions about `p.2`. -/
 theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.1.im ≠ 0) (h₂ : 0 < p.2.re) :
@@ -593,12 +365,6 @@ theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.
   exacts[continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
 #align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_pos
 
-/- warning: complex.continuous_at_cpow_const_of_re_pos -> Complex.continuousAt_cpow_const_of_re_pos is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex} {w : Complex}, (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re w)) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) x w) z)
-but is expected to have type
-  forall {z : Complex} {w : Complex}, (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re w)) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) x w) z)
-Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow_const` for a version that assumes `z ≠ 0` but makes no
 assumptions about `w`. -/
 theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z ≠ 0) (hw : 0 < re w) :
@@ -606,12 +372,6 @@ theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z
   Tendsto.comp (@continuousAt_cpow_of_re_pos (z, w) hz hw) (continuousAt_id.Prod continuousAt_const)
 #align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_pos
 
-/- warning: complex.continuous_at_of_real_cpow -> Complex.continuousAt_of_real_cpow is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Complex) Complex (Prod.topologicalSpace.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (p : Prod.{0, 0} Real Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Prod.fst.{0, 0} Real Complex p)) (Prod.snd.{0, 0} Real Complex p)) (Prod.mk.{0, 0} Real Complex x y))
-but is expected to have type
-  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Complex) Complex (instTopologicalSpaceProd.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (p : Prod.{0, 0} Real Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' (Prod.fst.{0, 0} Real Complex p)) (Prod.snd.{0, 0} Real Complex p)) (Prod.mk.{0, 0} Real Complex x y))
-Case conversion may be inaccurate. Consider using '#align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpowₓ'. -/
 /-- Continuity of `(x, y) ↦ x ^ y` as a function on `ℝ × ℂ`. -/
 theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun p => ↑p.1 ^ p.2 : ℝ × ℂ → ℂ) (x, y) :=
@@ -644,24 +404,12 @@ theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
     · exact (continuous_exp.comp (continuous_const.mul continuous_snd)).ContinuousAt
 #align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpow
 
-/- warning: complex.continuous_at_of_real_cpow_const -> Complex.continuousAt_of_real_cpow_const is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (a : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) y) x)
-but is expected to have type
-  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (a : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' a) y) x)
-Case conversion may be inaccurate. Consider using '#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_constₓ'. -/
 theorem continuousAt_of_real_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => a ^ y : ℝ → ℂ) x :=
   @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_of_real_cpow x y h)
     (continuous_id.prod_mk continuous_const).ContinuousAt
 #align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_const
 
-/- warning: complex.continuous_of_real_cpow_const -> Complex.continuous_of_real_cpow_const is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {y : Complex}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) -> (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' x) y))
-Case conversion may be inaccurate. Consider using '#align complex.continuous_of_real_cpow_const Complex.continuous_of_real_cpow_constₓ'. -/
 theorem continuous_of_real_cpow_const {y : ℂ} (hs : 0 < y.re) :
     Continuous (fun x => x ^ y : ℝ → ℂ) :=
   continuous_iff_continuousAt.mpr fun x => continuousAt_of_real_cpow_const x y (Or.inl hs)
@@ -676,12 +424,6 @@ end CpowLimits2
 
 namespace NNReal
 
-/- warning: nnreal.continuous_at_rpow -> NNReal.continuousAt_rpow is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} NNReal Real) NNReal (Prod.topologicalSpace.{0, 0} NNReal Real NNReal.topologicalSpace (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) NNReal.topologicalSpace (fun (p : Prod.{0, 0} NNReal Real) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (Prod.fst.{0, 0} NNReal Real p) (Prod.snd.{0, 0} NNReal Real p)) (Prod.mk.{0, 0} NNReal Real x y))
-but is expected to have type
-  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} NNReal Real) NNReal (instTopologicalSpaceProd.{0, 0} NNReal Real NNReal.instTopologicalSpaceNNReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) NNReal.instTopologicalSpaceNNReal (fun (p : Prod.{0, 0} NNReal Real) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Prod.fst.{0, 0} NNReal Real p) (Prod.snd.{0, 0} NNReal Real p)) (Prod.mk.{0, 0} NNReal Real x y))
-Case conversion may be inaccurate. Consider using '#align nnreal.continuous_at_rpow NNReal.continuousAt_rpowₓ'. -/
 theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
     ContinuousAt (fun p : ℝ≥0 × ℝ => p.1 ^ p.2) (x, y) :=
   by
@@ -701,12 +443,6 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
 
-/- warning: nnreal.eventually_pow_one_div_le -> NNReal.eventually_pow_one_div_le is a dubious translation:
-lean 3 declaration is
-  forall (x : NNReal) {y : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
-but is expected to have type
-  forall (x : NNReal) {y : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Nat.cast.{0} Real Real.natCast n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
-Case conversion may be inaccurate. Consider using '#align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_leₓ'. -/
 theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -721,12 +457,6 @@ end NNReal
 
 open Filter
 
-/- warning: filter.tendsto.nnrpow -> Filter.Tendsto.nnrpow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {u : α -> NNReal} {v : α -> Real} {x : NNReal} {y : Real}, (Filter.Tendsto.{u1, 0} α NNReal u f (nhds.{0} NNReal NNReal.topologicalSpace x)) -> (Filter.Tendsto.{u1, 0} α Real v f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (Filter.Tendsto.{u1, 0} α NNReal (fun (a : α) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (u a) (v a)) f (nhds.{0} NNReal NNReal.topologicalSpace (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x y)))
-but is expected to have type
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {u : α -> NNReal} {v : α -> Real} {x : NNReal} {y : Real}, (Filter.Tendsto.{u1, 0} α NNReal u f (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal x)) -> (Filter.Tendsto.{u1, 0} α Real v f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (Filter.Tendsto.{u1, 0} α NNReal (fun (a : α) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (u a) (v a)) f (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x y)))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.nnrpow Filter.Tendsto.nnrpowₓ'. -/
 theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0} {v : α → ℝ} {x : ℝ≥0}
     {y : ℝ} (hx : Tendsto u f (𝓝 x)) (hy : Tendsto v f (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) :
     Tendsto (fun a => u a ^ v a) f (𝓝 (x ^ y)) :=
@@ -735,12 +465,6 @@ theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0}
 
 namespace NNReal
 
-/- warning: nnreal.continuous_at_rpow_const -> NNReal.continuousAt_rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (ContinuousAt.{0, 0} NNReal NNReal NNReal.topologicalSpace NNReal.topologicalSpace (fun (z : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z y) x)
-but is expected to have type
-  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (ContinuousAt.{0, 0} NNReal NNReal NNReal.instTopologicalSpaceNNReal NNReal.instTopologicalSpaceNNReal (fun (z : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z y) x)
-Case conversion may be inaccurate. Consider using '#align nnreal.continuous_at_rpow_const NNReal.continuousAt_rpow_constₓ'. -/
 theorem continuousAt_rpow_const {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 ≤ y) :
     ContinuousAt (fun z => z ^ y) x :=
   h.elim (fun h => tendsto_id.nnrpow tendsto_const_nhds (Or.inl h)) fun h =>
@@ -748,12 +472,6 @@ theorem continuousAt_rpow_const {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 ≤ y
       tendsto_id.nnrpow tendsto_const_nhds (Or.inr h)
 #align nnreal.continuous_at_rpow_const NNReal.continuousAt_rpow_const
 
-/- warning: nnreal.continuous_rpow_const -> NNReal.continuous_rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (Continuous.{0, 0} NNReal NNReal NNReal.topologicalSpace NNReal.topologicalSpace (fun (x : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x y))
-but is expected to have type
-  forall {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (Continuous.{0, 0} NNReal NNReal NNReal.instTopologicalSpaceNNReal NNReal.instTopologicalSpaceNNReal (fun (x : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x y))
-Case conversion may be inaccurate. Consider using '#align nnreal.continuous_rpow_const NNReal.continuous_rpow_constₓ'. -/
 theorem continuous_rpow_const {y : ℝ} (h : 0 ≤ y) : Continuous fun x : ℝ≥0 => x ^ y :=
   continuous_iff_continuousAt.2 fun x => continuousAt_rpow_const (Or.inr h)
 #align nnreal.continuous_rpow_const NNReal.continuous_rpow_const
@@ -765,12 +483,6 @@ end NNReal
 
 namespace ENNReal
 
-/- warning: ennreal.eventually_pow_one_div_le -> ENNReal.eventually_pow_one_div_le is a dubious translation:
-lean 3 declaration is
-  forall {x : ENNReal}, (Ne.{1} ENNReal x (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {y : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))))
-but is expected to have type
-  forall {x : ENNReal}, (Ne.{1} ENNReal x (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {y : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Nat.cast.{0} Real Real.natCast n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))
-Case conversion may be inaccurate. Consider using '#align ennreal.eventually_pow_one_div_le ENNReal.eventually_pow_one_div_leₓ'. -/
 theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0∞} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -796,12 +508,6 @@ private theorem continuous_at_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h :
   ext1 x
   simp [coe_rpow_of_nonneg _ h.le]
 
-/- warning: ennreal.continuous_rpow_const -> ENNReal.continuous_rpow_const is a dubious translation:
-lean 3 declaration is
-  forall {y : Real}, Continuous.{0, 0} ENNReal ENNReal ENNReal.topologicalSpace ENNReal.topologicalSpace (fun (a : ENNReal) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a y)
-but is expected to have type
-  forall {y : Real}, Continuous.{0, 0} ENNReal ENNReal ENNReal.instTopologicalSpaceENNReal ENNReal.instTopologicalSpaceENNReal (fun (a : ENNReal) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a y)
-Case conversion may be inaccurate. Consider using '#align ennreal.continuous_rpow_const ENNReal.continuous_rpow_constₓ'. -/
 @[continuity]
 theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y :=
   by
@@ -815,12 +521,6 @@ theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y
     exact continuous_inv.continuous_at.comp (continuous_at_rpow_const_of_pos z_pos)
 #align ennreal.continuous_rpow_const ENNReal.continuous_rpow_const
 
-/- warning: ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos -> ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos is a dubious translation:
-lean 3 declaration is
-  forall {c : ENNReal}, (Ne.{1} ENNReal c (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {y : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (Filter.Tendsto.{0, 0} ENNReal ENNReal (fun (x : ENNReal) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) c (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) x y)) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))))
-but is expected to have type
-  forall {c : ENNReal}, (Ne.{1} ENNReal c (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {y : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (Filter.Tendsto.{0, 0} ENNReal ENNReal (fun (x : ENNReal) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) c (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) x y)) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
-Case conversion may be inaccurate. Consider using '#align ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos ENNReal.tendsto_const_mul_rpow_nhds_zero_of_posₓ'. -/
 theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞) {y : ℝ} (hy : 0 < y) :
     Tendsto (fun x : ℝ≥0∞ => c * x ^ y) (𝓝 0) (𝓝 0) :=
   by
@@ -831,12 +531,6 @@ theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞
 
 end ENNReal
 
-/- warning: filter.tendsto.ennrpow_const -> Filter.Tendsto.ennrpow_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal} (r : Real), (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.topologicalSpace a)) -> (Filter.Tendsto.{u1, 0} α ENNReal (fun (x : α) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (m x) r) f (nhds.{0} ENNReal ENNReal.topologicalSpace (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a r)))
-but is expected to have type
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal} (r : Real), (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal a)) -> (Filter.Tendsto.{u1, 0} α ENNReal (fun (x : α) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (m x) r) f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a r)))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.ennrpow_const Filter.Tendsto.ennrpow_constₓ'. -/
 theorem Filter.Tendsto.ennrpow_const {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} (r : ℝ)
     (hm : Tendsto m f (𝓝 a)) : Tendsto (fun x => m x ^ r) f (𝓝 (a ^ r)) :=
   (ENNReal.continuous_rpow_const.Tendsto a).comp hm

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

@@ -47,10 +47,7 @@ Case conversion may be inaccurate. Consider using '#align zero_cpow_eq_nhds zero
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
-  exact
-    this.mono fun x hx => by
-      dsimp only
-      rw [zero_cpow hx, Pi.zero_apply]
+  exact this.mono fun x hx => by dsimp only; rw [zero_cpow hx, Pi.zero_apply]
   exact IsOpen.eventually_mem isOpen_ne hb
 #align zero_cpow_eq_nhds zero_cpow_eq_nhds
 
@@ -63,10 +60,7 @@ Case conversion may be inaccurate. Consider using '#align cpow_eq_nhds cpow_eq_n
 theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a] fun x => exp (log x * b) :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0
-  exact
-    this.mono fun x hx => by
-      dsimp only
-      rw [cpow_def_of_ne_zero hx]
+  exact this.mono fun x hx => by dsimp only; rw [cpow_def_of_ne_zero hx]
   exact IsOpen.eventually_mem isOpen_ne ha
 #align cpow_eq_nhds cpow_eq_nhds
 
@@ -80,10 +74,7 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
     (fun x => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
   suffices : ∀ᶠ x : ℂ × ℂ in 𝓝 p, x.1 ≠ 0
-  exact
-    this.mono fun x hx => by
-      dsimp only
-      rw [cpow_def_of_ne_zero hx]
+  exact this.mono fun x hx => by dsimp only; rw [cpow_def_of_ne_zero hx]
   refine' IsOpen.eventually_mem _ hp_fst
   change IsOpen ({ x : ℂ × ℂ | x.1 = 0 }ᶜ)
   rw [isOpen_compl_iff]
@@ -99,9 +90,7 @@ Case conversion may be inaccurate. Consider using '#align continuous_at_const_cp
 -- Continuity of `λ x, a ^ x`: union of these two lemmas is optimal.
 theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
-  have cpow_eq : (fun x : ℂ => a ^ x) = fun x => exp (log a * x) :=
-    by
-    ext1 b
+  have cpow_eq : (fun x : ℂ => a ^ x) = fun x => exp (log a * x) := by ext1 b;
     rw [cpow_def_of_ne_zero ha]
   rw [cpow_eq]
   exact continuous_exp.continuous_at.comp (ContinuousAt.mul continuousAt_const continuousAt_id)
@@ -116,8 +105,7 @@ Case conversion may be inaccurate. Consider using '#align continuous_at_const_cp
 theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
   by_cases ha : a = 0
-  · rw [ha, continuousAt_congr (zero_cpow_eq_nhds h)]
-    exact continuousAt_const
+  · rw [ha, continuousAt_congr (zero_cpow_eq_nhds h)]; exact continuousAt_const
   · exact continuousAt_const_cpow ha
 #align continuous_at_const_cpow' continuousAt_const_cpow'
 
@@ -133,11 +121,8 @@ works for `z = 0` but assumes `0 < re w`. -/
 theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im ≠ 0) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) p :=
   by
-  have hp_fst_ne_zero : p.fst ≠ 0 := by
-    intro h
-    cases hp_fst <;>
-      · rw [h] at hp_fst
-        simpa using hp_fst
+  have hp_fst_ne_zero : p.fst ≠ 0 := by intro h;
+    cases hp_fst <;> · rw [h] at hp_fst; simpa using hp_fst
   rw [continuousAt_congr (cpow_eq_nhds' hp_fst_ne_zero)]
   refine' continuous_exp.continuous_at.comp _
   refine'
@@ -301,10 +286,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow Real.continuousAt_const_rpowₓ'. -/
 theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a) b :=
   by
-  have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re :=
-    by
-    ext1 x
-    rw [rpow_eq_pow, rpow_def]
+  have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
   rw [this]
   refine' complex.continuous_re.continuous_at.comp _
   refine' (continuousAt_const_cpow _).comp complex.continuous_of_real.continuous_at
@@ -320,10 +302,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'ₓ'. -/
 theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow a) b :=
   by
-  have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re :=
-    by
-    ext1 x
-    rw [rpow_eq_pow, rpow_def]
+  have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re := by ext1 x; rw [rpow_eq_pow, rpow_def]
   rw [this]
   refine' complex.continuous_re.continuous_at.comp _
   refine' (continuousAt_const_cpow' _).comp complex.continuous_of_real.continuous_at
@@ -341,10 +320,7 @@ theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) :=
   by
   suffices : ∀ᶠ x : ℝ × ℝ in 𝓝 p, x.1 < 0
-  exact
-    this.mono fun x hx => by
-      dsimp only
-      rw [rpow_def_of_neg hx]
+  exact this.mono fun x hx => by dsimp only; rw [rpow_def_of_neg hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_fst continuous_const) hp_fst
 #align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_neg
 
@@ -358,10 +334,7 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
   suffices : ∀ᶠ x : ℝ × ℝ in 𝓝 p, 0 < x.1
-  exact
-    this.mono fun x hx => by
-      dsimp only
-      rw [rpow_def_of_pos hx]
+  exact this.mono fun x hx => by dsimp only; rw [rpow_def_of_pos hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_const continuous_fst) hp_fst
 #align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_pos
 
@@ -835,8 +808,7 @@ theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y
   apply continuous_iff_continuousAt.2 fun x => _
   rcases lt_trichotomy 0 y with (hy | rfl | hy)
   · exact continuous_at_rpow_const_of_pos hy
-  · simp only [rpow_zero]
-    exact continuousAt_const
+  · simp only [rpow_zero]; exact continuousAt_const
   · obtain ⟨z, hz⟩ : ∃ z, y = -z := ⟨-y, (neg_neg _).symm⟩
     have z_pos : 0 < z := by simpa [hz] using hy
     simp_rw [hz, rpow_neg]

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

@@ -5,7 +5,7 @@ Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébasti
   Rémy Degenne, David Loeffler
 
 ! This file was ported from Lean 3 source module analysis.special_functions.pow.continuity
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Pow.Asymptotics
 /-!
 # Continuity of power functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains lemmas about continuity of the power functions on `ℂ`, `ℝ`, `ℝ≥0`, and `ℝ≥0∞`.
 -/
 
@@ -819,7 +822,6 @@ private theorem continuous_at_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h :
   convert continuous_coe.continuous_at.comp (NNReal.continuousAt_rpow_const (Or.inr h.le)) using 1
   ext1 x
   simp [coe_rpow_of_nonneg _ h.le]
-#align ennreal.continuous_at_rpow_const_of_pos ennreal.continuous_at_rpow_const_of_pos
 
 /- warning: ennreal.continuous_rpow_const -> ENNReal.continuous_rpow_const is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -35,6 +35,12 @@ open Complex
 
 variable {α : Type _}
 
+/- warning: zero_cpow_eq_nhds -> zero_cpow_eq_nhds is a dubious translation:
+lean 3 declaration is
+  forall {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) b) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) x) (OfNat.ofNat.{0} (Complex -> Complex) 0 (OfNat.mk.{0} (Complex -> Complex) 0 (Zero.zero.{0} (Complex -> Complex) (Pi.instZero.{0, 0} Complex (fun (ᾰ : Complex) => Complex) (fun (i : Complex) => Complex.hasZero))))))
+but is expected to have type
+  forall {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) b) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) x) (OfNat.ofNat.{0} (Complex -> Complex) 0 (Zero.toOfNat0.{0} (Complex -> Complex) (Pi.instZero.{0, 0} Complex (fun (a._@.Mathlib.Order.Filter.Basic._hyg.19136 : Complex) => Complex) (fun (i : Complex) => Complex.instZeroComplex)))))
+Case conversion may be inaccurate. Consider using '#align zero_cpow_eq_nhds zero_cpow_eq_nhdsₓ'. -/
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
@@ -45,6 +51,12 @@ theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^
   exact IsOpen.eventually_mem isOpen_ne hb
 #align zero_cpow_eq_nhds zero_cpow_eq_nhds
 
+/- warning: cpow_eq_nhds -> cpow_eq_nhds is a dubious translation:
+lean 3 declaration is
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) a) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) x b) (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.log x) b)))
+but is expected to have type
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} Complex Complex (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) a) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) x b) (fun (x : Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.log x) b)))
+Case conversion may be inaccurate. Consider using '#align cpow_eq_nhds cpow_eq_nhdsₓ'. -/
 theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a] fun x => exp (log x * b) :=
   by
   suffices : ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0
@@ -55,6 +67,12 @@ theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) : (fun x => x ^ b) =ᶠ[𝓝 a]
   exact IsOpen.eventually_mem isOpen_ne ha
 #align cpow_eq_nhds cpow_eq_nhds
 
+/- warning: cpow_eq_nhds' -> cpow_eq_nhds' is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} Complex Complex}, (Ne.{1} Complex (Prod.fst.{0, 0} Complex Complex p) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Complex Complex) Complex (nhds.{0} (Prod.{0, 0} Complex Complex) (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) p) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (fun (x : Prod.{0, 0} Complex Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.log (Prod.fst.{0, 0} Complex Complex x)) (Prod.snd.{0, 0} Complex Complex x))))
+but is expected to have type
+  forall {p : Prod.{0, 0} Complex Complex}, (Ne.{1} Complex (Prod.fst.{0, 0} Complex Complex p) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Complex Complex) Complex (nhds.{0} (Prod.{0, 0} Complex Complex) (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) p) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (fun (x : Prod.{0, 0} Complex Complex) => Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.log (Prod.fst.{0, 0} Complex Complex x)) (Prod.snd.{0, 0} Complex Complex x))))
+Case conversion may be inaccurate. Consider using '#align cpow_eq_nhds' cpow_eq_nhds'ₓ'. -/
 theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
     (fun x => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -69,6 +87,12 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
   exact isClosed_eq continuous_fst continuous_const
 #align cpow_eq_nhds' cpow_eq_nhds'
 
+/- warning: continuous_at_const_cpow -> continuousAt_const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a x) b)
+but is expected to have type
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a x) b)
+Case conversion may be inaccurate. Consider using '#align continuous_at_const_cpow continuousAt_const_cpowₓ'. -/
 -- Continuity of `λ x, a ^ x`: union of these two lemmas is optimal.
 theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
@@ -80,6 +104,12 @@ theorem continuousAt_const_cpow {a b : ℂ} (ha : a ≠ 0) : ContinuousAt (fun x
   exact continuous_exp.continuous_at.comp (ContinuousAt.mul continuousAt_const continuousAt_id)
 #align continuous_at_const_cpow continuousAt_const_cpow
 
+/- warning: continuous_at_const_cpow' -> continuousAt_const_cpow' is a dubious translation:
+lean 3 declaration is
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a x) b)
+but is expected to have type
+  forall {a : Complex} {b : Complex}, (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a x) b)
+Case conversion may be inaccurate. Consider using '#align continuous_at_const_cpow' continuousAt_const_cpow'ₓ'. -/
 theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x => a ^ x) b :=
   by
   by_cases ha : a = 0
@@ -88,6 +118,12 @@ theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x
   · exact continuousAt_const_cpow ha
 #align continuous_at_const_cpow' continuousAt_const_cpow'
 
+/- warning: continuous_at_cpow -> continuousAt_cpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} Complex Complex}, (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
+but is expected to have type
+  forall {p : Prod.{0, 0} Complex Complex}, (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
+Case conversion may be inaccurate. Consider using '#align continuous_at_cpow continuousAt_cpowₓ'. -/
 /-- The function `z ^ w` is continuous in `(z, w)` provided that `z` does not belong to the interval
 `(-∞, 0]` on the real line. See also `complex.continuous_at_cpow_zero_of_re_pos` for a version that
 works for `z = 0` but assumes `0 < re w`. -/
@@ -106,17 +142,35 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
   exact continuousAt_clog hp_fst
 #align continuous_at_cpow continuousAt_cpow
 
+/- warning: continuous_at_cpow_const -> continuousAt_cpow_const is a dubious translation:
+lean 3 declaration is
+  forall {a : Complex} {b : Complex}, (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => Complex.cpow x b) a)
+but is expected to have type
+  forall {a : Complex} {b : Complex}, (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => Complex.cpow x b) a)
+Case conversion may be inaccurate. Consider using '#align continuous_at_cpow_const continuousAt_cpow_constₓ'. -/
 theorem continuousAt_cpow_const {a b : ℂ} (ha : 0 < a.re ∨ a.im ≠ 0) :
     ContinuousAt (fun x => cpow x b) a :=
   Tendsto.comp (@continuousAt_cpow (a, b) ha) (continuousAt_id.Prod continuousAt_const)
 #align continuous_at_cpow_const continuousAt_cpow_const
 
+/- warning: filter.tendsto.cpow -> Filter.Tendsto.cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Complex} {g : α -> Complex} {a : Complex} {b : Complex}, (Filter.Tendsto.{u1, 0} α Complex f l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) a)) -> (Filter.Tendsto.{u1, 0} α Complex g l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) b)) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Filter.Tendsto.{u1, 0} α Complex (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)) l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Complex} {g : α -> Complex} {a : Complex} {b : Complex}, (Filter.Tendsto.{u1, 0} α Complex f l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) a)) -> (Filter.Tendsto.{u1, 0} α Complex g l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) b)) -> (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re a)) (Ne.{1} Real (Complex.im a) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Filter.Tendsto.{u1, 0} α Complex (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) (g x)) l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a b)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.cpow Filter.Tendsto.cpowₓ'. -/
 theorem Filter.Tendsto.cpow {l : Filter α} {f g : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 a))
     (hg : Tendsto g l (𝓝 b)) (ha : 0 < a.re ∨ a.im ≠ 0) :
     Tendsto (fun x => f x ^ g x) l (𝓝 (a ^ b)) :=
   (@continuousAt_cpow (a, b) ha).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.cpow Filter.Tendsto.cpow
 
+/- warning: filter.tendsto.const_cpow -> Filter.Tendsto.const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Complex} {a : Complex} {b : Complex}, (Filter.Tendsto.{u1, 0} α Complex f l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) b)) -> (Or (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) -> (Filter.Tendsto.{u1, 0} α Complex (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a (f x)) l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Complex} {a : Complex} {b : Complex}, (Filter.Tendsto.{u1, 0} α Complex f l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) b)) -> (Or (Ne.{1} Complex a (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) -> (Filter.Tendsto.{u1, 0} α Complex (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a (f x)) l (nhds.{0} Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) a b)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.const_cpow Filter.Tendsto.const_cpowₓ'. -/
 theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 b))
     (h : a ≠ 0 ∨ b ≠ 0) : Tendsto (fun x => a ^ f x) l (𝓝 (a ^ b)) :=
   by
@@ -127,45 +181,99 @@ theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (
 
 variable [TopologicalSpace α] {f g : α → ℂ} {s : Set α} {a : α}
 
+/- warning: continuous_within_at.cpow -> ContinuousWithinAt.cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {s : Set.{u1} α} {a : α}, (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f s a) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) g s a) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)) s a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {s : Set.{u1} α} {a : α}, (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f s a) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) g s a) -> (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) (g x)) s a)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.cpow ContinuousWithinAt.cpowₓ'. -/
 theorem ContinuousWithinAt.cpow (hf : ContinuousWithinAt f s a) (hg : ContinuousWithinAt g s a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousWithinAt (fun x => f x ^ g x) s a :=
   hf.cpow hg h0
 #align continuous_within_at.cpow ContinuousWithinAt.cpow
 
+/- warning: continuous_within_at.const_cpow -> ContinuousWithinAt.const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {a : α} {b : Complex}, (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f s a) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) b (f x)) s a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {a : α} {b : Complex}, (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f s a) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) -> (ContinuousWithinAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) b (f x)) s a)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.const_cpow ContinuousWithinAt.const_cpowₓ'. -/
 theorem ContinuousWithinAt.const_cpow {b : ℂ} (hf : ContinuousWithinAt f s a)
     (h : b ≠ 0 ∨ f a ≠ 0) : ContinuousWithinAt (fun x => b ^ f x) s a :=
   hf.const_cpow h
 #align continuous_within_at.const_cpow ContinuousWithinAt.const_cpow
 
+/- warning: continuous_at.cpow -> ContinuousAt.cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {a : α}, (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f a) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) g a) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {a : α}, (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f a) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) g a) -> (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) (g x)) a)
+Case conversion may be inaccurate. Consider using '#align continuous_at.cpow ContinuousAt.cpowₓ'. -/
 theorem ContinuousAt.cpow (hf : ContinuousAt f a) (hg : ContinuousAt g a)
     (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousAt (fun x => f x ^ g x) a :=
   hf.cpow hg h0
 #align continuous_at.cpow ContinuousAt.cpow
 
+/- warning: continuous_at.const_cpow -> ContinuousAt.const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {a : α} {b : Complex}, (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f a) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) b (f x)) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {a : α} {b : Complex}, (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f a) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) -> (ContinuousAt.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) b (f x)) a)
+Case conversion may be inaccurate. Consider using '#align continuous_at.const_cpow ContinuousAt.const_cpowₓ'. -/
 theorem ContinuousAt.const_cpow {b : ℂ} (hf : ContinuousAt f a) (h : b ≠ 0 ∨ f a ≠ 0) :
     ContinuousAt (fun x => b ^ f x) a :=
   hf.const_cpow h
 #align continuous_at.const_cpow ContinuousAt.const_cpow
 
+/- warning: continuous_on.cpow -> ContinuousOn.cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f s) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) g s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f s) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) g s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) (g x)) s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.cpow ContinuousOn.cpowₓ'. -/
 theorem ContinuousOn.cpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h0 : ∀ a ∈ s, 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ g x) s := fun a ha =>
   (hf a ha).cpow (hg a ha) (h0 a ha)
 #align continuous_on.cpow ContinuousOn.cpow
 
+/- warning: continuous_on.const_cpow -> ContinuousOn.const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {b : Complex}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f s) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) b (f x)) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {b : Complex}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f s) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) b (f x)) s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.const_cpow ContinuousOn.const_cpowₓ'. -/
 theorem ContinuousOn.const_cpow {b : ℂ} (hf : ContinuousOn f s) (h : b ≠ 0 ∨ ∀ a ∈ s, f a ≠ 0) :
     ContinuousOn (fun x => b ^ f x) s := fun a ha => (hf a ha).const_cpow (h.imp id fun h => h a ha)
 #align continuous_on.const_cpow ContinuousOn.const_cpow
 
+/- warning: continuous.cpow -> Continuous.cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex}, (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) g) -> (forall (a : α), Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) (g x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {g : α -> Complex}, (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) g) -> (forall (a : α), Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align continuous.cpow Continuous.cpowₓ'. -/
 theorem Continuous.cpow (hf : Continuous f) (hg : Continuous g)
     (h0 : ∀ a, 0 < (f a).re ∨ (f a).im ≠ 0) : Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.cpow hg.ContinuousAt (h0 a)
 #align continuous.cpow Continuous.cpow
 
+/- warning: continuous.const_cpow -> Continuous.const_cpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {b : Complex}, (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (forall (a : α), Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) b (f x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {b : Complex}, (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f) -> (Or (Ne.{1} Complex b (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (forall (a : α), Ne.{1} Complex (f a) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) -> (Continuous.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) b (f x)))
+Case conversion may be inaccurate. Consider using '#align continuous.const_cpow Continuous.const_cpowₓ'. -/
 theorem Continuous.const_cpow {b : ℂ} (hf : Continuous f) (h : b ≠ 0 ∨ ∀ a, f a ≠ 0) :
     Continuous fun x => b ^ f x :=
   continuous_iff_continuousAt.2 fun a => hf.ContinuousAt.const_cpow <| h.imp id fun h => h a
 #align continuous.const_cpow Continuous.const_cpow
 
+/- warning: continuous_on.cpow_const -> ContinuousOn.cpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {b : Complex}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) f s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (f x) b) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Complex} {s : Set.{u1} α} {b : Complex}, (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) f s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (f a))) (Ne.{1} Real (Complex.im (f a)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (ContinuousOn.{u1, 0} α Complex _inst_1 (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : α) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (f x) b) s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.cpow_const ContinuousOn.cpow_constₓ'. -/
 theorem ContinuousOn.cpow_const {b : ℂ} (hf : ContinuousOn f s)
     (h : ∀ a : α, a ∈ s → 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ b) s :=
   hf.cpow continuousOn_const h
@@ -182,6 +290,12 @@ section RpowLimits
 
 namespace Real
 
+/- warning: real.continuous_at_const_rpow -> Real.continuousAt_const_rpow is a dubious translation:
+lean 3 declaration is
+  forall {a : Real} {b : Real}, (Ne.{1} Real a (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
+but is expected to have type
+  forall {a : Real} {b : Real}, (Ne.{1} Real a (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow Real.continuousAt_const_rpowₓ'. -/
 theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re :=
@@ -195,6 +309,12 @@ theorem continuousAt_const_rpow {a b : ℝ} (h : a ≠ 0) : ContinuousAt (rpow a
   exact h
 #align real.continuous_at_const_rpow Real.continuousAt_const_rpow
 
+/- warning: real.continuous_at_const_rpow' -> Real.continuousAt_const_rpow' is a dubious translation:
+lean 3 declaration is
+  forall {a : Real} {b : Real}, (Ne.{1} Real b (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
+but is expected to have type
+  forall {a : Real} {b : Real}, (Ne.{1} Real b (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Real.rpow a) b)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'ₓ'. -/
 theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow a) b :=
   by
   have : rpow a = fun x : ℝ => ((a : ℂ) ^ (x : ℂ)).re :=
@@ -208,6 +328,12 @@ theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow
   exact h
 #align real.continuous_at_const_rpow' Real.continuousAt_const_rpow'
 
+/- warning: real.rpow_eq_nhds_of_neg -> Real.rpow_eq_nhds_of_neg is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.hasLt (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))) (Real.cos (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Prod.snd.{0, 0} Real Real x) Real.pi))))
+but is expected to have type
+  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.instLTReal (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))) (Real.cos (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Prod.snd.{0, 0} Real Real x) Real.pi))))
+Case conversion may be inaccurate. Consider using '#align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_negₓ'. -/
 theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) :=
   by
@@ -219,6 +345,12 @@ theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
   exact IsOpen.eventually_mem (isOpen_lt continuous_fst continuous_const) hp_fst
 #align real.rpow_eq_nhds_of_neg Real.rpow_eq_nhds_of_neg
 
+/- warning: real.rpow_eq_nhds_of_pos -> Real.rpow_eq_nhds_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.fst.{0, 0} Real Real p)) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))))
+but is expected to have type
+  forall {p : Prod.{0, 0} Real Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.fst.{0, 0} Real Real p)) -> (Filter.EventuallyEq.{0, 0} (Prod.{0, 0} Real Real) Real (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) p) (fun (x : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real x) (Prod.snd.{0, 0} Real Real x)) (fun (x : Prod.{0, 0} Real Real) => Real.exp (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log (Prod.fst.{0, 0} Real Real x)) (Prod.snd.{0, 0} Real Real x))))
+Case conversion may be inaccurate. Consider using '#align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_posₓ'. -/
 theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) :=
   by
@@ -230,6 +362,12 @@ theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
   exact IsOpen.eventually_mem (isOpen_lt continuous_const continuous_fst) hp_fst
 #align real.rpow_eq_nhds_of_pos Real.rpow_eq_nhds_of_pos
 
+/- warning: real.continuous_at_rpow_of_ne -> Real.continuousAt_rpow_of_ne is a dubious translation:
+lean 3 declaration is
+  forall (p : Prod.{0, 0} Real Real), (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+but is expected to have type
+  forall (p : Prod.{0, 0} Real Real), (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_of_ne Real.continuousAt_rpow_of_neₓ'. -/
 theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -247,6 +385,12 @@ theorem continuousAt_rpow_of_ne (p : ℝ × ℝ) (hp : p.1 ≠ 0) :
     exact hp.lt.ne.symm
 #align real.continuous_at_rpow_of_ne Real.continuousAt_rpow_of_ne
 
+/- warning: real.continuous_at_rpow_of_pos -> Real.continuousAt_rpow_of_pos is a dubious translation:
+lean 3 declaration is
+  forall (p : Prod.{0, 0} Real Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{0, 0} Real Real p)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+but is expected to have type
+  forall (p : Prod.{0, 0} Real Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{0, 0} Real Real p)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_of_pos Real.continuousAt_rpow_of_posₓ'. -/
 theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   by
@@ -266,11 +410,23 @@ theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
     ContinuousAt, zero_rpow hp.ne'] using B.sup (C.mono_right (pure_le_nhds _))
 #align real.continuous_at_rpow_of_pos Real.continuousAt_rpow_of_pos
 
+/- warning: real.continuous_at_rpow -> Real.continuousAt_rpow is a dubious translation:
+lean 3 declaration is
+  forall (p : Prod.{0, 0} Real Real), (Or (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Prod.snd.{0, 0} Real Real p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+but is expected to have type
+  forall (p : Prod.{0, 0} Real Real), (Or (Ne.{1} Real (Prod.fst.{0, 0} Real Real p) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Prod.snd.{0, 0} Real Real p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Real) Real (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (p : Prod.{0, 0} Real Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Prod.fst.{0, 0} Real Real p) (Prod.snd.{0, 0} Real Real p)) p)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow Real.continuousAt_rpowₓ'. -/
 theorem continuousAt_rpow (p : ℝ × ℝ) (h : p.1 ≠ 0 ∨ 0 < p.2) :
     ContinuousAt (fun p : ℝ × ℝ => p.1 ^ p.2) p :=
   h.elim (fun h => continuousAt_rpow_of_ne p h) fun h => continuousAt_rpow_of_pos p h
 #align real.continuous_at_rpow Real.continuousAt_rpow
 
+/- warning: real.continuous_at_rpow_const -> Real.continuousAt_rpow_const is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (q : Real), (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) q)) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x q) x)
+but is expected to have type
+  forall (x : Real) (q : Real), (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) q)) -> (ContinuousAt.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : Real) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x q) x)
+Case conversion may be inaccurate. Consider using '#align real.continuous_at_rpow_const Real.continuousAt_rpow_constₓ'. -/
 theorem continuousAt_rpow_const (x : ℝ) (q : ℝ) (h : x ≠ 0 ∨ 0 < q) :
     ContinuousAt (fun x : ℝ => x ^ q) x :=
   by
@@ -286,11 +442,23 @@ section
 
 variable {α : Type _}
 
+/- warning: filter.tendsto.rpow -> Filter.Tendsto.rpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {g : α -> Real} {x : Real} {y : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Filter.Tendsto.{u1, 0} α Real g l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (Filter.Tendsto.{u1, 0} α Real (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x y)))
+but is expected to have type
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {g : α -> Real} {x : Real} {y : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Filter.Tendsto.{u1, 0} α Real g l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (Filter.Tendsto.{u1, 0} α Real (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x y)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.rpow Filter.Tendsto.rpowₓ'. -/
 theorem Filter.Tendsto.rpow {l : Filter α} {f g : α → ℝ} {x y : ℝ} (hf : Tendsto f l (𝓝 x))
     (hg : Tendsto g l (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) : Tendsto (fun t => f t ^ g t) l (𝓝 (x ^ y)) :=
   (Real.continuousAt_rpow (x, y) h).Tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.rpow Filter.Tendsto.rpow
 
+/- warning: filter.tendsto.rpow_const -> Filter.Tendsto.rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {x : Real} {p : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (Filter.Tendsto.{u1, 0} α Real (fun (a : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f a) p) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x p)))
+but is expected to have type
+  forall {α : Type.{u1}} {l : Filter.{u1} α} {f : α -> Real} {x : Real} {p : Real}, (Filter.Tendsto.{u1, 0} α Real f l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) x)) -> (Or (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (Filter.Tendsto.{u1, 0} α Real (fun (a : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f a) p) l (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x p)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.rpow_const Filter.Tendsto.rpow_constₓ'. -/
 theorem Filter.Tendsto.rpow_const {l : Filter α} {f : α → ℝ} {x p : ℝ} (hf : Tendsto f l (𝓝 x))
     (h : x ≠ 0 ∨ 0 ≤ p) : Tendsto (fun a => f a ^ p) l (𝓝 (x ^ p)) :=
   if h0 : 0 = p then h0 ▸ by simp [tendsto_const_nhds]
@@ -299,40 +467,88 @@ theorem Filter.Tendsto.rpow_const {l : Filter α} {f : α → ℝ} {x p : ℝ} (
 
 variable [TopologicalSpace α] {f g : α → ℝ} {s : Set α} {x : α} {p : ℝ}
 
+/- warning: continuous_at.rpow -> ContinuousAt.rpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {x : α}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {x : α}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.rpow ContinuousAt.rpowₓ'. -/
 theorem ContinuousAt.rpow (hf : ContinuousAt f x) (hg : ContinuousAt g x) (h : f x ≠ 0 ∨ 0 < g x) :
     ContinuousAt (fun t => f t ^ g t) x :=
   hf.rpow hg h
 #align continuous_at.rpow ContinuousAt.rpow
 
+/- warning: continuous_within_at.rpow -> ContinuousWithinAt.rpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α} {x : α}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α} {x : α}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.rpow ContinuousWithinAt.rpowₓ'. -/
 theorem ContinuousWithinAt.rpow (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : f x ≠ 0 ∨ 0 < g x) : ContinuousWithinAt (fun t => f t ^ g t) s x :=
   hf.rpow hg h
 #align continuous_within_at.rpow ContinuousWithinAt.rpow
 
+/- warning: continuous_on.rpow -> ContinuousOn.rpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x)))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f t) (g t)) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real} {s : Set.{u1} α}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x)))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (t : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f t) (g t)) s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.rpow ContinuousOn.rpowₓ'. -/
 theorem ContinuousOn.rpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
     (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 < g x) : ContinuousOn (fun t => f t ^ g t) s := fun t ht =>
   (hf t ht).rpow (hg t ht) (h t ht)
 #align continuous_on.rpow ContinuousOn.rpow
 
+/- warning: continuous.rpow -> Continuous.rpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (g x))) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) (g x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {g : α -> Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (g x))) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align continuous.rpow Continuous.rpowₓ'. -/
 theorem Continuous.rpow (hf : Continuous f) (hg : Continuous g) (h : ∀ x, f x ≠ 0 ∨ 0 < g x) :
     Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow hg.ContinuousAt (h x)
 #align continuous.rpow Continuous.rpow
 
+/- warning: continuous_within_at.rpow_const -> ContinuousWithinAt.rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {x : α} {p : Real}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {x : α} {p : Real}, (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (ContinuousWithinAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.rpow_const ContinuousWithinAt.rpow_constₓ'. -/
 theorem ContinuousWithinAt.rpow_const (hf : ContinuousWithinAt f s x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousWithinAt (fun x => f x ^ p) s x :=
   hf.rpow_const h
 #align continuous_within_at.rpow_const ContinuousWithinAt.rpow_const
 
+/- warning: continuous_at.rpow_const -> ContinuousAt.rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {x : α} {p : Real}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {x : α} {p : Real}, (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f x) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (ContinuousAt.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.rpow_const ContinuousAt.rpow_constₓ'. -/
 theorem ContinuousAt.rpow_const (hf : ContinuousAt f x) (h : f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousAt (fun x => f x ^ p) x :=
   hf.rpow_const h
 #align continuous_at.rpow_const ContinuousAt.rpow_const
 
+/- warning: continuous_on.rpow_const -> ContinuousOn.rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {p : Real}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {s : Set.{u1} α} {p : Real}, (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p))) -> (ContinuousOn.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p) s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.rpow_const ContinuousOn.rpow_constₓ'. -/
 theorem ContinuousOn.rpow_const (hf : ContinuousOn f s) (h : ∀ x ∈ s, f x ≠ 0 ∨ 0 ≤ p) :
     ContinuousOn (fun x => f x ^ p) s := fun x hx => (hf x hx).rpow_const (h x hx)
 #align continuous_on.rpow_const ContinuousOn.rpow_const
 
+/- warning: continuous.rpow_const -> Continuous.rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {p : Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (f x) p))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real} {p : Real}, (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f) -> (forall (x : α), Or (Ne.{1} Real (f x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)) -> (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (x : α) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (f x) p))
+Case conversion may be inaccurate. Consider using '#align continuous.rpow_const Continuous.rpow_constₓ'. -/
 theorem Continuous.rpow_const (hf : Continuous f) (h : ∀ x, f x ≠ 0 ∨ 0 ≤ p) :
     Continuous fun x => f x ^ p :=
   continuous_iff_continuousAt.2 fun x => hf.ContinuousAt.rpow_const (h x)
@@ -352,6 +568,12 @@ section CpowLimits2
 
 namespace Complex
 
+/- warning: complex.continuous_at_cpow_zero_of_re_pos -> Complex.continuousAt_cpow_zero_of_re_pos is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (Prod.mk.{0, 0} Complex Complex (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) z))
+but is expected to have type
+  forall {z : Complex}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) (Prod.mk.{0, 0} Complex Complex (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) z))
+Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_zero_of_re_pos Complex.continuousAt_cpow_zero_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow` and `complex.continuous_at_cpow_of_re_pos`. -/
 theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) (0, z) :=
@@ -377,6 +599,12 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
         real.pi_pos.le
 #align complex.continuous_at_cpow_zero_of_re_pos Complex.continuousAt_cpow_zero_of_re_pos
 
+/- warning: complex.continuous_at_cpow_of_re_pos -> Complex.continuousAt_cpow_of_re_pos is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} Complex Complex}, (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re (Prod.snd.{0, 0} Complex Complex p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (Prod.topologicalSpace.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
+but is expected to have type
+  forall {p : Prod.{0, 0} Complex Complex}, (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.fst.{0, 0} Complex Complex p))) (Ne.{1} Real (Complex.im (Prod.fst.{0, 0} Complex Complex p)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re (Prod.snd.{0, 0} Complex Complex p))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Complex Complex) Complex (instTopologicalSpaceProd.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Prod.{0, 0} Complex Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Prod.fst.{0, 0} Complex Complex x) (Prod.snd.{0, 0} Complex Complex x)) p)
+Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow` for a version that assumes `p.1 ≠ 0` but makes no
 assumptions about `p.2`. -/
 theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.1.im ≠ 0) (h₂ : 0 < p.2.re) :
@@ -389,6 +617,12 @@ theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.
   exacts[continuousAt_cpow h₁, continuous_at_cpow_zero_of_re_pos h₂]
 #align complex.continuous_at_cpow_of_re_pos Complex.continuousAt_cpow_of_re_pos
 
+/- warning: complex.continuous_at_cpow_const_of_re_pos -> Complex.continuousAt_cpow_const_of_re_pos is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re w)) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) x w) z)
+but is expected to have type
+  forall {z : Complex} {w : Complex}, (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re w)) -> (ContinuousAt.{0, 0} Complex Complex (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) x w) z)
+Case conversion may be inaccurate. Consider using '#align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_posₓ'. -/
 /-- See also `continuous_at_cpow_const` for a version that assumes `z ≠ 0` but makes no
 assumptions about `w`. -/
 theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z ≠ 0) (hw : 0 < re w) :
@@ -396,6 +630,12 @@ theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z
   Tendsto.comp (@continuousAt_cpow_of_re_pos (z, w) hz hw) (continuousAt_id.Prod continuousAt_const)
 #align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_pos
 
+/- warning: complex.continuous_at_of_real_cpow -> Complex.continuousAt_of_real_cpow is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Complex) Complex (Prod.topologicalSpace.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (p : Prod.{0, 0} Real Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Prod.fst.{0, 0} Real Complex p)) (Prod.snd.{0, 0} Real Complex p)) (Prod.mk.{0, 0} Real Complex x y))
+but is expected to have type
+  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} Real Complex) Complex (instTopologicalSpaceProd.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (p : Prod.{0, 0} Real Complex) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' (Prod.fst.{0, 0} Real Complex p)) (Prod.snd.{0, 0} Real Complex p)) (Prod.mk.{0, 0} Real Complex x y))
+Case conversion may be inaccurate. Consider using '#align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpowₓ'. -/
 /-- Continuity of `(x, y) ↦ x ^ y` as a function on `ℝ × ℂ`. -/
 theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun p => ↑p.1 ^ p.2 : ℝ × ℂ → ℂ) (x, y) :=
@@ -428,12 +668,24 @@ theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
     · exact (continuous_exp.comp (continuous_const.mul continuous_snd)).ContinuousAt
 #align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpow
 
+/- warning: complex.continuous_at_of_real_cpow_const -> Complex.continuousAt_of_real_cpow_const is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (ContinuousAt.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (a : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) y) x)
+but is expected to have type
+  forall (x : Real) (y : Complex), (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (ContinuousAt.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (a : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' a) y) x)
+Case conversion may be inaccurate. Consider using '#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_constₓ'. -/
 theorem continuousAt_of_real_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => a ^ y : ℝ → ℂ) x :=
   @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_of_real_cpow x y h)
     (continuous_id.prod_mk continuous_const).ContinuousAt
 #align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_const
 
+/- warning: complex.continuous_of_real_cpow_const -> Complex.continuous_of_real_cpow_const is a dubious translation:
+lean 3 declaration is
+  forall {y : Complex}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re y)) -> (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))) (fun (x : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) y))
+but is expected to have type
+  forall {y : Complex}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re y)) -> (Continuous.{0, 0} Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))) (fun (x : Real) => HPow.hPow.{0, 0, 0} Complex Complex Complex (instHPow.{0, 0} Complex Complex Complex.instPowComplex) (Complex.ofReal' x) y))
+Case conversion may be inaccurate. Consider using '#align complex.continuous_of_real_cpow_const Complex.continuous_of_real_cpow_constₓ'. -/
 theorem continuous_of_real_cpow_const {y : ℂ} (hs : 0 < y.re) :
     Continuous (fun x => x ^ y : ℝ → ℂ) :=
   continuous_iff_continuousAt.mpr fun x => continuousAt_of_real_cpow_const x y (Or.inl hs)
@@ -448,6 +700,12 @@ end CpowLimits2
 
 namespace NNReal
 
+/- warning: nnreal.continuous_at_rpow -> NNReal.continuousAt_rpow is a dubious translation:
+lean 3 declaration is
+  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} NNReal Real) NNReal (Prod.topologicalSpace.{0, 0} NNReal Real NNReal.topologicalSpace (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) NNReal.topologicalSpace (fun (p : Prod.{0, 0} NNReal Real) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (Prod.fst.{0, 0} NNReal Real p) (Prod.snd.{0, 0} NNReal Real p)) (Prod.mk.{0, 0} NNReal Real x y))
+but is expected to have type
+  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (ContinuousAt.{0, 0} (Prod.{0, 0} NNReal Real) NNReal (instTopologicalSpaceProd.{0, 0} NNReal Real NNReal.instTopologicalSpaceNNReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) NNReal.instTopologicalSpaceNNReal (fun (p : Prod.{0, 0} NNReal Real) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Prod.fst.{0, 0} NNReal Real p) (Prod.snd.{0, 0} NNReal Real p)) (Prod.mk.{0, 0} NNReal Real x y))
+Case conversion may be inaccurate. Consider using '#align nnreal.continuous_at_rpow NNReal.continuousAt_rpowₓ'. -/
 theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
     ContinuousAt (fun p : ℝ≥0 × ℝ => p.1 ^ p.2) (x, y) :=
   by
@@ -467,6 +725,12 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).ContinuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
 
+/- warning: nnreal.eventually_pow_one_div_le -> NNReal.eventually_pow_one_div_le is a dubious translation:
+lean 3 declaration is
+  forall (x : NNReal) {y : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
+but is expected to have type
+  forall (x : NNReal) {y : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Nat.cast.{0} Real Real.natCast n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+Case conversion may be inaccurate. Consider using '#align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_leₓ'. -/
 theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -481,6 +745,12 @@ end NNReal
 
 open Filter
 
+/- warning: filter.tendsto.nnrpow -> Filter.Tendsto.nnrpow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {u : α -> NNReal} {v : α -> Real} {x : NNReal} {y : Real}, (Filter.Tendsto.{u1, 0} α NNReal u f (nhds.{0} NNReal NNReal.topologicalSpace x)) -> (Filter.Tendsto.{u1, 0} α Real v f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (Filter.Tendsto.{u1, 0} α NNReal (fun (a : α) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) (u a) (v a)) f (nhds.{0} NNReal NNReal.topologicalSpace (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x y)))
+but is expected to have type
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {u : α -> NNReal} {v : α -> Real} {x : NNReal} {y : Real}, (Filter.Tendsto.{u1, 0} α NNReal u f (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal x)) -> (Filter.Tendsto.{u1, 0} α Real v f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) y)) -> (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (Filter.Tendsto.{u1, 0} α NNReal (fun (a : α) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (u a) (v a)) f (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x y)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.nnrpow Filter.Tendsto.nnrpowₓ'. -/
 theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0} {v : α → ℝ} {x : ℝ≥0}
     {y : ℝ} (hx : Tendsto u f (𝓝 x)) (hy : Tendsto v f (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) :
     Tendsto (fun a => u a ^ v a) f (𝓝 (x ^ y)) :=
@@ -489,6 +759,12 @@ theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0}
 
 namespace NNReal
 
+/- warning: nnreal.continuous_at_rpow_const -> NNReal.continuousAt_rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y)) -> (ContinuousAt.{0, 0} NNReal NNReal NNReal.topologicalSpace NNReal.topologicalSpace (fun (z : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) z y) x)
+but is expected to have type
+  forall {x : NNReal} {y : Real}, (Or (Ne.{1} NNReal x (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y)) -> (ContinuousAt.{0, 0} NNReal NNReal NNReal.instTopologicalSpaceNNReal NNReal.instTopologicalSpaceNNReal (fun (z : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) z y) x)
+Case conversion may be inaccurate. Consider using '#align nnreal.continuous_at_rpow_const NNReal.continuousAt_rpow_constₓ'. -/
 theorem continuousAt_rpow_const {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 ≤ y) :
     ContinuousAt (fun z => z ^ y) x :=
   h.elim (fun h => tendsto_id.nnrpow tendsto_const_nhds (Or.inl h)) fun h =>
@@ -496,6 +772,12 @@ theorem continuousAt_rpow_const {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 ≤ y
       tendsto_id.nnrpow tendsto_const_nhds (Or.inr h)
 #align nnreal.continuous_at_rpow_const NNReal.continuousAt_rpow_const
 
+/- warning: nnreal.continuous_rpow_const -> NNReal.continuous_rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (Continuous.{0, 0} NNReal NNReal NNReal.topologicalSpace NNReal.topologicalSpace (fun (x : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) x y))
+but is expected to have type
+  forall {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (Continuous.{0, 0} NNReal NNReal NNReal.instTopologicalSpaceNNReal NNReal.instTopologicalSpaceNNReal (fun (x : NNReal) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) x y))
+Case conversion may be inaccurate. Consider using '#align nnreal.continuous_rpow_const NNReal.continuous_rpow_constₓ'. -/
 theorem continuous_rpow_const {y : ℝ} (h : 0 ≤ y) : Continuous fun x : ℝ≥0 => x ^ y :=
   continuous_iff_continuousAt.2 fun x => continuousAt_rpow_const (Or.inr h)
 #align nnreal.continuous_rpow_const NNReal.continuous_rpow_const
@@ -507,6 +789,12 @@ end NNReal
 
 namespace ENNReal
 
+/- warning: ennreal.eventually_pow_one_div_le -> ENNReal.eventually_pow_one_div_le is a dubious translation:
+lean 3 declaration is
+  forall {x : ENNReal}, (Ne.{1} ENNReal x (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {y : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))))
+but is expected to have type
+  forall {x : ENNReal}, (Ne.{1} ENNReal x (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {y : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) y) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Nat.cast.{0} Real Real.natCast n))) y) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.eventually_pow_one_div_le ENNReal.eventually_pow_one_div_leₓ'. -/
 theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0∞} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y :=
   by
@@ -533,6 +821,12 @@ private theorem continuous_at_rpow_const_of_pos {x : ℝ≥0∞} {y : ℝ} (h :
   simp [coe_rpow_of_nonneg _ h.le]
 #align ennreal.continuous_at_rpow_const_of_pos ennreal.continuous_at_rpow_const_of_pos
 
+/- warning: ennreal.continuous_rpow_const -> ENNReal.continuous_rpow_const is a dubious translation:
+lean 3 declaration is
+  forall {y : Real}, Continuous.{0, 0} ENNReal ENNReal ENNReal.topologicalSpace ENNReal.topologicalSpace (fun (a : ENNReal) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a y)
+but is expected to have type
+  forall {y : Real}, Continuous.{0, 0} ENNReal ENNReal ENNReal.instTopologicalSpaceENNReal ENNReal.instTopologicalSpaceENNReal (fun (a : ENNReal) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a y)
+Case conversion may be inaccurate. Consider using '#align ennreal.continuous_rpow_const ENNReal.continuous_rpow_constₓ'. -/
 @[continuity]
 theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y :=
   by
@@ -547,6 +841,12 @@ theorem continuous_rpow_const {y : ℝ} : Continuous fun a : ℝ≥0∞ => a ^ y
     exact continuous_inv.continuous_at.comp (continuous_at_rpow_const_of_pos z_pos)
 #align ennreal.continuous_rpow_const ENNReal.continuous_rpow_const
 
+/- warning: ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos -> ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {c : ENNReal}, (Ne.{1} ENNReal c (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {y : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (Filter.Tendsto.{0, 0} ENNReal ENNReal (fun (x : ENNReal) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) c (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) x y)) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))))
+but is expected to have type
+  forall {c : ENNReal}, (Ne.{1} ENNReal c (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {y : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (Filter.Tendsto.{0, 0} ENNReal ENNReal (fun (x : ENNReal) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) c (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) x y)) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.tendsto_const_mul_rpow_nhds_zero_of_pos ENNReal.tendsto_const_mul_rpow_nhds_zero_of_posₓ'. -/
 theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞) {y : ℝ} (hy : 0 < y) :
     Tendsto (fun x : ℝ≥0∞ => c * x ^ y) (𝓝 0) (𝓝 0) :=
   by
@@ -557,6 +857,12 @@ theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞
 
 end ENNReal
 
+/- warning: filter.tendsto.ennrpow_const -> Filter.Tendsto.ennrpow_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal} (r : Real), (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.topologicalSpace a)) -> (Filter.Tendsto.{u1, 0} α ENNReal (fun (x : α) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) (m x) r) f (nhds.{0} ENNReal ENNReal.topologicalSpace (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.Real.hasPow) a r)))
+but is expected to have type
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal} (r : Real), (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal a)) -> (Filter.Tendsto.{u1, 0} α ENNReal (fun (x : α) => HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) (m x) r) f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (HPow.hPow.{0, 0, 0} ENNReal Real ENNReal (instHPow.{0, 0} ENNReal Real ENNReal.instPowENNRealReal) a r)))
+Case conversion may be inaccurate. Consider using '#align filter.tendsto.ennrpow_const Filter.Tendsto.ennrpow_constₓ'. -/
 theorem Filter.Tendsto.ennrpow_const {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} (r : ℝ)
     (hm : Tendsto m f (𝓝 a)) : Tendsto (fun x => m x ^ r) f (𝓝 (a ^ r)) :=
   (ENNReal.continuous_rpow_const.Tendsto a).comp hm

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

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

@@ -440,7 +440,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
   rw [tsub_add_cancel_of_le hy.le] at hm
   refine' eventually_atTop.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
-    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
+    NNReal.rpow_natCast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
 #align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_le
 
 end NNReal

@@ -357,7 +357,7 @@ assumptions about `p.2`. -/
 theorem continuousAt_cpow_of_re_pos {p : ℂ × ℂ} (h₁ : 0 ≤ p.1.re ∨ p.1.im ≠ 0) (h₂ : 0 < p.2.re) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) p := by
   cases' p with z w
-  rw [← not_lt_zero_iff, lt_iff_le_and_ne, not_and_or, Ne.def, Classical.not_not,
+  rw [← not_lt_zero_iff, lt_iff_le_and_ne, not_and_or, Ne, Classical.not_not,
     not_le_zero_iff] at h₁
   rcases h₁ with (h₁ | (rfl : z = 0))
   exacts [continuousAt_cpow h₁, continuousAt_cpow_zero_of_re_pos h₂]

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -17,7 +17,8 @@ This file contains lemmas about continuity of the power functions on `ℂ`, `ℝ
 
 noncomputable section
 
-open Classical Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
+open scoped Classical
+open Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
 
 open Filter Finset Set
 

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>

@@ -33,9 +33,8 @@ open Complex
 variable {α : Type*}
 
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 := by
-  suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
-  exact
-    this.mono fun x hx => by
+  suffices ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0 from
+    this.mono fun x hx ↦ by
       dsimp only
       rw [zero_cpow hx, Pi.zero_apply]
   exact IsOpen.eventually_mem isOpen_ne hb
@@ -43,9 +42,8 @@ theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^
 
 theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) :
     (fun x => x ^ b) =ᶠ[𝓝 a] fun x => exp (log x * b) := by
-  suffices : ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0
-  exact
-    this.mono fun x hx => by
+  suffices ∀ᶠ x : ℂ in 𝓝 a, x ≠ 0 from
+    this.mono fun x hx ↦ by
       dsimp only
       rw [cpow_def_of_ne_zero hx]
   exact IsOpen.eventually_mem isOpen_ne ha
@@ -53,9 +51,8 @@ theorem cpow_eq_nhds {a b : ℂ} (ha : a ≠ 0) :
 
 theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
     (fun x => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) := by
-  suffices : ∀ᶠ x : ℂ × ℂ in 𝓝 p, x.1 ≠ 0
-  exact
-    this.mono fun x hx => by
+  suffices ∀ᶠ x : ℂ × ℂ in 𝓝 p, x.1 ≠ 0 from
+    this.mono fun x hx ↦ by
       dsimp only
       rw [cpow_def_of_ne_zero hx]
   refine' IsOpen.eventually_mem _ hp_fst
@@ -191,9 +188,8 @@ theorem continuousAt_const_rpow' {a b : ℝ} (h : b ≠ 0) : ContinuousAt (rpow
 
 theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) * cos (x.2 * π) := by
-  suffices : ∀ᶠ x : ℝ × ℝ in 𝓝 p, x.1 < 0
-  exact
-    this.mono fun x hx => by
+  suffices ∀ᶠ x : ℝ × ℝ in 𝓝 p, x.1 < 0 from
+    this.mono fun x hx ↦ by
       dsimp only
       rw [rpow_def_of_neg hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_fst continuous_const) hp_fst
@@ -201,9 +197,8 @@ theorem rpow_eq_nhds_of_neg {p : ℝ × ℝ} (hp_fst : p.fst < 0) :
 
 theorem rpow_eq_nhds_of_pos {p : ℝ × ℝ} (hp_fst : 0 < p.fst) :
     (fun x : ℝ × ℝ => x.1 ^ x.2) =ᶠ[𝓝 p] fun x => exp (log x.1 * x.2) := by
-  suffices : ∀ᶠ x : ℝ × ℝ in 𝓝 p, 0 < x.1
-  exact
-    this.mono fun x hx => by
+  suffices ∀ᶠ x : ℝ × ℝ in 𝓝 p, 0 < x.1 from
+    this.mono fun x hx ↦ by
       dsimp only
       rw [rpow_def_of_pos hx]
   exact IsOpen.eventually_mem (isOpen_lt continuous_const continuous_fst) hp_fst

Add a few missing lemmas about the coercion NNReal → Real. Remove a bunch of protected on the existing coercion lemmas (so that it matches the convention for other coercions). Rename NNReal.coe_eq to NNReal.coe_inj

From LeanAPAP

@@ -434,9 +434,7 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
   rw [this]
   refine' continuous_real_toNNReal.continuousAt.comp (ContinuousAt.comp _ _)
   · apply Real.continuousAt_rpow
-    simp only [Ne.def] at h
-    rw [← NNReal.coe_eq_zero x] at h
-    exact h
+    simpa using h
   · exact ((continuous_subtype_val.comp continuous_fst).prod_mk continuous_snd).continuousAt
 #align nnreal.continuous_at_rpow NNReal.continuousAt_rpow
 

Use X, Y, Z for topological spaces.

@@ -390,7 +390,7 @@ theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
       tauto
     have B : ContinuousAt (fun p => ⟨↑p.1, p.2⟩ : ℝ × ℂ → ℂ × ℂ) ⟨0, y⟩ :=
       continuous_ofReal.continuousAt.prod_map continuousAt_id
-    exact ContinuousAt.comp (α := ℝ × ℂ) (f := fun p => ⟨↑p.1, p.2⟩) (x := ⟨0, y⟩) A B
+    exact A.comp_of_eq B rfl
   · -- x < 0 : difficult case
     suffices ContinuousAt (fun p => (-(p.1 : ℂ)) ^ p.2 * exp (π * I * p.2) : ℝ × ℂ → ℂ) (x, y) by
       refine' this.congr (eventually_of_mem (prod_mem_nhds (Iio_mem_nhds hx) univ_mem) _)

The current design for abs is flawed:

• The Abs notation typeclass has exactly two instances: one for [Neg α] [Sup α], one for [Inv α] [Sup α]. This means that:
  • We can't write a meaningful hover for Abs.abs
  • Fields have two Abs instances!
• We have the multiplicative definition but:
  • All the lemmas in Algebra.Order.Group.Abs are about the additive version.
  • The only lemmas about the multiplicative version are in Algebra.Order.Group.PosPart, and they get additivised to duplicates of the lemmas in Algebra.Order.Group.Abs!

This PR changes the notation typeclass with two new definitions (related through to_additive): mabs and abs. abs inherits the |a| notation and mabs gets |a|ₘ instead.

The first half of Algebra.Order.Group.Abs gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in Algebra.Order.Group.PosPart.

Part of #9411.

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

@@ -348,7 +348,7 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
     refine' ⟨Real.exp (π * C), eventually_map.2 _⟩
     refine'
       (((continuous_im.comp continuous_snd).abs.tendsto (_, z)).eventually (gt_mem_nhds hC)).mono
-        fun z hz => Real.exp_le_exp.2 <| (neg_le_abs_self _).trans _
+        fun z hz => Real.exp_le_exp.2 <| (neg_le_abs _).trans _
     rw [_root_.abs_mul]
     exact
       mul_le_mul (abs_le.2 ⟨(neg_pi_lt_arg _).le, arg_le_pi _⟩) hz.le (_root_.abs_nonneg _)

This better matches other lemma names.

From LeanAPAP

@@ -429,7 +429,7 @@ theorem continuousAt_rpow {x : ℝ≥0} {y : ℝ} (h : x ≠ 0 ∨ 0 < y) :
     (fun p : ℝ≥0 × ℝ => p.1 ^ p.2) =
       Real.toNNReal ∘ (fun p : ℝ × ℝ => p.1 ^ p.2) ∘ fun p : ℝ≥0 × ℝ => (p.1.1, p.2) := by
     ext p
-    erw [coe_rpow, Real.coe_toNNReal _ (Real.rpow_nonneg_of_nonneg p.1.2 _)]
+    erw [coe_rpow, Real.coe_toNNReal _ (Real.rpow_nonneg p.1.2 _)]
     rfl
   rw [this]
   refine' continuous_real_toNNReal.continuousAt.comp (ContinuousAt.comp _ _)

In preparation of future PRs dealing with estimates of the complex logarithm and its Taylor series, this introduces Complex.slitPlane for the set of complex numbers not on the closed negative real axis (in Analysis.SpecialFunctions.Complex.Arg), adds a bunch of API lemmas, and replaces hypotheses of the form 0 < x.re ∨ x.im ≠ 0 by x ∈ slitPlane in several other files.

(We do not introduce a new file for that to avoid circular imports with Analysis.SpecialFunctions.Complex.Arg.)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -83,14 +83,9 @@ theorem continuousAt_const_cpow' {a b : ℂ} (h : b ≠ 0) : ContinuousAt (fun x
 /-- The function `z ^ w` is continuous in `(z, w)` provided that `z` does not belong to the interval
 `(-∞, 0]` on the real line. See also `Complex.continuousAt_cpow_zero_of_re_pos` for a version that
 works for `z = 0` but assumes `0 < re w`. -/
-theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im ≠ 0) :
+theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : p.fst ∈ slitPlane) :
     ContinuousAt (fun x : ℂ × ℂ => x.1 ^ x.2) p := by
-  have hp_fst_ne_zero : p.fst ≠ 0 := by
-    intro h
-    cases' hp_fst with hp_fst hp_fst <;>
-      · rw [h] at hp_fst
-        simp at hp_fst
-  rw [continuousAt_congr (cpow_eq_nhds' hp_fst_ne_zero)]
+  rw [continuousAt_congr (cpow_eq_nhds' <| slitPlane_ne_zero hp_fst)]
   refine' continuous_exp.continuousAt.comp _
   exact
     ContinuousAt.mul
@@ -98,13 +93,13 @@ theorem continuousAt_cpow {p : ℂ × ℂ} (hp_fst : 0 < p.fst.re ∨ p.fst.im 
       continuous_snd.continuousAt
 #align continuous_at_cpow continuousAt_cpow
 
-theorem continuousAt_cpow_const {a b : ℂ} (ha : 0 < a.re ∨ a.im ≠ 0) :
+theorem continuousAt_cpow_const {a b : ℂ} (ha : a ∈ slitPlane) :
     ContinuousAt (fun x => cpow x b) a :=
   Tendsto.comp (@continuousAt_cpow (a, b) ha) (continuousAt_id.prod continuousAt_const)
 #align continuous_at_cpow_const continuousAt_cpow_const
 
 theorem Filter.Tendsto.cpow {l : Filter α} {f g : α → ℂ} {a b : ℂ} (hf : Tendsto f l (𝓝 a))
-    (hg : Tendsto g l (𝓝 b)) (ha : 0 < a.re ∨ a.im ≠ 0) :
+    (hg : Tendsto g l (𝓝 b)) (ha : a ∈ slitPlane) :
     Tendsto (fun x => f x ^ g x) l (𝓝 (a ^ b)) :=
   (@continuousAt_cpow (a, b) ha).tendsto.comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.cpow Filter.Tendsto.cpow
@@ -119,7 +114,7 @@ theorem Filter.Tendsto.const_cpow {l : Filter α} {f : α → ℂ} {a b : ℂ} (
 variable [TopologicalSpace α] {f g : α → ℂ} {s : Set α} {a : α}
 
 nonrec theorem ContinuousWithinAt.cpow (hf : ContinuousWithinAt f s a)
-    (hg : ContinuousWithinAt g s a) (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) :
+    (hg : ContinuousWithinAt g s a) (h0 : f a ∈ slitPlane) :
     ContinuousWithinAt (fun x => f x ^ g x) s a :=
   hf.cpow hg h0
 #align continuous_within_at.cpow ContinuousWithinAt.cpow
@@ -130,7 +125,7 @@ nonrec theorem ContinuousWithinAt.const_cpow {b : ℂ} (hf : ContinuousWithinAt
 #align continuous_within_at.const_cpow ContinuousWithinAt.const_cpow
 
 nonrec theorem ContinuousAt.cpow (hf : ContinuousAt f a) (hg : ContinuousAt g a)
-    (h0 : 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousAt (fun x => f x ^ g x) a :=
+    (h0 : f a ∈ slitPlane) : ContinuousAt (fun x => f x ^ g x) a :=
   hf.cpow hg h0
 #align continuous_at.cpow ContinuousAt.cpow
 
@@ -140,7 +135,7 @@ nonrec theorem ContinuousAt.const_cpow {b : ℂ} (hf : ContinuousAt f a) (h : b
 #align continuous_at.const_cpow ContinuousAt.const_cpow
 
 theorem ContinuousOn.cpow (hf : ContinuousOn f s) (hg : ContinuousOn g s)
-    (h0 : ∀ a ∈ s, 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ g x) s := fun a ha =>
+    (h0 : ∀ a ∈ s, f a ∈ slitPlane) : ContinuousOn (fun x => f x ^ g x) s := fun a ha =>
   (hf a ha).cpow (hg a ha) (h0 a ha)
 #align continuous_on.cpow ContinuousOn.cpow
 
@@ -149,7 +144,7 @@ theorem ContinuousOn.const_cpow {b : ℂ} (hf : ContinuousOn f s) (h : b ≠ 0 
 #align continuous_on.const_cpow ContinuousOn.const_cpow
 
 theorem Continuous.cpow (hf : Continuous f) (hg : Continuous g)
-    (h0 : ∀ a, 0 < (f a).re ∨ (f a).im ≠ 0) : Continuous fun x => f x ^ g x :=
+    (h0 : ∀ a, f a ∈ slitPlane) : Continuous fun x => f x ^ g x :=
   continuous_iff_continuousAt.2 fun a => hf.continuousAt.cpow hg.continuousAt (h0 a)
 #align continuous.cpow Continuous.cpow
 
@@ -159,7 +154,7 @@ theorem Continuous.const_cpow {b : ℂ} (hf : Continuous f) (h : b ≠ 0 ∨ ∀
 #align continuous.const_cpow Continuous.const_cpow
 
 theorem ContinuousOn.cpow_const {b : ℂ} (hf : ContinuousOn f s)
-    (h : ∀ a : α, a ∈ s → 0 < (f a).re ∨ (f a).im ≠ 0) : ContinuousOn (fun x => f x ^ b) s :=
+    (h : ∀ a : α, a ∈ s → f a ∈ slitPlane) : ContinuousOn (fun x => f x ^ b) s :=
   hf.cpow continuousOn_const h
 #align continuous_on.cpow_const ContinuousOn.cpow_const
 

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -451,7 +451,7 @@ theorem eventually_pow_one_div_le (x : ℝ≥0) {y : ℝ≥0} (hy : 1 < y) :
   rw [tsub_add_cancel_of_le hy.le] at hm
   refine' eventually_atTop.2 ⟨m + 1, fun n hn => _⟩
   simpa only [NNReal.rpow_one_div_le_iff (Nat.cast_pos.2 <| m.succ_pos.trans_le hn),
-    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow hy.le (m.le_succ.trans hn))
+    NNReal.rpow_nat_cast] using hm.le.trans (pow_le_pow_right hy.le (m.le_succ.trans hn))
 #align nnreal.eventually_pow_one_div_le NNReal.eventually_pow_one_div_le
 
 end NNReal

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -395,7 +395,7 @@ theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
       tauto
     have B : ContinuousAt (fun p => ⟨↑p.1, p.2⟩ : ℝ × ℂ → ℂ × ℂ) ⟨0, y⟩ :=
       continuous_ofReal.continuousAt.prod_map continuousAt_id
-    exact @ContinuousAt.comp (ℝ × ℂ) (ℂ × ℂ) ℂ _ _ _ _ (fun p => ⟨↑p.1, p.2⟩) ⟨0, y⟩ A B
+    exact ContinuousAt.comp (α := ℝ × ℂ) (f := fun p => ⟨↑p.1, p.2⟩) (x := ⟨0, y⟩) A B
   · -- x < 0 : difficult case
     suffices ContinuousAt (fun p => (-(p.1 : ℂ)) ^ p.2 * exp (π * I * p.2) : ℝ × ℂ → ℂ) (x, y) by
       refine' this.congr (eventually_of_mem (prod_mem_nhds (Iio_mem_nhds hx) univ_mem) _)
@@ -410,7 +410,7 @@ theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
 
 theorem continuousAt_ofReal_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => (a : ℂ) ^ y : ℝ → ℂ) x :=
-  @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_ofReal_cpow x y h)
+  ContinuousAt.comp (x := x) (continuousAt_ofReal_cpow x y h)
     (continuous_id.prod_mk continuous_const).continuousAt
 #align complex.continuous_at_of_real_cpow_const Complex.continuousAt_ofReal_cpow_const
 

I've also got a change to make this required, but I'd like to land this first.

@@ -487,7 +487,7 @@ namespace ENNReal
 theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0∞} (hy : 1 < y) :
     ∀ᶠ n : ℕ in atTop, x ^ (1 / n : ℝ) ≤ y := by
   lift x to ℝ≥0 using hx
-  by_cases y = ∞
+  by_cases h : y = ∞
   · exact eventually_of_forall fun n => h.symm ▸ le_top
   · lift y to ℝ≥0 using h
     have := NNReal.eventually_pow_one_div_le x (mod_cast hy : 1 < y)

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -490,7 +490,7 @@ theorem eventually_pow_one_div_le {x : ℝ≥0∞} (hx : x ≠ ∞) {y : ℝ≥0
   by_cases y = ∞
   · exact eventually_of_forall fun n => h.symm ▸ le_top
   · lift y to ℝ≥0 using h
-    have := NNReal.eventually_pow_one_div_le x (by exact_mod_cast hy : 1 < y)
+    have := NNReal.eventually_pow_one_div_le x (mod_cast hy : 1 < y)
     refine' this.congr (eventually_of_forall fun n => _)
     rw [coe_rpow_of_nonneg x (by positivity : 0 ≤ (1 / n : ℝ)), coe_le_coe]
 #align ennreal.eventually_pow_one_div_le ENNReal.eventually_pow_one_div_le

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -21,8 +21,6 @@ open Classical Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
 
 open Filter Finset Set
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 section CpowLimits
 
 /-!

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

This has nice performance benefits.

@@ -32,7 +32,7 @@ section CpowLimits
 
 open Complex
 
-variable {α : Type _}
+variable {α : Type*}
 
 theorem zero_cpow_eq_nhds {b : ℂ} (hb : b ≠ 0) : (fun x : ℂ => (0 : ℂ) ^ x) =ᶠ[𝓝 b] 0 := by
   suffices : ∀ᶠ x : ℂ in 𝓝 b, x ≠ 0
@@ -269,7 +269,7 @@ end Real
 
 section
 
-variable {α : Type _}
+variable {α : Type*}
 
 theorem Filter.Tendsto.rpow {l : Filter α} {f g : α → ℝ} {x y : ℝ} (hf : Tendsto f l (𝓝 x))
     (hg : Tendsto g l (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) : Tendsto (fun t => f t ^ g t) l (𝓝 (x ^ y)) :=
@@ -460,7 +460,7 @@ end NNReal
 
 open Filter
 
-theorem Filter.Tendsto.nnrpow {α : Type _} {f : Filter α} {u : α → ℝ≥0} {v : α → ℝ} {x : ℝ≥0}
+theorem Filter.Tendsto.nnrpow {α : Type*} {f : Filter α} {u : α → ℝ≥0} {v : α → ℝ} {x : ℝ≥0}
     {y : ℝ} (hx : Tendsto u f (𝓝 x)) (hy : Tendsto v f (𝓝 y)) (h : x ≠ 0 ∨ 0 < y) :
     Tendsto (fun a => u a ^ v a) f (𝓝 (x ^ y)) :=
   Tendsto.comp (NNReal.continuousAt_rpow h) (hx.prod_mk_nhds hy)
@@ -531,7 +531,7 @@ theorem tendsto_const_mul_rpow_nhds_zero_of_pos {c : ℝ≥0∞} (hc : c ≠ ∞
 
 end ENNReal
 
-theorem Filter.Tendsto.ennrpow_const {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} (r : ℝ)
+theorem Filter.Tendsto.ennrpow_const {α : Type*} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} (r : ℝ)
     (hm : Tendsto m f (𝓝 a)) : Tendsto (fun x => m x ^ r) f (𝓝 (a ^ r)) :=
   (ENNReal.continuous_rpow_const.tendsto a).comp hm
 #align filter.tendsto.ennrpow_const Filter.Tendsto.ennrpow_const

@@ -21,7 +21,7 @@ open Classical Real Topology NNReal ENNReal Filter BigOperators ComplexConjugate
 
 open Filter Finset Set
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 section CpowLimits
 

• depends on: #5966

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

@@ -3,14 +3,11 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
   Rémy Degenne, David Loeffler
-
-! This file was ported from Lean 3 source module analysis.special_functions.pow.continuity
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
 
+#align_import analysis.special_functions.pow.continuity from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Continuity of power functions
 

@@ -354,7 +354,7 @@ theorem continuousAt_cpow_zero_of_re_pos {z : ℂ} (hz : 0 < z.re) :
           ((continuous_re.comp continuous_snd).tendsto _) _ <;>
       simp [hz, Real.zero_rpow hz.ne']
   · simp only [Function.comp, Real.norm_eq_abs, abs_of_pos (Real.exp_pos _)]
-    rcases exists_gt (|im z|) with ⟨C, hC⟩
+    rcases exists_gt |im z| with ⟨C, hC⟩
     refine' ⟨Real.exp (π * C), eventually_map.2 _⟩
     refine'
       (((continuous_im.comp continuous_snd).abs.tendsto (_, z)).eventually (gt_mem_nhds hC)).mono

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -64,7 +64,7 @@ theorem cpow_eq_nhds' {p : ℂ × ℂ} (hp_fst : p.fst ≠ 0) :
       dsimp only
       rw [cpow_def_of_ne_zero hx]
   refine' IsOpen.eventually_mem _ hp_fst
-  change IsOpen ({ x : ℂ × ℂ | x.1 = 0 }ᶜ)
+  change IsOpen { x : ℂ × ℂ | x.1 = 0 }ᶜ
   rw [isOpen_compl_iff]
   exact isClosed_eq continuous_fst continuous_const
 #align cpow_eq_nhds' cpow_eq_nhds'

@@ -385,7 +385,7 @@ theorem continuousAt_cpow_const_of_re_pos {z w : ℂ} (hz : 0 ≤ re z ∨ im z
 #align complex.continuous_at_cpow_const_of_re_pos Complex.continuousAt_cpow_const_of_re_pos
 
 /-- Continuity of `(x, y) ↦ x ^ y` as a function on `ℝ × ℂ`. -/
-theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
+theorem continuousAt_ofReal_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun p => (p.1 : ℂ) ^ p.2 : ℝ × ℂ → ℂ) (x, y) := by
   rcases lt_trichotomy (0 : ℝ) x with (hx | rfl | hx)
   · -- x > 0 : easy case
@@ -404,25 +404,25 @@ theorem continuousAt_of_real_cpow (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0)
   · -- x < 0 : difficult case
     suffices ContinuousAt (fun p => (-(p.1 : ℂ)) ^ p.2 * exp (π * I * p.2) : ℝ × ℂ → ℂ) (x, y) by
       refine' this.congr (eventually_of_mem (prod_mem_nhds (Iio_mem_nhds hx) univ_mem) _)
-      exact fun p hp => (of_real_cpow_of_nonpos (le_of_lt hp.1) p.2).symm
+      exact fun p hp => (ofReal_cpow_of_nonpos (le_of_lt hp.1) p.2).symm
     have A : ContinuousAt (fun p => ⟨-↑p.1, p.2⟩ : ℝ × ℂ → ℂ × ℂ) (x, y) :=
       ContinuousAt.prod_map continuous_ofReal.continuousAt.neg continuousAt_id
     apply ContinuousAt.mul
     · refine' (continuousAt_cpow (Or.inl _)).comp A
       rwa [neg_re, ofReal_re, neg_pos]
     · exact (continuous_exp.comp (continuous_const.mul continuous_snd)).continuousAt
-#align complex.continuous_at_of_real_cpow Complex.continuousAt_of_real_cpow
+#align complex.continuous_at_of_real_cpow Complex.continuousAt_ofReal_cpow
 
-theorem continuousAt_of_real_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
+theorem continuousAt_ofReal_cpow_const (x : ℝ) (y : ℂ) (h : 0 < y.re ∨ x ≠ 0) :
     ContinuousAt (fun a => (a : ℂ) ^ y : ℝ → ℂ) x :=
-  @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_of_real_cpow x y h)
+  @ContinuousAt.comp _ _ _ _ _ _ _ _ x (continuousAt_ofReal_cpow x y h)
     (continuous_id.prod_mk continuous_const).continuousAt
-#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_of_real_cpow_const
+#align complex.continuous_at_of_real_cpow_const Complex.continuousAt_ofReal_cpow_const
 
-theorem continuous_of_real_cpow_const {y : ℂ} (hs : 0 < y.re) :
+theorem continuous_ofReal_cpow_const {y : ℂ} (hs : 0 < y.re) :
     Continuous (fun x => (x : ℂ) ^ y : ℝ → ℂ) :=
-  continuous_iff_continuousAt.mpr fun x => continuousAt_of_real_cpow_const x y (Or.inl hs)
-#align complex.continuous_of_real_cpow_const Complex.continuous_of_real_cpow_const
+  continuous_iff_continuousAt.mpr fun x => continuousAt_ofReal_cpow_const x y (Or.inl hs)
+#align complex.continuous_of_real_cpow_const Complex.continuous_ofReal_cpow_const
 
 end Complex
 

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -243,12 +243,12 @@ theorem continuousAt_rpow_of_pos (p : ℝ × ℝ) (hp : 0 < p.2) :
   dsimp only at hp
   obtain hx | rfl := ne_or_eq x 0
   · exact continuousAt_rpow_of_ne (x, y) hx
-  have A : Tendsto (fun p : ℝ × ℝ => exp (log p.1 * p.2)) (𝓝[≠] 0 ×ᶠ 𝓝 y) (𝓝 0) :=
+  have A : Tendsto (fun p : ℝ × ℝ => exp (log p.1 * p.2)) (𝓝[≠] 0 ×ˢ 𝓝 y) (𝓝 0) :=
     tendsto_exp_atBot.comp
       ((tendsto_log_nhdsWithin_zero.comp tendsto_fst).atBot_mul hp tendsto_snd)
-  have B : Tendsto (fun p : ℝ × ℝ => p.1 ^ p.2) (𝓝[≠] 0 ×ᶠ 𝓝 y) (𝓝 0) :=
+  have B : Tendsto (fun p : ℝ × ℝ => p.1 ^ p.2) (𝓝[≠] 0 ×ˢ 𝓝 y) (𝓝 0) :=
     squeeze_zero_norm (fun p => abs_rpow_le_exp_log_mul p.1 p.2) A
-  have C : Tendsto (fun p : ℝ × ℝ => p.1 ^ p.2) (𝓝[{0}] 0 ×ᶠ 𝓝 y) (pure 0) := by
+  have C : Tendsto (fun p : ℝ × ℝ => p.1 ^ p.2) (𝓝[{0}] 0 ×ˢ 𝓝 y) (pure 0) := by
     rw [nhdsWithin_singleton, tendsto_pure, pure_prod, eventually_map]
     exact (lt_mem_nhds hp).mono fun y hy => zero_rpow hy.ne'
   simpa only [← sup_prod, ← nhdsWithin_union, compl_union_self, nhdsWithin_univ, nhds_prod_eq,