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

@@ -279,20 +279,20 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 -/
 
-#print Real.not_summable_nat_cast_inv /-
+#print Real.not_summable_natCast_inv /-
 /-- Harmonic series is not unconditionally summable. -/
-theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
+theorem Real.not_summable_natCast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
   by
   have : ¬Summable (fun n => (n ^ 1)⁻¹ : ℕ → ℝ) := mt Real.summable_nat_pow_inv.1 (lt_irrefl 1)
   simpa
-#align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
+#align real.not_summable_nat_cast_inv Real.not_summable_natCast_inv
 -/
 
-#print Real.not_summable_one_div_nat_cast /-
+#print Real.not_summable_one_div_natCast /-
 /-- Harmonic series is not unconditionally summable. -/
-theorem Real.not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
-  simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv
-#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
+theorem Real.not_summable_one_div_natCast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
+  simpa only [inv_eq_one_div] using Real.not_summable_natCast_inv
+#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_natCast
 -/
 
 #print Real.tendsto_sum_range_one_div_nat_succ_atTop /-
@@ -301,7 +301,7 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop :=
   by
   rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]
-  · exact_mod_cast mt (summable_nat_add_iff 1).1 Real.not_summable_one_div_nat_cast
+  · exact_mod_cast mt (summable_nat_add_iff 1).1 Real.not_summable_one_div_natCast
   · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 -/

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

@@ -272,7 +272,7 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ
   refine'
     Summable.of_nat_of_neg (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
       (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
-  on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
+  on_goal 2 => simp_rw [Int.cast_neg, Int.cast_natCast, abs_neg]
   all_goals
     simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
     rwa [Real.summable_nat_rpow, neg_lt_neg_iff]

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Analysis.SpecialFunctions.Pow.Nnreal
+import Analysis.SpecialFunctions.Pow.NNReal
 
 #align_import analysis.p_series from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 
@@ -62,7 +62,7 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   have : ∀ k ∈ Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ f (2 ^ n) := fun k hk =>
     hf (pow_pos zero_lt_two _) (mem_Ico.mp hk).1
   convert sum_le_sum this
-  simp [pow_succ, two_mul]
+  simp [pow_succ', two_mul]
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
 -/
 
@@ -90,7 +90,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
   convert sum_le_sum this
-  simp [pow_succ, two_mul]
+  simp [pow_succ', two_mul]
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
 -/
 
@@ -99,7 +99,7 @@ theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m)
     ∑ k in range (n + 1), 2 ^ k • f (2 ^ k) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
   convert add_le_add_left (nsmul_le_nsmul_right (sum_condensed_le' hf n) 2) (f 1)
-  simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
+  simp [sum_range_succ', add_comm, pow_succ', mul_nsmul', sum_nsmul]
 #align finset.sum_condensed_le Finset.sum_condensed_le
 -/
 

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

@@ -258,7 +258,7 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   by
   refine'
     ⟨fun h => real.summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>
-      summable_int_of_summable_nat (real.summable_one_div_nat_pow.mpr h)
+      Summable.of_nat_of_neg (real.summable_one_div_nat_pow.mpr h)
         (((real.summable_one_div_nat_pow.mpr h).hMul_left <| 1 / (-1) ^ p).congr fun n => _)⟩
   conv_rhs => rw [Int.cast_neg, neg_eq_neg_one_mul, mul_pow, ← div_div]
   conv_lhs => rw [mul_div, mul_one]
@@ -270,7 +270,7 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
 theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ => |(n : ℝ)| ^ (-b) :=
   by
   refine'
-    summable_int_of_summable_nat (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
+    Summable.of_nat_of_neg (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
       (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
   on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
   all_goals

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

@@ -214,7 +214,7 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
         ((h.tendsto_cofinite_zero.eventually (gt_mem_nhds zero_lt_one)).And
             (eventually_cofinite_ne 0)).exists
       apply hk₀
-      rw [← pos_iff_ne_zero, ← @Nat.cast_pos ℝ] at hk₀ 
+      rw [← pos_iff_ne_zero, ← @Nat.cast_pos ℝ] at hk₀
       simpa [inv_lt_one_iff_of_pos (rpow_pos_of_pos hk₀ _), one_lt_rpow_iff_of_pos hk₀, hp,
         hp.not_lt, hk₀] using hk₁
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
@@ -359,7 +359,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) 
       by
       apply sum_le_sum_of_subset_of_nonneg
       · intro x hx
-        simp only [mem_Ioo] at hx 
+        simp only [mem_Ioo] at hx
         simp only [hx, hx.2.le, mem_Ioc, le_max_iff, or_true_iff, and_self_iff]
       · intro i hi hident
         exact inv_nonneg.2 (sq_nonneg _)

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

@@ -193,7 +193,7 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
   · rw [← summable_condensed_iff_of_nonneg]
     · simp_rw [Nat.cast_pow, Nat.cast_two, ← rpow_nat_cast, ← rpow_mul zero_lt_two.le, mul_comm _ p,
         rpow_mul zero_lt_two.le, rpow_nat_cast, ← inv_pow, ← mul_pow,
-        summable_geometric_iff_norm_lt_1]
+        summable_geometric_iff_norm_lt_one]
       nth_rw 1 [← rpow_one 2]
       rw [← division_def, ← rpow_sub zero_lt_two, norm_eq_abs,
         abs_of_pos (rpow_pos_of_pos zero_lt_two _), rpow_lt_one_iff zero_lt_two.le]

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

@@ -58,7 +58,7 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
-    exacts [n.one_le_two_pow, Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ]
+    exacts [n.one_le_two_pow, Nat.pow_le_pow_right zero_lt_two n.le_succ]
   have : ∀ k ∈ Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ f (2 ^ n) := fun k hk =>
     hf (pow_pos zero_lt_two _) (mem_Ico.mp hk).1
   convert sum_le_sum this
@@ -85,7 +85,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
     exacts [add_le_add_right n.one_le_two_pow _,
-      add_le_add_right (Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ) _]
+      add_le_add_right (Nat.pow_le_pow_right zero_lt_two n.le_succ) _]
   have : ∀ k ∈ Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f (2 ^ (n + 1)) ≤ f k := fun k hk =>
     hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
@@ -98,7 +98,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     ∑ k in range (n + 1), 2 ^ k • f (2 ^ k) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
-  convert add_le_add_left (nsmul_le_nsmul_of_le_right (sum_condensed_le' hf n) 2) (f 1)
+  convert add_le_add_left (nsmul_le_nsmul_right (sum_condensed_le' hf n) 2) (f 1)
   simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
 #align finset.sum_condensed_le Finset.sum_condensed_le
 -/
@@ -128,8 +128,8 @@ theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
   refine'
     iSup_le fun n =>
       le_trans _
-        (add_le_add_left
-          (nsmul_le_nsmul_of_le_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
+        (add_le_add_left (nsmul_le_nsmul_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _)
+          _)
   simpa using Finset.sum_condensed_le hf n
 #align ennreal.tsum_condensed_le ENNReal.tsum_condensed_le
 -/
@@ -379,7 +379,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) 
       simp_rw [← one_div]
       apply add_le_add_right
       refine' div_le_div zero_le_one le_rfl (zero_lt_one.trans_le A) _
-      simpa using pow_le_pow A one_le_two
+      simpa using pow_le_pow_right A one_le_two
     _ = 2 / (k + 1) := by ring
 #align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_le
 -/

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
+import Analysis.SpecialFunctions.Pow.Nnreal
 
 #align_import analysis.p_series from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -259,7 +259,7 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   refine'
     ⟨fun h => real.summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>
       summable_int_of_summable_nat (real.summable_one_div_nat_pow.mpr h)
-        (((real.summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1) ^ p).congr fun n => _)⟩
+        (((real.summable_one_div_nat_pow.mpr h).hMul_left <| 1 / (-1) ^ p).congr fun n => _)⟩
   conv_rhs => rw [Int.cast_neg, neg_eq_neg_one_mul, mul_pow, ← div_div]
   conv_lhs => rw [mul_div, mul_one]
   rfl

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.p_series
-! 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.Nnreal
 
+#align_import analysis.p_series from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Convergence of `p`-series
 

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

@@ -52,6 +52,7 @@ namespace Finset
 
 variable {M : Type _} [OrderedAddCommMonoid M] {f : ℕ → M}
 
+#print Finset.le_sum_condensed' /-
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     ∑ k in Ico 1 (2 ^ n), f k ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
@@ -66,14 +67,18 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   convert sum_le_sum this
   simp [pow_succ, two_mul]
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
+-/
 
+#print Finset.le_sum_condensed /-
 theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     ∑ k in range (2 ^ n), f k ≤ f 0 + ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
   convert add_le_add_left (le_sum_condensed' hf n) (f 0)
   rw [← sum_range_add_sum_Ico _ n.one_le_two_pow, sum_range_succ, sum_range_zero, zero_add]
 #align finset.le_sum_condensed Finset.le_sum_condensed
+-/
 
+#print Finset.sum_condensed_le' /-
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     ∑ k in range n, 2 ^ k • f (2 ^ (k + 1)) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
@@ -90,13 +95,16 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
   convert sum_le_sum this
   simp [pow_succ, two_mul]
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
+-/
 
+#print Finset.sum_condensed_le /-
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     ∑ k in range (n + 1), 2 ^ k • f (2 ^ k) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
   convert add_le_add_left (nsmul_le_nsmul_of_le_right (sum_condensed_le' hf n) 2) (f 1)
   simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
 #align finset.sum_condensed_le Finset.sum_condensed_le
+-/
 
 end Finset
 
@@ -104,6 +112,7 @@ namespace ENNReal
 
 variable {f : ℕ → ℝ≥0∞}
 
+#print ENNReal.le_tsum_condensed /-
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     ∑' k, f k ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
@@ -112,7 +121,9 @@ theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   simp only [nsmul_eq_mul, Nat.cast_pow, Nat.cast_two]
   apply ENNReal.sum_le_tsum
 #align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
+-/
 
+#print ENNReal.tsum_condensed_le /-
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
     ∑' k : ℕ, 2 ^ k * f (2 ^ k) ≤ f 1 + 2 * ∑' k, f k :=
   by
@@ -124,11 +135,13 @@ theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
           (nsmul_le_nsmul_of_le_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
   simpa using Finset.sum_condensed_le hf n
 #align ennreal.tsum_condensed_le ENNReal.tsum_condensed_le
+-/
 
 end ENNReal
 
 namespace NNReal
 
+#print NNReal.summable_condensed_iff /-
 /-- Cauchy condensation test for a series of `nnreal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f :=
@@ -143,9 +156,11 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
       ENNReal.coe_le_coe.2 (hf hm hmn)
     simpa [h, ENNReal.add_eq_top] using ENNReal.le_tsum_condensed hf
 #align nnreal.summable_condensed_iff NNReal.summable_condensed_iff
+-/
 
 end NNReal
 
+#print summable_condensed_iff_of_nonneg /-
 /-- Cauchy condensation test for series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
@@ -155,6 +170,7 @@ theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0
   simp only [NNReal.coe_le_coe] at *
   exact_mod_cast NNReal.summable_condensed_iff h_mono
 #align summable_condensed_iff_of_nonneg summable_condensed_iff_of_nonneg
+-/
 
 open Real
 
@@ -168,6 +184,7 @@ and only if `∑ n, 2 ^ n / ((2 ^ n) ^ p)` converges, and the latter series is a
 common ratio `2 ^ {1 - p}`. -/
 
 
+#print Real.summable_nat_rpow_inv /-
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
@@ -204,6 +221,7 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
       simpa [inv_lt_one_iff_of_pos (rpow_pos_of_pos hk₀ _), one_lt_rpow_iff_of_pos hk₀, hp,
         hp.not_lt, hk₀] using hk₁
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
+-/
 
 #print Real.summable_nat_rpow /-
 @[simp]
@@ -212,25 +230,32 @@ theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → 
 #align real.summable_nat_rpow Real.summable_nat_rpow
 -/
 
+#print Real.summable_one_div_nat_rpow /-
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpow
+-/
 
+#print Real.summable_nat_pow_inv /-
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
 theorem Real.summable_nat_pow_inv {p : ℕ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
   simp only [← rpow_nat_cast, Real.summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
+-/
 
+#print Real.summable_one_div_nat_pow /-
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_pow {p : ℕ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
+-/
 
+#print Real.summable_one_div_int_pow /-
 /-- Summability of the `p`-series over `ℤ`. -/
 theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (n : ℝ) ^ p) ↔ 1 < p :=
   by
@@ -242,7 +267,9 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   conv_lhs => rw [mul_div, mul_one]
   rfl
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
+-/
 
+#print Real.summable_abs_int_rpow /-
 theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ => |(n : ℝ)| ^ (-b) :=
   by
   refine'
@@ -253,19 +280,25 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ
     simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
     rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
+-/
 
+#print Real.not_summable_nat_cast_inv /-
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
   by
   have : ¬Summable (fun n => (n ^ 1)⁻¹ : ℕ → ℝ) := mt Real.summable_nat_pow_inv.1 (lt_irrefl 1)
   simpa
 #align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
+-/
 
+#print Real.not_summable_one_div_nat_cast /-
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
   simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv
 #align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
+-/
 
+#print Real.tendsto_sum_range_one_div_nat_succ_atTop /-
 /-- **Divergence of the Harmonic Series** -/
 theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop :=
@@ -274,20 +307,27 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
   · exact_mod_cast mt (summable_nat_add_iff 1).1 Real.not_summable_one_div_nat_cast
   · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
+-/
 
+#print NNReal.summable_rpow_inv /-
 @[simp]
 theorem NNReal.summable_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ≥0) ↔ 1 < p := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow_inv NNReal.summable_rpow_inv
+-/
 
+#print NNReal.summable_rpow /-
 @[simp]
 theorem NNReal.summable_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ≥0) ↔ p < -1 := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow NNReal.summable_rpow
+-/
 
+#print NNReal.summable_one_div_rpow /-
 theorem NNReal.summable_one_div_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ≥0) ↔ 1 < p := by
   simp
 #align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpow
+-/
 
 section
 
@@ -295,6 +335,7 @@ open Finset
 
 variable {α : Type _} [LinearOrderedField α]
 
+#print sum_Ioc_inv_sq_le_sub /-
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     ∑ i in Ioc k n, ((i ^ 2)⁻¹ : α) ≤ k⁻¹ - n⁻¹ :=
   by
@@ -312,7 +353,9 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   · ring_nf; exact B.le
   · nlinarith
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
+-/
 
+#print sum_Ioo_inv_sq_le /-
 theorem sum_Ioo_inv_sq_le (k n : ℕ) : ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) ≤ 2 / (k + 1) :=
   calc
     ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) ≤ ∑ i in Ioc k (max (k + 1) n), (i ^ 2)⁻¹ :=
@@ -342,6 +385,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) 
       simpa using pow_le_pow A one_le_two
     _ = 2 / (k + 1) := by ring
 #align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_le
+-/
 
 end
 

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

@@ -53,10 +53,10 @@ namespace Finset
 variable {M : Type _} [OrderedAddCommMonoid M] {f : ℕ → M}
 
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
-    (∑ k in Ico 1 (2 ^ n), f k) ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
+    ∑ k in Ico 1 (2 ^ n), f k ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
   induction' n with n ihn; · simp
-  suffices (∑ k in Ico (2 ^ n) (2 ^ (n + 1)), f k) ≤ 2 ^ n • f (2 ^ n)
+  suffices ∑ k in Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ 2 ^ n • f (2 ^ n)
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
@@ -68,14 +68,14 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
 
 theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
-    (∑ k in range (2 ^ n), f k) ≤ f 0 + ∑ k in range n, 2 ^ k • f (2 ^ k) :=
+    ∑ k in range (2 ^ n), f k ≤ f 0 + ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
   convert add_le_add_left (le_sum_condensed' hf n) (f 0)
   rw [← sum_range_add_sum_Ico _ n.one_le_two_pow, sum_range_succ, sum_range_zero, zero_add]
 #align finset.le_sum_condensed Finset.le_sum_condensed
 
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
-    (∑ k in range n, 2 ^ k • f (2 ^ (k + 1))) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
+    ∑ k in range n, 2 ^ k • f (2 ^ (k + 1)) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
   induction' n with n ihn; · simp
   suffices 2 ^ n • f (2 ^ (n + 1)) ≤ ∑ k in Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f k
@@ -92,7 +92,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
 
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
-    (∑ k in range (n + 1), 2 ^ k • f (2 ^ k)) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
+    ∑ k in range (n + 1), 2 ^ k • f (2 ^ k) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
   convert add_le_add_left (nsmul_le_nsmul_of_le_right (sum_condensed_le' hf n) 2) (f 1)
   simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
@@ -105,7 +105,7 @@ namespace ENNReal
 variable {f : ℕ → ℝ≥0∞}
 
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
-    (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
+    ∑' k, f k ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
   rw [ENNReal.tsum_eq_iSup_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
   refine' iSup_le fun n => (Finset.le_sum_condensed hf n).trans (add_le_add_left _ _)
@@ -114,7 +114,7 @@ theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
 #align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
 
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
-    (∑' k : ℕ, 2 ^ k * f (2 ^ k)) ≤ f 1 + 2 * ∑' k, f k :=
+    ∑' k : ℕ, 2 ^ k * f (2 ^ k) ≤ f 1 + 2 * ∑' k, f k :=
   by
   rw [ENNReal.tsum_eq_iSup_nat' (tendsto_at_top_mono Nat.le_succ tendsto_id), two_mul, ← two_nsmul]
   refine'
@@ -296,7 +296,7 @@ open Finset
 variable {α : Type _} [LinearOrderedField α]
 
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
-    (∑ i in Ioc k n, ((i ^ 2)⁻¹ : α)) ≤ k⁻¹ - n⁻¹ :=
+    ∑ i in Ioc k n, ((i ^ 2)⁻¹ : α) ≤ k⁻¹ - n⁻¹ :=
   by
   refine' Nat.le_induction _ _ n h
   · simp only [Ioc_self, sum_empty, sub_self]
@@ -313,9 +313,9 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   · nlinarith
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 
-theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ 2 / (k + 1) :=
+theorem sum_Ioo_inv_sq_le (k n : ℕ) : ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) ≤ 2 / (k + 1) :=
   calc
-    (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ ∑ i in Ioc k (max (k + 1) n), (i ^ 2)⁻¹ :=
+    ∑ i in Ioo k n, ((i ^ 2)⁻¹ : α) ≤ ∑ i in Ioc k (max (k + 1) n), (i ^ 2)⁻¹ :=
       by
       apply sum_le_sum_of_subset_of_nonneg
       · intro x hx

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

@@ -341,7 +341,6 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α))
       refine' div_le_div zero_le_one le_rfl (zero_lt_one.trans_le A) _
       simpa using pow_le_pow A one_le_two
     _ = 2 / (k + 1) := by ring
-    
 #align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_le
 
 end

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

@@ -60,7 +60,7 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
-    exacts[n.one_le_two_pow, Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ]
+    exacts [n.one_le_two_pow, Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ]
   have : ∀ k ∈ Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ f (2 ^ n) := fun k hk =>
     hf (pow_pos zero_lt_two _) (mem_Ico.mp hk).1
   convert sum_le_sum this
@@ -82,7 +82,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
-    exacts[add_le_add_right n.one_le_two_pow _,
+    exacts [add_le_add_right n.one_le_two_pow _,
       add_le_add_right (Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ) _]
   have : ∀ k ∈ Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f (2 ^ (n + 1)) ≤ f k := fun k hk =>
     hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
@@ -200,7 +200,7 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
         ((h.tendsto_cofinite_zero.eventually (gt_mem_nhds zero_lt_one)).And
             (eventually_cofinite_ne 0)).exists
       apply hk₀
-      rw [← pos_iff_ne_zero, ← @Nat.cast_pos ℝ] at hk₀
+      rw [← pos_iff_ne_zero, ← @Nat.cast_pos ℝ] at hk₀ 
       simpa [inv_lt_one_iff_of_pos (rpow_pos_of_pos hk₀ _), one_lt_rpow_iff_of_pos hk₀, hp,
         hp.not_lt, hk₀] using hk₁
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
@@ -319,7 +319,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α))
       by
       apply sum_le_sum_of_subset_of_nonneg
       · intro x hx
-        simp only [mem_Ioo] at hx
+        simp only [mem_Ioo] at hx 
         simp only [hx, hx.2.le, mem_Ioc, le_max_iff, or_true_iff, and_self_iff]
       · intro i hi hident
         exact inv_nonneg.2 (sq_nonneg _)

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

@@ -36,7 +36,7 @@ p-series, Cauchy condensation test
 
 open Filter
 
-open BigOperators ENNReal NNReal Topology
+open scoped BigOperators ENNReal NNReal Topology
 
 /-!
 ### Cauchy condensation test

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

@@ -52,12 +52,6 @@ namespace Finset
 
 variable {M : Type _} [OrderedAddCommMonoid M] {f : ℕ → M}
 
-/- warning: finset.le_sum_condensed' -> Finset.le_sum_condensed' is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)) (fun (k : Nat) => f k)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))))
-but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)) (fun (k : Nat) => f k)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))))
-Case conversion may be inaccurate. Consider using '#align finset.le_sum_condensed' Finset.le_sum_condensed'ₓ'. -/
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in Ico 1 (2 ^ n), f k) ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
@@ -73,12 +67,6 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   simp [pow_succ, two_mul]
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
 
-/- warning: finset.le_sum_condensed -> Finset.le_sum_condensed is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)) (fun (k : Nat) => f k)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k))))))
-but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)) (fun (k : Nat) => f k)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k))))))
-Case conversion may be inaccurate. Consider using '#align finset.le_sum_condensed Finset.le_sum_condensedₓ'. -/
 theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (2 ^ n), f k) ≤ f 0 + ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
@@ -86,12 +74,6 @@ theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m)
   rw [← sum_range_add_sum_Ico _ n.one_le_two_pow, sum_range_succ, sum_range_zero, zero_add]
 #align finset.le_sum_condensed Finset.le_sum_condensed
 
-/- warning: finset.sum_condensed_le' -> Finset.sum_condensed_le' is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => f k)))
-but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => f k)))
-Case conversion may be inaccurate. Consider using '#align finset.sum_condensed_le' Finset.sum_condensed_le'ₓ'. -/
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range n, 2 ^ k • f (2 ^ (k + 1))) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
@@ -109,12 +91,6 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
   simp [pow_succ, two_mul]
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
 
-/- warning: finset.sum_condensed_le -> Finset.sum_condensed_le is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => f k)))))
-but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => f k)))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_condensed_le Finset.sum_condensed_leₓ'. -/
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (n + 1), 2 ^ k • f (2 ^ k)) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
@@ -128,12 +104,6 @@ namespace ENNReal
 
 variable {f : ℕ → ℝ≥0∞}
 
-/- warning: ennreal.le_tsum_condensed -> ENNReal.le_tsum_condensed is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => f k)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{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)))))))) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => 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)))))))) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k))))))
-but is expected to have type
-  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => f k)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{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.instCanonicallyOrderedCommSemiringENNReal)))))))) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k))))))
-Case conversion may be inaccurate. Consider using '#align ennreal.le_tsum_condensed ENNReal.le_tsum_condensedₓ'. -/
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
@@ -143,12 +113,6 @@ theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   apply ENNReal.sum_le_tsum
 #align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
 
-/- warning: ennreal.tsum_condensed_le -> ENNReal.tsum_condensed_le is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => 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)))))))) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{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)))))))) (f (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (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)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => f k)))))
-but is expected to have type
-  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{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.instCanonicallyOrderedCommSemiringENNReal)))))))) (f (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => f k)))))
-Case conversion may be inaccurate. Consider using '#align ennreal.tsum_condensed_le ENNReal.tsum_condensed_leₓ'. -/
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
     (∑' k : ℕ, 2 ^ k * f (2 ^ k)) ≤ f 1 + 2 * ∑' k, f k :=
   by
@@ -165,12 +129,6 @@ end ENNReal
 
 namespace NNReal
 
-/- warning: nnreal.summable_condensed_iff -> NNReal.summable_condensed_iff is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> NNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (f n) (f m))) -> (Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (k : Nat) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace f))
-but is expected to have type
-  forall {f : Nat -> NNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (f n) (f m))) -> (Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (k : Nat) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal f))
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_condensed_iff NNReal.summable_condensed_iffₓ'. -/
 /-- Cauchy condensation test for a series of `nnreal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f :=
@@ -188,12 +146,6 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
 
 end NNReal
 
-/- warning: summable_condensed_iff_of_nonneg -> summable_condensed_iff_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f n)) -> (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} Real Real.hasLe (f n) (f m))) -> (Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (k : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f))
-but is expected to have type
-  forall {f : Nat -> Real}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f n)) -> (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} Real Real.instLEReal (f n) (f m))) -> (Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (k : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Nat.cast.{0} Real Real.natCast k)) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f))
-Case conversion may be inaccurate. Consider using '#align summable_condensed_iff_of_nonneg summable_condensed_iff_of_nonnegₓ'. -/
 /-- Cauchy condensation test for series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
@@ -216,12 +168,6 @@ and only if `∑ n, 2 ^ n / ((2 ^ n) ^ p)` converges, and the latter series is a
 common ratio `2 ^ {1 - p}`. -/
 
 
-/- warning: real.summable_nat_rpow_inv -> Real.summable_nat_rpow_inv is a dubious translation:
-lean 3 declaration is
-  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
-but is expected to have type
-  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
-Case conversion may be inaccurate. Consider using '#align real.summable_nat_rpow_inv Real.summable_nat_rpow_invₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
@@ -266,24 +212,12 @@ theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → 
 #align real.summable_nat_rpow Real.summable_nat_rpow
 -/
 
-/- warning: real.summable_one_div_nat_rpow -> Real.summable_one_div_nat_rpow is a dubious translation:
-lean 3 declaration is
-  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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))) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
-but is expected to have type
-  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
-Case conversion may be inaccurate. Consider using '#align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpowₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpow
 
-/- warning: real.summable_nat_pow_inv -> Real.summable_nat_pow_inv is a dubious translation:
-lean 3 declaration is
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((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) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
-but is expected to have type
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
-Case conversion may be inaccurate. Consider using '#align real.summable_nat_pow_inv Real.summable_nat_pow_invₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
@@ -291,24 +225,12 @@ theorem Real.summable_nat_pow_inv {p : ℕ} : Summable (fun n => (n ^ p)⁻¹ :
   simp only [← rpow_nat_cast, Real.summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
 
-/- warning: real.summable_one_div_nat_pow -> Real.summable_one_div_nat_pow is a dubious translation:
-lean 3 declaration is
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((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) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
-but is expected to have type
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
-Case conversion may be inaccurate. Consider using '#align real.summable_one_div_nat_pow Real.summable_one_div_nat_powₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_pow {p : ℕ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 
-/- warning: real.summable_one_div_int_pow -> Real.summable_one_div_int_pow is a dubious translation:
-lean 3 declaration is
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Int Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
-but is expected to have type
-  forall {p : Nat}, Iff (Summable.{0, 0} Real Int Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Int.cast.{0} Real Real.intCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
-Case conversion may be inaccurate. Consider using '#align real.summable_one_div_int_pow Real.summable_one_div_int_powₓ'. -/
 /-- Summability of the `p`-series over `ℤ`. -/
 theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (n : ℝ) ^ p) ↔ 1 < p :=
   by
@@ -321,12 +243,6 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   rfl
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
-/- warning: real.summable_abs_int_rpow -> Real.summable_abs_int_rpow is a dubious translation:
-lean 3 declaration is
-  forall {b : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) b) -> (Summable.{0, 0} Real Int Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n)) (Neg.neg.{0} Real Real.hasNeg b)))
-but is expected to have type
-  forall {b : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) b) -> (Summable.{0, 0} Real Int Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Int.cast.{0} Real Real.intCast n)) (Neg.neg.{0} Real Real.instNegReal b)))
-Case conversion may be inaccurate. Consider using '#align real.summable_abs_int_rpow Real.summable_abs_int_rpowₓ'. -/
 theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ => |(n : ℝ)| ^ (-b) :=
   by
   refine'
@@ -338,12 +254,6 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ
     rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
-/- warning: real.not_summable_nat_cast_inv -> Real.not_summable_nat_cast_inv is a dubious translation:
-lean 3 declaration is
-  Not (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)))
-but is expected to have type
-  Not (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)))
-Case conversion may be inaccurate. Consider using '#align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_invₓ'. -/
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
   by
@@ -351,23 +261,11 @@ theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → 
   simpa
 #align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
 
-/- warning: real.not_summable_one_div_nat_cast -> Real.not_summable_one_div_nat_cast is a dubious translation:
-lean 3 declaration is
-  Not (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)))
-but is expected to have type
-  Not (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)))
-Case conversion may be inaccurate. Consider using '#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_castₓ'. -/
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
   simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv
 #align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
 
-/- warning: real.tendsto_sum_range_one_div_nat_succ_at_top -> Real.tendsto_sum_range_one_div_nat_succ_atTop is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => 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))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((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))) i) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{0} Real Real.preorder)
-but is expected to have type
-  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast i) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{0} Real Real.instPreorderReal)
-Case conversion may be inaccurate. Consider using '#align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTopₓ'. -/
 /-- **Divergence of the Harmonic Series** -/
 theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop :=
@@ -377,34 +275,16 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
   · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
-/- warning: nnreal.summable_rpow_inv -> NNReal.summable_rpow_inv is a dubious translation:
-lean 3 declaration is
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
-but is expected to have type
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_rpow_inv NNReal.summable_rpow_invₓ'. -/
 @[simp]
 theorem NNReal.summable_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ≥0) ↔ 1 < p := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow_inv NNReal.summable_rpow_inv
 
-/- warning: nnreal.summable_rpow -> NNReal.summable_rpow is a dubious translation:
-lean 3 declaration is
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p)) (LT.lt.{0} Real Real.hasLt p (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p)) (LT.lt.{0} Real Real.instLTReal p (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_rpow NNReal.summable_rpowₓ'. -/
 @[simp]
 theorem NNReal.summable_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ≥0) ↔ p < -1 := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow NNReal.summable_rpow
 
-/- warning: nnreal.summable_one_div_rpow -> NNReal.summable_one_div_rpow is a dubious translation:
-lean 3 declaration is
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
-but is expected to have type
-  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
-Case conversion may be inaccurate. Consider using '#align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpowₓ'. -/
 theorem NNReal.summable_one_div_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ≥0) ↔ 1 < p := by
   simp
 #align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpow
@@ -415,12 +295,6 @@ open Finset
 
 variable {α : Type _} [LinearOrderedField α]
 
-/- warning: sum_Ioc_inv_sq_le_sub -> sum_Ioc_inv_sq_le_sub is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {k : Nat} {n : Nat}, (Ne.{1} Nat k (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (LE.le.{0} Nat Nat.hasLe k n) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k n) (fun (i : Nat) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) k)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) n))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {k : Nat} {n : Nat}, (Ne.{1} Nat k (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (LE.le.{0} Nat instLENat k n) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.sum.{u1, 0} α Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k n) (fun (i : Nat) => Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) i (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) k)) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) n))))
-Case conversion may be inaccurate. Consider using '#align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_subₓ'. -/
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     (∑ i in Ioc k n, ((i ^ 2)⁻¹ : α)) ≤ k⁻¹ - n⁻¹ :=
   by
@@ -439,12 +313,6 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   · nlinarith
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 
-/- warning: sum_Ioo_inv_sq_le -> sum_Ioo_inv_sq_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (k : Nat) (n : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k n) (fun (i : Nat) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 2 (OfNat.mk.{u1} α 2 (bit0.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) k) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (k : Nat) (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.sum.{u1, 0} α Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (Finset.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k n) (fun (i : Nat) => Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) i (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 2 (instOfNat.{u1} α 2 (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) k) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))))
-Case conversion may be inaccurate. Consider using '#align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_leₓ'. -/
 theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ 2 / (k + 1) :=
   calc
     (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ ∑ i in Ioc k (max (k + 1) n), (i ^ 2)⁻¹ :=

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

@@ -61,8 +61,7 @@ Case conversion may be inaccurate. Consider using '#align finset.le_sum_condense
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in Ico 1 (2 ^ n), f k) ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
-  induction' n with n ihn
-  · simp
+  induction' n with n ihn; · simp
   suffices (∑ k in Ico (2 ^ n) (2 ^ (n + 1)), f k) ≤ 2 ^ n • f (2 ^ n)
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
@@ -96,8 +95,7 @@ Case conversion may be inaccurate. Consider using '#align finset.sum_condensed_l
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range n, 2 ^ k • f (2 ^ (k + 1))) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
-  induction' n with n ihn
-  · simp
+  induction' n with n ihn; · simp
   suffices 2 ^ n • f (2 ^ (n + 1)) ≤ ∑ k in Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f k
     by
     rw [sum_range_succ, ← sum_Ico_consecutive]
@@ -263,10 +261,8 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
 
 #print Real.summable_nat_rpow /-
 @[simp]
-theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ) ↔ p < -1 :=
-  by
-  rcases neg_surjective p with ⟨p, rfl⟩
-  simp [rpow_neg]
+theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ) ↔ p < -1 := by
+  rcases neg_surjective p with ⟨p, rfl⟩; simp [rpow_neg]
 #align real.summable_nat_rpow Real.summable_nat_rpow
 -/
 
@@ -439,8 +435,7 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   have B : 0 < (n : α) + 1 := by linarith
   field_simp [B.ne']
   rw [div_le_div_iff _ A, ← sub_nonneg]
-  · ring_nf
-    exact B.le
+  · ring_nf; exact B.le
   · nlinarith
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.p_series
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
 /-!
 # Convergence of `p`-series
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that the series `∑' k in ℕ, 1 / k ^ p` converges if and only if `p > 1`.
 The proof is based on the
 [Cauchy condensation test](https://en.wikipedia.org/wiki/Cauchy_condensation_test): `∑ k, f k`

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

@@ -49,6 +49,12 @@ namespace Finset
 
 variable {M : Type _} [OrderedAddCommMonoid M] {f : ℕ → M}
 
+/- warning: finset.le_sum_condensed' -> Finset.le_sum_condensed' is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)) (fun (k : Nat) => f k)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)) (fun (k : Nat) => f k)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))))
+Case conversion may be inaccurate. Consider using '#align finset.le_sum_condensed' Finset.le_sum_condensed'ₓ'. -/
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in Ico 1 (2 ^ n), f k) ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
@@ -65,6 +71,12 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   simp [pow_succ, two_mul]
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
 
+/- warning: finset.le_sum_condensed -> Finset.le_sum_condensed is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)) (fun (k : Nat) => f k)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k))))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)) (fun (k : Nat) => f k)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k))))))
+Case conversion may be inaccurate. Consider using '#align finset.le_sum_condensed Finset.le_sum_condensedₓ'. -/
 theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (2 ^ n), f k) ≤ f 0 + ∑ k in range n, 2 ^ k • f (2 ^ k) :=
   by
@@ -72,6 +84,12 @@ theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m)
   rw [← sum_range_add_sum_Ico _ n.one_le_two_pow, sum_range_succ, sum_range_zero, zero_add]
 #align finset.le_sum_condensed Finset.le_sum_condensed
 
+/- warning: finset.sum_condensed_le' -> Finset.sum_condensed_le' is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => f k)))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range n) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => f k)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_condensed_le' Finset.sum_condensed_le'ₓ'. -/
 theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range n, 2 ^ k • f (2 ^ (k + 1))) ≤ ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
@@ -90,6 +108,12 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
   simp [pow_succ, two_mul]
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
 
+/- warning: finset.sum_condensed_le -> Finset.sum_condensed_le is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toHasLe.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (SMul.smul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (k : Nat) => f k)))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} M] {f : Nat -> M}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (f n) (f m))) -> (forall (n : Nat), LE.le.{u1} M (Preorder.toLE.{u1} M (PartialOrder.toPreorder.{u1} M (OrderedAddCommMonoid.toPartialOrder.{u1} M _inst_1))) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1))))) (f (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HSMul.hSMul.{0, u1, u1} Nat M M (instHSMul.{0, u1} Nat M (AddMonoid.SMul.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1)))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Finset.sum.{u1, 0} M Nat (OrderedAddCommMonoid.toAddCommMonoid.{u1} M _inst_1) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (k : Nat) => f k)))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_condensed_le Finset.sum_condensed_leₓ'. -/
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (n + 1), 2 ^ k • f (2 ^ k)) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k :=
   by
@@ -103,6 +127,12 @@ namespace ENNReal
 
 variable {f : ℕ → ℝ≥0∞}
 
+/- warning: ennreal.le_tsum_condensed -> ENNReal.le_tsum_condensed is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => f k)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{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)))))))) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => 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)))))))) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k))))))
+but is expected to have type
+  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => f k)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{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.instCanonicallyOrderedCommSemiringENNReal)))))))) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k))))))
+Case conversion may be inaccurate. Consider using '#align ennreal.le_tsum_condensed ENNReal.le_tsum_condensedₓ'. -/
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
@@ -112,6 +142,12 @@ theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   apply ENNReal.sum_le_tsum
 #align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
 
+/- warning: ennreal.tsum_condensed_le -> ENNReal.tsum_condensed_le is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => 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)))))))) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{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)))))))) (f (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (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)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{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))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (k : Nat) => f k)))))
+but is expected to have type
+  forall {f : Nat -> ENNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) m) -> (LE.le.{0} Nat instLENat m n) -> (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))))) (f n) (f m))) -> (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))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{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.instCanonicallyOrderedCommSemiringENNReal)))))))) (f (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (k : Nat) => f k)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.tsum_condensed_le ENNReal.tsum_condensed_leₓ'. -/
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
     (∑' k : ℕ, 2 ^ k * f (2 ^ k)) ≤ f 1 + 2 * ∑' k, f k :=
   by
@@ -128,6 +164,12 @@ end ENNReal
 
 namespace NNReal
 
+/- warning: nnreal.summable_condensed_iff -> NNReal.summable_condensed_iff is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> NNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (f n) (f m))) -> (Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (k : Nat) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (Distrib.toHasMul.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (OfNat.ofNat.{0} NNReal 2 (OfNat.mk.{0} NNReal 2 (bit0.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))) (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace f))
+but is expected to have type
+  forall {f : Nat -> NNReal}, (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (f n) (f m))) -> (Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (k : Nat) => HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (OfNat.ofNat.{0} NNReal 2 (instOfNat.{0} NNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal f))
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_condensed_iff NNReal.summable_condensed_iffₓ'. -/
 /-- Cauchy condensation test for a series of `nnreal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f :=
@@ -145,6 +187,12 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
 
 end NNReal
 
+/- warning: summable_condensed_iff_of_nonneg -> summable_condensed_iff_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (f n)) -> (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) m) -> (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} Real Real.hasLe (f n) (f m))) -> (Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (k : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) k) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) k)))) (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f))
+but is expected to have type
+  forall {f : Nat -> Real}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (f n)) -> (forall {{m : Nat}} {{n : Nat}}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) m) -> (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} Real Real.instLEReal (f n) (f m))) -> (Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (k : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Nat.cast.{0} Real Real.natCast k)) (f (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) k)))) (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f))
+Case conversion may be inaccurate. Consider using '#align summable_condensed_iff_of_nonneg summable_condensed_iff_of_nonnegₓ'. -/
 /-- Cauchy condensation test for series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
@@ -167,6 +215,12 @@ and only if `∑ n, 2 ^ n / ((2 ^ n) ^ p)` converges, and the latter series is a
 common ratio `2 ^ {1 - p}`. -/
 
 
+/- warning: real.summable_nat_rpow_inv -> Real.summable_nat_rpow_inv is a dubious translation:
+lean 3 declaration is
+  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
+but is expected to have type
+  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
+Case conversion may be inaccurate. Consider using '#align real.summable_nat_rpow_inv Real.summable_nat_rpow_invₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
@@ -204,19 +258,33 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
         hp.not_lt, hk₀] using hk₁
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
 
+#print Real.summable_nat_rpow /-
 @[simp]
 theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ) ↔ p < -1 :=
   by
   rcases neg_surjective p with ⟨p, rfl⟩
   simp [rpow_neg]
 #align real.summable_nat_rpow Real.summable_nat_rpow
+-/
 
+/- warning: real.summable_one_div_nat_rpow -> Real.summable_one_div_nat_rpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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))) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) ((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) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
+but is expected to have type
+  forall {p : Real}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
+Case conversion may be inaccurate. Consider using '#align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpowₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpow
 
+/- warning: real.summable_nat_pow_inv -> Real.summable_nat_pow_inv is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((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) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
+but is expected to have type
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
+Case conversion may be inaccurate. Consider using '#align real.summable_nat_pow_inv Real.summable_nat_pow_invₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
@@ -224,12 +292,24 @@ theorem Real.summable_nat_pow_inv {p : ℕ} : Summable (fun n => (n ^ p)⁻¹ :
   simp only [← rpow_nat_cast, Real.summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
 
+/- warning: real.summable_one_div_nat_pow -> Real.summable_one_div_nat_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((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) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
+but is expected to have type
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Nat.cast.{0} Real Real.natCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
+Case conversion may be inaccurate. Consider using '#align real.summable_one_div_nat_pow Real.summable_one_div_nat_powₓ'. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_pow {p : ℕ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 
+/- warning: real.summable_one_div_int_pow -> Real.summable_one_div_int_pow is a dubious translation:
+lean 3 declaration is
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Int Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n) p))) (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) p)
+but is expected to have type
+  forall {p : Nat}, Iff (Summable.{0, 0} Real Int Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => 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)) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Int.cast.{0} Real Real.intCast n) (Nat.cast.{0} Real Real.natCast p)))) (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) p)
+Case conversion may be inaccurate. Consider using '#align real.summable_one_div_int_pow Real.summable_one_div_int_powₓ'. -/
 /-- Summability of the `p`-series over `ℤ`. -/
 theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (n : ℝ) ^ p) ↔ 1 < p :=
   by
@@ -242,6 +322,12 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   rfl
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
+/- warning: real.summable_abs_int_rpow -> Real.summable_abs_int_rpow is a dubious translation:
+lean 3 declaration is
+  forall {b : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) b) -> (Summable.{0, 0} Real Int Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n)) (Neg.neg.{0} Real Real.hasNeg b)))
+but is expected to have type
+  forall {b : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) b) -> (Summable.{0, 0} Real Int Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Int) => HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Int.cast.{0} Real Real.intCast n)) (Neg.neg.{0} Real Real.instNegReal b)))
+Case conversion may be inaccurate. Consider using '#align real.summable_abs_int_rpow Real.summable_abs_int_rpowₓ'. -/
 theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ => |(n : ℝ)| ^ (-b) :=
   by
   refine'
@@ -253,6 +339,12 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ
     rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
+/- warning: real.not_summable_nat_cast_inv -> Real.not_summable_nat_cast_inv is a dubious translation:
+lean 3 declaration is
+  Not (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)))
+but is expected to have type
+  Not (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast n)))
+Case conversion may be inaccurate. Consider using '#align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_invₓ'. -/
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
   by
@@ -260,11 +352,23 @@ theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → 
   simpa
 #align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
 
+/- warning: real.not_summable_one_div_nat_cast -> Real.not_summable_one_div_nat_cast is a dubious translation:
+lean 3 declaration is
+  Not (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)))
+but is expected to have type
+  Not (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)))
+Case conversion may be inaccurate. Consider using '#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_castₓ'. -/
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
   simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv
 #align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
 
+/- warning: real.tendsto_sum_range_one_div_nat_succ_at_top -> Real.tendsto_sum_range_one_div_nat_succ_atTop is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => 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))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((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))) i) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{0} Real Real.preorder)
+but is expected to have type
+  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => 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)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast i) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{0} Real Real.instPreorderReal)
+Case conversion may be inaccurate. Consider using '#align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTopₓ'. -/
 /-- **Divergence of the Harmonic Series** -/
 theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop :=
@@ -274,16 +378,34 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
   · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
+/- warning: nnreal.summable_rpow_inv -> NNReal.summable_rpow_inv is a dubious translation:
+lean 3 declaration is
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
+but is expected to have type
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_rpow_inv NNReal.summable_rpow_invₓ'. -/
 @[simp]
 theorem NNReal.summable_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ≥0) ↔ 1 < p := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow_inv NNReal.summable_rpow_inv
 
+/- warning: nnreal.summable_rpow -> NNReal.summable_rpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p)) (LT.lt.{0} Real Real.hasLt p (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p)) (LT.lt.{0} Real Real.instLTReal p (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_rpow NNReal.summable_rpowₓ'. -/
 @[simp]
 theorem NNReal.summable_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ≥0) ↔ p < -1 := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow NNReal.summable_rpow
 
+/- warning: nnreal.summable_one_div_rpow -> NNReal.summable_one_div_rpow is a dubious translation:
+lean 3 declaration is
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) (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))))))) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.Real.hasPow) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n) p))) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) p)
+but is expected to have type
+  forall {p : Real}, Iff (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (HPow.hPow.{0, 0, 0} NNReal Real NNReal (instHPow.{0, 0} NNReal Real NNReal.instPowNNRealReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n) p))) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) p)
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpowₓ'. -/
 theorem NNReal.summable_one_div_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ≥0) ↔ 1 < p := by
   simp
 #align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpow
@@ -294,6 +416,12 @@ open Finset
 
 variable {α : Type _} [LinearOrderedField α]
 
+/- warning: sum_Ioc_inv_sq_le_sub -> sum_Ioc_inv_sq_le_sub is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {k : Nat} {n : Nat}, (Ne.{1} Nat k (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (LE.le.{0} Nat Nat.hasLe k n) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k n) (fun (i : Nat) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) k)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) n))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {k : Nat} {n : Nat}, (Ne.{1} Nat k (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (LE.le.{0} Nat instLENat k n) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.sum.{u1, 0} α Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k n) (fun (i : Nat) => Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) i (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) k)) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) n))))
+Case conversion may be inaccurate. Consider using '#align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_subₓ'. -/
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     (∑ i in Ioc k n, ((i ^ 2)⁻¹ : α)) ≤ k⁻¹ - n⁻¹ :=
   by
@@ -313,6 +441,12 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   · nlinarith
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 
+/- warning: sum_Ioo_inv_sq_le -> sum_Ioo_inv_sq_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (k : Nat) (n : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k n) (fun (i : Nat) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) i) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 2 (OfNat.mk.{u1} α 2 (bit0.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))) k) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (k : Nat) (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (Finset.sum.{u1, 0} α Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))) (Finset.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k n) (fun (i : Nat) => Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) i (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 2 (instOfNat.{u1} α 2 (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) k) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_leₓ'. -/
 theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ 2 / (k + 1) :=
   calc
     (∑ i in Ioo k n, ((i ^ 2)⁻¹ : α)) ≤ ∑ i in Ioc k (max (k + 1) n), (i ^ 2)⁻¹ :=

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.p_series
-! leanprover-community/mathlib commit 38f16f960f5006c6c0c2bac7b0aba5273188f4e5
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
 
 /-!
 # Convergence of `p`-series

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -106,8 +106,8 @@ variable {f : ℕ → ℝ≥0∞}
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
-  rw [ENNReal.tsum_eq_supᵢ_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
-  refine' supᵢ_le fun n => (Finset.le_sum_condensed hf n).trans (add_le_add_left _ _)
+  rw [ENNReal.tsum_eq_iSup_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
+  refine' iSup_le fun n => (Finset.le_sum_condensed hf n).trans (add_le_add_left _ _)
   simp only [nsmul_eq_mul, Nat.cast_pow, Nat.cast_two]
   apply ENNReal.sum_le_tsum
 #align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
@@ -115,9 +115,9 @@ theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
     (∑' k : ℕ, 2 ^ k * f (2 ^ k)) ≤ f 1 + 2 * ∑' k, f k :=
   by
-  rw [ENNReal.tsum_eq_supᵢ_nat' (tendsto_at_top_mono Nat.le_succ tendsto_id), two_mul, ← two_nsmul]
+  rw [ENNReal.tsum_eq_iSup_nat' (tendsto_at_top_mono Nat.le_succ tendsto_id), two_mul, ← two_nsmul]
   refine'
-    supᵢ_le fun n =>
+    iSup_le fun n =>
       le_trans _
         (add_le_add_left
           (nsmul_le_nsmul_of_le_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.p_series
-! leanprover-community/mathlib commit afdb4fa3b32d41106a4a09b371ce549ad7958abd
+! leanprover-community/mathlib commit 38f16f960f5006c6c0c2bac7b0aba5273188f4e5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -242,6 +242,17 @@ theorem Real.summable_one_div_int_pow {p : ℕ} : (Summable fun n : ℤ => 1 / (
   rfl
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
+theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) : Summable fun n : ℤ => |(n : ℝ)| ^ (-b) :=
+  by
+  refine'
+    summable_int_of_summable_nat (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
+      (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
+  on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
+  all_goals
+    simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
+    rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
+#align real.summable_abs_int_rpow Real.summable_abs_int_rpow
+
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -33,7 +33,7 @@ p-series, Cauchy condensation test
 
 open Filter
 
-open BigOperators Ennreal NNReal Topology
+open BigOperators ENNReal NNReal Topology
 
 /-!
 ### Cauchy condensation test
@@ -99,32 +99,32 @@ theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m)
 
 end Finset
 
-namespace Ennreal
+namespace ENNReal
 
 variable {f : ℕ → ℝ≥0∞}
 
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) :=
   by
-  rw [Ennreal.tsum_eq_supᵢ_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
+  rw [ENNReal.tsum_eq_supᵢ_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
   refine' supᵢ_le fun n => (Finset.le_sum_condensed hf n).trans (add_le_add_left _ _)
   simp only [nsmul_eq_mul, Nat.cast_pow, Nat.cast_two]
-  apply Ennreal.sum_le_tsum
-#align ennreal.le_tsum_condensed Ennreal.le_tsum_condensed
+  apply ENNReal.sum_le_tsum
+#align ennreal.le_tsum_condensed ENNReal.le_tsum_condensed
 
 theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) :
     (∑' k : ℕ, 2 ^ k * f (2 ^ k)) ≤ f 1 + 2 * ∑' k, f k :=
   by
-  rw [Ennreal.tsum_eq_supᵢ_nat' (tendsto_at_top_mono Nat.le_succ tendsto_id), two_mul, ← two_nsmul]
+  rw [ENNReal.tsum_eq_supᵢ_nat' (tendsto_at_top_mono Nat.le_succ tendsto_id), two_mul, ← two_nsmul]
   refine'
     supᵢ_le fun n =>
       le_trans _
         (add_le_add_left
-          (nsmul_le_nsmul_of_le_right (Ennreal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
+          (nsmul_le_nsmul_of_le_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
   simpa using Finset.sum_condensed_le hf n
-#align ennreal.tsum_condensed_le Ennreal.tsum_condensed_le
+#align ennreal.tsum_condensed_le ENNReal.tsum_condensed_le
 
-end Ennreal
+end ENNReal
 
 namespace NNReal
 
@@ -132,15 +132,15 @@ namespace NNReal
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f :=
   by
-  simp only [← Ennreal.tsum_coe_ne_top_iff_summable, Ne.def, not_iff_not, Ennreal.coe_mul,
-    Ennreal.coe_pow, Ennreal.coe_two]
+  simp only [← ENNReal.tsum_coe_ne_top_iff_summable, Ne.def, not_iff_not, ENNReal.coe_mul,
+    ENNReal.coe_pow, ENNReal.coe_two]
   constructor <;> intro h
   · replace hf : ∀ m n, 1 < m → m ≤ n → (f n : ℝ≥0∞) ≤ f m := fun m n hm hmn =>
-      Ennreal.coe_le_coe.2 (hf (zero_lt_one.trans hm) hmn)
-    simpa [h, Ennreal.add_eq_top, Ennreal.mul_eq_top] using Ennreal.tsum_condensed_le hf
+      ENNReal.coe_le_coe.2 (hf (zero_lt_one.trans hm) hmn)
+    simpa [h, ENNReal.add_eq_top, ENNReal.mul_eq_top] using ENNReal.tsum_condensed_le hf
   · replace hf : ∀ m n, 0 < m → m ≤ n → (f n : ℝ≥0∞) ≤ f m := fun m n hm hmn =>
-      Ennreal.coe_le_coe.2 (hf hm hmn)
-    simpa [h, Ennreal.add_eq_top] using Ennreal.le_tsum_condensed hf
+      ENNReal.coe_le_coe.2 (hf hm hmn)
+    simpa [h, ENNReal.add_eq_top] using ENNReal.le_tsum_condensed hf
 #align nnreal.summable_condensed_iff NNReal.summable_condensed_iff
 
 end NNReal

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.p_series
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit afdb4fa3b32d41106a4a09b371ce549ad7958abd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -137,7 +137,7 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
   constructor <;> intro h
   · replace hf : ∀ m n, 1 < m → m ≤ n → (f n : ℝ≥0∞) ≤ f m := fun m n hm hmn =>
       Ennreal.coe_le_coe.2 (hf (zero_lt_one.trans hm) hmn)
-    simpa [h, Ennreal.add_eq_top] using Ennreal.tsum_condensed_le hf
+    simpa [h, Ennreal.add_eq_top, Ennreal.mul_eq_top] using Ennreal.tsum_condensed_le hf
   · replace hf : ∀ m n, 0 < m → m ≤ n → (f n : ℝ≥0∞) ≤ f m := fun m n hm hmn =>
       Ennreal.coe_le_coe.2 (hf hm hmn)
     simpa [h, Ennreal.add_eq_top] using Ennreal.le_tsum_condensed hf

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

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.

@@ -172,8 +172,8 @@ theorem summable_nat_rpow_inv {p : ℝ} :
   /- Cauchy condensation test applies only to antitone sequences, so we consider the
     cases `0 ≤ p` and `p < 0` separately. -/
   · rw [← summable_condensed_iff_of_nonneg]
-    · simp_rw [Nat.cast_pow, Nat.cast_two, ← rpow_nat_cast, ← rpow_mul zero_lt_two.le, mul_comm _ p,
-        rpow_mul zero_lt_two.le, rpow_nat_cast, ← inv_pow, ← mul_pow,
+    · simp_rw [Nat.cast_pow, Nat.cast_two, ← rpow_natCast, ← rpow_mul zero_lt_two.le, mul_comm _ p,
+        rpow_mul zero_lt_two.le, rpow_natCast, ← inv_pow, ← mul_pow,
         summable_geometric_iff_norm_lt_one]
       nth_rw 1 [← rpow_one 2]
       rw [← division_def, ← rpow_sub zero_lt_two, norm_eq_abs,
@@ -216,7 +216,7 @@ if and only if `1 < p`. -/
 -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/looping.20in.20.60simp.60.20set/near/361134234
 theorem summable_nat_pow_inv {p : ℕ} :
     Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
-  simp only [← rpow_nat_cast, summable_nat_rpow_inv, Nat.one_lt_cast]
+  simp only [← rpow_natCast, summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
@@ -246,22 +246,22 @@ theorem summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
 /-- Harmonic series is not unconditionally summable. -/
-theorem not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) := by
+theorem not_summable_natCast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) := by
   have : ¬Summable (fun n => ((n : ℝ) ^ 1)⁻¹ : ℕ → ℝ) :=
     mt (summable_nat_pow_inv (p := 1)).1 (lt_irrefl 1)
   simpa
-#align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
+#align real.not_summable_nat_cast_inv Real.not_summable_natCast_inv
 
 /-- Harmonic series is not unconditionally summable. -/
-theorem not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
-  simpa only [inv_eq_one_div] using not_summable_nat_cast_inv
-#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
+theorem not_summable_one_div_natCast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
+  simpa only [inv_eq_one_div] using not_summable_natCast_inv
+#align real.not_summable_one_div_nat_cast Real.not_summable_one_div_natCast
 
 /-- **Divergence of the Harmonic Series** -/
 theorem tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop := by
   rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]
-  · exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 not_summable_one_div_nat_cast
+  · exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 not_summable_one_div_natCast
   · exact fun i => by positivity
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
@@ -354,7 +354,7 @@ lemma Real.not_summable_indicator_one_div_natCast {m : ℕ} (hm : m ≠ 0) (k :
     simp only [indicator_apply, mem_setOf_eq, cast_add, cast_one]
   simp_rw [indicator_apply, mem_setOf, cast_add, cast_one, ← eq_sub_iff_add_eq, ← h]
   rw [summable_indicator_mod_iff (fun n₁ n₂ h ↦ by gcongr) (k - 1)]
-  exact mt (summable_nat_add_iff (f := fun n : ℕ ↦ 1 / (n : ℝ)) 1).mp not_summable_one_div_nat_cast
+  exact mt (summable_nat_add_iff (f := fun n : ℕ ↦ 1 / (n : ℝ)) 1).mp not_summable_one_div_natCast
 
 /-!
 ## Translating the `p`-series by a real number
@@ -376,7 +376,7 @@ lemma Real.summable_one_div_nat_add_rpow (a : ℝ) (s : ℝ) :
     positivity
   · simp_rw [Pi.div_def, div_div, mul_one_div, one_div_div]
     refine (?_ : Tendsto (fun x : ℝ ↦ |x + b| ^ s / |x + c| ^ s) atTop (𝓝 1)).comp
-      tendsto_nat_cast_atTop_atTop
+      tendsto_natCast_atTop_atTop
     have : Tendsto (fun x : ℝ ↦ 1 + (b - c) / x) atTop (𝓝 1) := by
       simpa using tendsto_const_nhds.add ((tendsto_const_nhds (X := ℝ)).div_atTop tendsto_id)
     have : Tendsto (fun x ↦ (x + b) / (x + c)) atTop (𝓝 1) := by

In all cases, the original proof works now. I presume this is due to simp changes in Lean 4.7, but haven't verified.

@@ -223,7 +223,7 @@ theorem summable_nat_pow_inv {p : ℕ} :
 if and only if `1 < p`. -/
 theorem summable_one_div_nat_pow {p : ℕ} :
     Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
-  -- porting note (#10745): was `simp`
+  -- porting note (#10745): explicitly supplied two simp lemmas
   simp only [one_div, Real.summable_nat_pow_inv]
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 

This renames

• Int.cast_ofNat to Int.cast_natCast
• Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

@@ -233,7 +233,7 @@ theorem summable_one_div_int_pow {p : ℕ} :
   refine ⟨fun h ↦ summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective),
     fun h ↦ .of_nat_of_neg (summable_one_div_nat_pow.mpr h)
       (((summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n ↦ ?_)⟩
-  rw [Int.cast_neg, Int.cast_ofNat, neg_eq_neg_one_mul (n : ℝ), mul_pow, mul_one_div, div_div]
+  rw [Int.cast_neg, Int.cast_natCast, neg_eq_neg_one_mul (n : ℝ), mul_pow, mul_one_div, div_div]
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
 theorem summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
@@ -241,7 +241,7 @@ theorem summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
   apply Summable.of_nat_of_neg
   on_goal 2 => simp_rw [Int.cast_neg, abs_neg]
   all_goals
-    simp_rw [Int.cast_ofNat, fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
+    simp_rw [Int.cast_natCast, fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
     rwa [summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
@@ -391,6 +391,6 @@ lemma Real.summable_one_div_nat_add_rpow (a : ℝ) (s : ℝ) :
 lemma Real.summable_one_div_int_add_rpow (a : ℝ) (s : ℝ) :
     Summable (fun n : ℤ ↦ 1 / |n + a| ^ s) ↔ 1 < s := by
   simp_rw [summable_int_iff_summable_nat_and_neg, ← abs_neg (↑(-_ : ℤ) + a), neg_add,
-    Int.cast_neg, neg_neg, Int.cast_ofNat, summable_one_div_nat_add_rpow, and_self]
+    Int.cast_neg, neg_neg, Int.cast_natCast, summable_one_div_nat_add_rpow, and_self]
 
 end shifted

@@ -125,7 +125,7 @@ open ENNReal in
 /-- Cauchy condensation test for a series of `NNReal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => (2 : ℝ≥0) ^ k * f (2 ^ k)) ↔ Summable f := by
-  simp only [← ENNReal.tsum_coe_ne_top_iff_summable, Ne.def, not_iff_not, ENNReal.coe_mul,
+  simp only [← ENNReal.tsum_coe_ne_top_iff_summable, Ne, not_iff_not, ENNReal.coe_mul,
     ENNReal.coe_pow, ENNReal.coe_two]
   constructor <;> intro h
   · replace hf : ∀ m n, 1 < m → m ≤ n → (f n : ℝ≥0∞) ≤ f m := fun m n hm hmn =>
@@ -331,7 +331,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, (i ^ 2 : α)⁻¹) 
       rw [Nat.Ico_succ_right, Nat.Icc_succ_left, Nat.cast_succ]
     _ ≤ ((k + 1 : α) ^ 2)⁻¹ + (k + 1 : α)⁻¹ := by
       refine' add_le_add le_rfl ((sum_Ioc_inv_sq_le_sub _ (le_max_left _ _)).trans _)
-      · simp only [Ne.def, Nat.succ_ne_zero, not_false_iff]
+      · simp only [Ne, Nat.succ_ne_zero, not_false_iff]
       · simp only [Nat.cast_succ, one_div, sub_le_self_iff, inv_nonneg, Nat.cast_nonneg]
     _ ≤ 1 / (k + 1) + 1 / (k + 1) := by
       have A : (1 : α) ≤ k + 1 := by simp only [le_add_iff_nonneg_left, Nat.cast_nonneg]

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -32,7 +32,7 @@ p-series, Cauchy condensation test
 /-!
 ### Cauchy condensation test
 
-In this section we prove the Cauchy condensation test: for `f : ℕ → ℝ≥0` or `f : ℕ → ℝ`,
+In this section we prove the Cauchy condensation test: for an antitone `f : ℕ → ℝ≥0` or `f : ℕ → ℝ`,
 `∑ k, f k` converges if and only if so does `∑ k, 2 ^ k f (2 ^ k)`. Instead of giving a monolithic
 proof, we split it into a series of lemmas with explicit estimates of partial sums of each series in
 terms of the partial sums of the other series.
@@ -56,7 +56,7 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   have : ∀ k ∈ Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ f (2 ^ n) := fun k hk =>
     hf (pow_pos zero_lt_two _) (mem_Ico.mp hk).1
   convert sum_le_sum this
-  simp [pow_succ, two_mul]
+  simp [pow_succ, mul_two]
 #align finset.le_sum_condensed' Finset.le_sum_condensed'
 
 theorem le_sum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
@@ -81,13 +81,13 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     exact hf (Nat.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
   convert sum_le_sum this
-  simp [pow_succ, two_mul]
+  simp [pow_succ, mul_two]
 #align finset.sum_condensed_le' Finset.sum_condensed_le'
 
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (n + 1), 2 ^ k • f (2 ^ k)) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k := by
   convert add_le_add_left (nsmul_le_nsmul_right (sum_condensed_le' hf n) 2) (f 1)
-  simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
+  simp [sum_range_succ', add_comm, pow_succ', mul_nsmul', sum_nsmul]
 #align finset.sum_condensed_le Finset.sum_condensed_le
 
 end Finset
@@ -139,7 +139,7 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
 end NNReal
 
 open NNReal in
-/-- Cauchy condensation test for series of nonnegative real numbers. -/
+/-- Cauchy condensation test for antitone series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => (2 : ℝ) ^ k * f (2 ^ k)) ↔ Summable f := by

Summability of n ↦ 1 / |n + a| ^ s and n ↦ n ^ k exp (-r * n)

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
+import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
 import Mathlib.Analysis.SumOverResidueClass
 
 #align_import analysis.p_series from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
@@ -354,3 +355,42 @@ lemma Real.not_summable_indicator_one_div_natCast {m : ℕ} (hm : m ≠ 0) (k :
   simp_rw [indicator_apply, mem_setOf, cast_add, cast_one, ← eq_sub_iff_add_eq, ← h]
   rw [summable_indicator_mod_iff (fun n₁ n₂ h ↦ by gcongr) (k - 1)]
   exact mt (summable_nat_add_iff (f := fun n : ℕ ↦ 1 / (n : ℝ)) 1).mp not_summable_one_div_nat_cast
+
+/-!
+## Translating the `p`-series by a real number
+-/
+section shifted
+
+open Filter Asymptotics Topology
+
+lemma Real.summable_one_div_nat_add_rpow (a : ℝ) (s : ℝ) :
+    Summable (fun n : ℕ ↦ 1 / |n + a| ^ s) ↔ 1 < s := by
+  suffices ∀ (b c : ℝ), Summable (fun n : ℕ ↦ 1 / |n + b| ^ s) →
+      Summable (fun n : ℕ ↦ 1 / |n + c| ^ s) by
+    simp_rw [← summable_one_div_nat_rpow, Iff.intro (this a 0) (this 0 a), add_zero, Nat.abs_cast]
+  refine fun b c h ↦ summable_of_isBigO_nat h (isBigO_of_div_tendsto_nhds ?_ 1 ?_)
+  · filter_upwards [eventually_gt_atTop (Nat.ceil |b|)] with n hn hx
+    have hna : 0 < n + b := by linarith [lt_of_abs_lt ((abs_neg b).symm ▸ Nat.lt_of_ceil_lt hn)]
+    exfalso
+    revert hx
+    positivity
+  · simp_rw [Pi.div_def, div_div, mul_one_div, one_div_div]
+    refine (?_ : Tendsto (fun x : ℝ ↦ |x + b| ^ s / |x + c| ^ s) atTop (𝓝 1)).comp
+      tendsto_nat_cast_atTop_atTop
+    have : Tendsto (fun x : ℝ ↦ 1 + (b - c) / x) atTop (𝓝 1) := by
+      simpa using tendsto_const_nhds.add ((tendsto_const_nhds (X := ℝ)).div_atTop tendsto_id)
+    have : Tendsto (fun x ↦ (x + b) / (x + c)) atTop (𝓝 1) := by
+      refine (this.comp (tendsto_id.atTop_add (tendsto_const_nhds (x := c)))).congr' ?_
+      filter_upwards [eventually_gt_atTop (-c)] with x hx
+      field_simp [(by linarith : 0 < x + c).ne']
+    apply (one_rpow s ▸ (continuousAt_rpow_const _ s (by simp)).tendsto.comp this).congr'
+    filter_upwards [eventually_gt_atTop (-b), eventually_gt_atTop (-c)] with x hb hc
+    rw [neg_lt_iff_pos_add] at hb hc
+    rw [Function.comp_apply, div_rpow hb.le hc.le, abs_of_pos hb, abs_of_pos hc]
+
+lemma Real.summable_one_div_int_add_rpow (a : ℝ) (s : ℝ) :
+    Summable (fun n : ℤ ↦ 1 / |n + a| ^ s) ↔ 1 < s := by
+  simp_rw [summable_int_iff_summable_nat_and_neg, ← abs_neg (↑(-_ : ℤ) + a), neg_add,
+    Int.cast_neg, neg_neg, Int.cast_ofNat, summable_one_div_nat_add_rpow, and_self]
+
+end shifted

This PR combines several results involving topological sums over ℤ. These results are used in #10011 (Hurwitz zeta functions) where sums over ℤ feature heavily.

• Fill in tsum and Summable variants for lemmas proved for HasSum

• Rename some lemmas (with deprecated aliases) to impose a consistent naming scheme

• Generalise several lemmas to allow the target space to be a topological monoid rather than a group.

• Speed up some slow proofs (the old summable_int_of_summable_nat took about 10s to compile on my machine, its replacement Summable.of_nat_of_neg is 1000 times faster)

@@ -228,27 +228,16 @@ theorem summable_one_div_nat_pow {p : ℕ} :
 
 /-- Summability of the `p`-series over `ℤ`. -/
 theorem summable_one_div_int_pow {p : ℕ} :
-    (Summable fun n : ℤ => 1 / (n : ℝ) ^ p) ↔ 1 < p := by
-  refine'
-    ⟨fun h => summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>
-      summable_int_of_summable_nat (summable_one_div_nat_pow.mpr h)
-        (((summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n => _)⟩
-  conv_rhs =>
-    rw [Int.cast_neg, neg_eq_neg_one_mul, mul_pow, ← div_div]
-  conv_lhs => rw [mul_div, mul_one]
+    (Summable fun n : ℤ ↦ 1 / (n : ℝ) ^ p) ↔ 1 < p := by
+  refine ⟨fun h ↦ summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective),
+    fun h ↦ .of_nat_of_neg (summable_one_div_nat_pow.mpr h)
+      (((summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n ↦ ?_)⟩
+  rw [Int.cast_neg, Int.cast_ofNat, neg_eq_neg_one_mul (n : ℝ), mul_pow, mul_one_div, div_div]
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
 theorem summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
     Summable fun n : ℤ => |(n : ℝ)| ^ (-b) := by
-  -- Porting note: was
-  -- refine'
-  --   summable_int_of_summable_nat (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
-  --     (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
-  -- on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
-  -- all_goals
-  --   simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
-  --   rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
-  apply summable_int_of_summable_nat
+  apply Summable.of_nat_of_neg
   on_goal 2 => simp_rw [Int.cast_neg, abs_neg]
   all_goals
     simp_rw [Int.cast_ofNat, fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]

This adds a file Analysis.SumOverResidueClass, whose main result is

/-- A decreasing sequence of real numbers is summable on a residue class
if and only if it is summable. -/
lemma summable_indicator_mod_iff {m : ℕ} [NeZero m] {f : ℕ → ℝ} (hf : Antitone f) (k : ZMod m) :
    Summable ({n : ℕ | (n : ZMod m) = k}.indicator f) ↔ Summable f

We then use this to show that the harmonic series still diverges when restricted to a residue class.

This is needed for the proof that the abscissa of absolute convergence of a Dirichlet L-series is 1.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
+import Mathlib.Analysis.SumOverResidueClass
 
 #align_import analysis.p_series from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
 
@@ -27,10 +28,6 @@ test once we need it.
 p-series, Cauchy condensation test
 -/
 
-open Filter
-
-open BigOperators ENNReal NNReal Topology
-
 /-!
 ### Cauchy condensation test
 
@@ -43,6 +40,8 @@ terms of the partial sums of the other series.
 
 namespace Finset
 
+open BigOperators
+
 variable {M : Type*} [OrderedAddCommMonoid M] {f : ℕ → M}
 
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
@@ -94,6 +93,8 @@ end Finset
 
 namespace ENNReal
 
+open Filter BigOperators
+
 variable {f : ℕ → ℝ≥0∞}
 
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
@@ -119,6 +120,7 @@ end ENNReal
 
 namespace NNReal
 
+open ENNReal in
 /-- Cauchy condensation test for a series of `NNReal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
     (Summable fun k : ℕ => (2 : ℝ≥0) ^ k * f (2 ^ k)) ↔ Summable f := by
@@ -135,6 +137,7 @@ theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m
 
 end NNReal
 
+open NNReal in
 /-- Cauchy condensation test for series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
@@ -144,7 +147,7 @@ theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0
   exact_mod_cast NNReal.summable_condensed_iff h_mono
 #align summable_condensed_iff_of_nonneg summable_condensed_iff_of_nonneg
 
-open Real
+section p_series
 
 /-!
 ### Convergence of the `p`-series
@@ -155,11 +158,14 @@ Cauchy condensation test we formalized above. This test implies that `∑ n, 1 /
 and only if `∑ n, 2 ^ n / ((2 ^ n) ^ p)` converges, and the latter series is a geometric series with
 common ratio `2 ^ {1 - p}`. -/
 
+namespace Real
+
+open Filter BigOperators
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
-theorem Real.summable_nat_rpow_inv {p : ℝ} :
+theorem summable_nat_rpow_inv {p : ℝ} :
     Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
   rcases le_or_lt 0 p with hp | hp
   /- Cauchy condensation test applies only to antitone sequences, so we consider the
@@ -191,14 +197,14 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} :
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
 
 @[simp]
-theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => (n : ℝ) ^ p : ℕ → ℝ) ↔ p < -1 := by
+theorem summable_nat_rpow {p : ℝ} : Summable (fun n => (n : ℝ) ^ p : ℕ → ℝ) ↔ p < -1 := by
   rcases neg_surjective p with ⟨p, rfl⟩
   simp [rpow_neg]
 #align real.summable_nat_rpow Real.summable_nat_rpow
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
-theorem Real.summable_one_div_nat_rpow {p : ℝ} :
+theorem summable_one_div_nat_rpow {p : ℝ} :
     Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpow
@@ -207,32 +213,32 @@ theorem Real.summable_one_div_nat_rpow {p : ℝ} :
 if and only if `1 < p`. -/
 -- Porting note: temporarily remove `@[simp]` because of a problem with `simp`
 -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/looping.20in.20.60simp.60.20set/near/361134234
-theorem Real.summable_nat_pow_inv {p : ℕ} :
+theorem summable_nat_pow_inv {p : ℕ} :
     Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
-  simp only [← rpow_nat_cast, Real.summable_nat_rpow_inv, Nat.one_lt_cast]
+  simp only [← rpow_nat_cast, summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
-theorem Real.summable_one_div_nat_pow {p : ℕ} :
+theorem summable_one_div_nat_pow {p : ℕ} :
     Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
   -- porting note (#10745): was `simp`
   simp only [one_div, Real.summable_nat_pow_inv]
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 
 /-- Summability of the `p`-series over `ℤ`. -/
-theorem Real.summable_one_div_int_pow {p : ℕ} :
+theorem summable_one_div_int_pow {p : ℕ} :
     (Summable fun n : ℤ => 1 / (n : ℝ) ^ p) ↔ 1 < p := by
   refine'
-    ⟨fun h => Real.summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>
-      summable_int_of_summable_nat (Real.summable_one_div_nat_pow.mpr h)
-        (((Real.summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n => _)⟩
+    ⟨fun h => summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>
+      summable_int_of_summable_nat (summable_one_div_nat_pow.mpr h)
+        (((summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n => _)⟩
   conv_rhs =>
     rw [Int.cast_neg, neg_eq_neg_one_mul, mul_pow, ← div_div]
   conv_lhs => rw [mul_div, mul_one]
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
-theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
+theorem summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
     Summable fun n : ℤ => |(n : ℝ)| ^ (-b) := by
   -- Porting note: was
   -- refine'
@@ -246,48 +252,56 @@ theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
   on_goal 2 => simp_rw [Int.cast_neg, abs_neg]
   all_goals
     simp_rw [Int.cast_ofNat, fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
-    rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
+    rwa [summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
 /-- Harmonic series is not unconditionally summable. -/
-theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) := by
+theorem not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) := by
   have : ¬Summable (fun n => ((n : ℝ) ^ 1)⁻¹ : ℕ → ℝ) :=
-    mt (Real.summable_nat_pow_inv (p := 1)).1 (lt_irrefl 1)
+    mt (summable_nat_pow_inv (p := 1)).1 (lt_irrefl 1)
   simpa
 #align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
 
 /-- Harmonic series is not unconditionally summable. -/
-theorem Real.not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
-  simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv
+theorem not_summable_one_div_nat_cast : ¬Summable (fun n => 1 / n : ℕ → ℝ) := by
+  simpa only [inv_eq_one_div] using not_summable_nat_cast_inv
 #align real.not_summable_one_div_nat_cast Real.not_summable_one_div_nat_cast
 
 /-- **Divergence of the Harmonic Series** -/
-theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
+theorem tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop := by
   rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]
-  · exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 Real.not_summable_one_div_nat_cast
+  · exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 not_summable_one_div_nat_cast
   · exact fun i => by positivity
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
+end Real
+
+namespace NNReal
+
 @[simp]
-theorem NNReal.summable_rpow_inv {p : ℝ} :
+theorem summable_rpow_inv {p : ℝ} :
     Summable (fun n => ((n : ℝ≥0) ^ p)⁻¹ : ℕ → ℝ≥0) ↔ 1 < p := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow_inv NNReal.summable_rpow_inv
 
 @[simp]
-theorem NNReal.summable_rpow {p : ℝ} : Summable (fun n => (n : ℝ≥0) ^ p : ℕ → ℝ≥0) ↔ p < -1 := by
+theorem summable_rpow {p : ℝ} : Summable (fun n => (n : ℝ≥0) ^ p : ℕ → ℝ≥0) ↔ p < -1 := by
   simp [← NNReal.summable_coe]
 #align nnreal.summable_rpow NNReal.summable_rpow
 
-theorem NNReal.summable_one_div_rpow {p : ℝ} :
+theorem summable_one_div_rpow {p : ℝ} :
     Summable (fun n => 1 / (n : ℝ≥0) ^ p : ℕ → ℝ≥0) ↔ 1 < p := by
   simp
 #align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpow
 
+end NNReal
+
+end p_series
+
 section
 
-open Finset
+open Finset BigOperators
 
 variable {α : Type*} [LinearOrderedField α]
 
@@ -335,7 +349,19 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, (i ^ 2 : α)⁻¹) 
       gcongr
       simpa using pow_le_pow_right A one_le_two
     _ = 2 / (k + 1) := by ring
-
 #align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_le
 
 end
+
+open Set Nat in
+/-- The harmonic series restricted to a residue class is not summable. -/
+lemma Real.not_summable_indicator_one_div_natCast {m : ℕ} (hm : m ≠ 0) (k : ZMod m) :
+    ¬ Summable ({n : ℕ | (n : ZMod m) = k}.indicator fun n : ℕ ↦ (1 / n : ℝ)) := by
+  have : NeZero m := ⟨hm⟩ -- instance is needed below
+  rw [← summable_nat_add_iff 1] -- shift by one to avoid non-monotonicity at zero
+  have h (n : ℕ) : {n : ℕ | (n : ZMod m) = k - 1}.indicator (fun n : ℕ ↦ (1 / (n + 1 :) : ℝ)) n =
+      if (n : ZMod m) = k - 1 then (1 / (n + 1) : ℝ) else (0 : ℝ) := by
+    simp only [indicator_apply, mem_setOf_eq, cast_add, cast_one]
+  simp_rw [indicator_apply, mem_setOf, cast_add, cast_one, ← eq_sub_iff_add_eq, ← h]
+  rw [summable_indicator_mod_iff (fun n₁ n₂ h ↦ by gcongr) (k - 1)]
+  exact mt (summable_nat_add_iff (f := fun n : ℕ ↦ 1 / (n : ℝ)) 1).mp not_summable_one_div_nat_cast

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -78,8 +78,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     -- Note(kmill): was `fun k hk => ...` but `mem_Ico.mp hk` was elaborating with some
     -- delayed assignment metavariables that weren't resolved in time. `intro` fixes this.
     intro k hk
-    exact hf ((@Nat.one_le_two_pow n).trans_lt <|
-      (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
+    exact hf (Nat.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
   convert sum_le_sum this
   simp [pow_succ, two_mul]
@@ -292,6 +291,7 @@ open Finset
 
 variable {α : Type*} [LinearOrderedField α]
 
+set_option tactic.skipAssignedInstances false in
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     (∑ i in Ioc k n, ((i : α) ^ 2)⁻¹) ≤ (k : α)⁻¹ - (n : α)⁻¹ := by
   refine' Nat.le_induction _ _ n h

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -206,7 +206,7 @@ theorem Real.summable_one_div_nat_rpow {p : ℝ} :
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
--- porting note: temporarily remove `@[simp]` because of a problem with `simp`
+-- Porting note: temporarily remove `@[simp]` because of a problem with `simp`
 -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/looping.20in.20.60simp.60.20set/near/361134234
 theorem Real.summable_nat_pow_inv {p : ℕ} :
     Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by

Classifies by adding issue number (#10745) to porting notes claiming was simp.

@@ -217,7 +217,7 @@ theorem Real.summable_nat_pow_inv {p : ℕ} :
 if and only if `1 < p`. -/
 theorem Real.summable_one_div_nat_pow {p : ℕ} :
     Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
-  -- Porting note: was `simp`
+  -- porting note (#10745): was `simp`
   simp only [one_div, Real.summable_nat_pow_inv]
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Alex Keizer <alex@keizer.dev> Co-authored-by: Tobias Grosser <tobias@grosser.es>

@@ -78,7 +78,8 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     -- Note(kmill): was `fun k hk => ...` but `mem_Ico.mp hk` was elaborating with some
     -- delayed assignment metavariables that weren't resolved in time. `intro` fixes this.
     intro k hk
-    exact hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
+    exact hf ((@Nat.one_le_two_pow n).trans_lt <|
+      (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
   convert sum_le_sum this
   simp [pow_succ, two_mul]

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

@@ -167,7 +167,7 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} :
   · rw [← summable_condensed_iff_of_nonneg]
     · simp_rw [Nat.cast_pow, Nat.cast_two, ← rpow_nat_cast, ← rpow_mul zero_lt_two.le, mul_comm _ p,
         rpow_mul zero_lt_two.le, rpow_nat_cast, ← inv_pow, ← mul_pow,
-        summable_geometric_iff_norm_lt_1]
+        summable_geometric_iff_norm_lt_one]
       nth_rw 1 [← rpow_one 2]
       rw [← division_def, ← rpow_sub zero_lt_two, norm_eq_abs,
         abs_of_pos (rpow_pos_of_pos zero_lt_two _), rpow_lt_one_iff zero_lt_two.le]

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -161,7 +161,7 @@ if and only if `1 < p`. -/
 @[simp]
 theorem Real.summable_nat_rpow_inv {p : ℝ} :
     Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
-  cases' le_or_lt 0 p with hp hp
+  rcases le_or_lt 0 p with hp | hp
   /- Cauchy condensation test applies only to antitone sequences, so we consider the
     cases `0 ≤ p` and `p < 0` separately. -/
   · rw [← summable_condensed_iff_of_nonneg]

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.

@@ -86,7 +86,7 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
 
 theorem sum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in range (n + 1), 2 ^ k • f (2 ^ k)) ≤ f 1 + 2 • ∑ k in Ico 2 (2 ^ n + 1), f k := by
-  convert add_le_add_left (nsmul_le_nsmul_of_le_right (sum_condensed_le' hf n) 2) (f 1)
+  convert add_le_add_left (nsmul_le_nsmul_right (sum_condensed_le' hf n) 2) (f 1)
   simp [sum_range_succ', add_comm, pow_succ, mul_nsmul', sum_nsmul]
 #align finset.sum_condensed_le Finset.sum_condensed_le
 
@@ -111,7 +111,7 @@ theorem tsum_condensed_le (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     iSup_le fun n =>
       le_trans _
         (add_le_add_left
-          (nsmul_le_nsmul_of_le_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
+          (nsmul_le_nsmul_right (ENNReal.sum_le_tsum <| Finset.Ico 2 (2 ^ n + 1)) _) _)
   simpa using Finset.sum_condensed_le hf n
 #align ennreal.tsum_condensed_le ENNReal.tsum_condensed_le
 
@@ -332,7 +332,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, (i ^ 2 : α)⁻¹) 
       have A : (1 : α) ≤ k + 1 := by simp only [le_add_iff_nonneg_left, Nat.cast_nonneg]
       simp_rw [← one_div]
       gcongr
-      simpa using pow_le_pow A one_le_two
+      simpa using pow_le_pow_right A one_le_two
     _ = 2 / (k + 1) := by ring
 
 #align sum_Ioo_inv_sq_le sum_Ioo_inv_sq_le

Following on from previous gcongr golfing PRs #4702 and #4784.

This is a replacement for #7901: this round of golfs, first introduced there, there exposed some performance issues in gcongr, hopefully fixed by #8731, and I am opening a new PR so that the performance can be checked against current master rather than master at the time of #7901.

@@ -173,11 +173,9 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} :
         abs_of_pos (rpow_pos_of_pos zero_lt_two _), rpow_lt_one_iff zero_lt_two.le]
       norm_num
     · intro n
-      exact inv_nonneg.2 (rpow_nonneg_of_nonneg n.cast_nonneg _)
+      positivity
     · intro m n hm hmn
-      exact
-        inv_le_inv_of_le (rpow_pos_of_pos (Nat.cast_pos.2 hm) _)
-          (rpow_le_rpow m.cast_nonneg (Nat.cast_le.2 hmn) hp)
+      gcongr
   -- If `p < 0`, then `1 / n ^ p` tends to infinity, thus the series diverges.
   · suffices ¬Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) by
       have : ¬1 < p := fun hp₁ => hp.not_le (zero_le_one.trans hp₁.le)
@@ -268,7 +266,7 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
     Tendsto (fun n => ∑ i in Finset.range n, (1 / (i + 1) : ℝ)) atTop atTop := by
   rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]
   · exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 Real.not_summable_one_div_nat_cast
-  · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
+  · exact fun i => by positivity
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
 @[simp]
@@ -333,8 +331,7 @@ theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, (i ^ 2 : α)⁻¹) 
     _ ≤ 1 / (k + 1) + 1 / (k + 1) := by
       have A : (1 : α) ≤ k + 1 := by simp only [le_add_iff_nonneg_left, Nat.cast_nonneg]
       simp_rw [← one_div]
-      apply add_le_add_right
-      refine' div_le_div zero_le_one le_rfl (zero_lt_one.trans_le A) _
+      gcongr
       simpa using pow_le_pow A one_le_two
     _ = 2 / (k + 1) := by ring
 

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>

@@ -27,9 +27,6 @@ test once we need it.
 p-series, Cauchy condensation test
 -/
 
-
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open Filter
 
 open BigOperators ENNReal NNReal Topology
@@ -77,8 +74,11 @@ theorem sum_condensed_le' (hf : ∀ ⦃m n⦄, 1 < m → m ≤ n → f n ≤ f m
     exacts [add_le_add ihn this,
       (add_le_add_right n.one_le_two_pow _ : 1 + 1 ≤ 2 ^ n + 1),
       add_le_add_right (Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ) _]
-  have : ∀ k ∈ Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f (2 ^ (n + 1)) ≤ f k := fun k hk =>
-    hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
+  have : ∀ k ∈ Ico (2 ^ n + 1) (2 ^ (n + 1) + 1), f (2 ^ (n + 1)) ≤ f k := by
+    -- Note(kmill): was `fun k hk => ...` but `mem_Ico.mp hk` was elaborating with some
+    -- delayed assignment metavariables that weren't resolved in time. `intro` fixes this.
+    intro k hk
+    exact hf (n.one_le_two_pow.trans_lt <| (Nat.lt_succ_of_le le_rfl).trans_le (mem_Ico.mp hk).1)
       (Nat.le_of_lt_succ <| (mem_Ico.mp hk).2)
   convert sum_le_sum this
   simp [pow_succ, two_mul]
@@ -313,7 +313,7 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     positivity
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 
-theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i : α) ^ 2)⁻¹) ≤ 2 / (k + 1) :=
+theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, (i ^ 2 : α)⁻¹) ≤ 2 / (k + 1) :=
   calc
     (∑ i in Ioo k n, ((i : α) ^ 2)⁻¹) ≤ ∑ i in Ioc k (max (k + 1) n), ((i : α) ^ 2)⁻¹ := by
       apply sum_le_sum_of_subset_of_nonneg

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -304,7 +304,7 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     add_le_iff_nonpos_right, neg_add_le_iff_le_add, add_zero]
   have A : 0 < (n : α) := by simpa using hk.bot_lt.trans_le hn
   have B : 0 < (n : α) + 1 := by linarith
-  field_simp [B.ne']
+  field_simp
   rw [div_le_div_iff _ A, ← sub_nonneg]
   · ring_nf
     rw [add_comm]

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

This has nice performance benefits.

@@ -46,7 +46,7 @@ terms of the partial sums of the other series.
 
 namespace Finset
 
-variable {M : Type _} [OrderedAddCommMonoid M] {f : ℕ → M}
+variable {M : Type*} [OrderedAddCommMonoid M] {f : ℕ → M}
 
 theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) (n : ℕ) :
     (∑ k in Ico 1 (2 ^ n), f k) ≤ ∑ k in range n, 2 ^ k • f (2 ^ k) := by
@@ -291,7 +291,7 @@ section
 
 open Finset
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
     (∑ i in Ioc k n, ((i : α) ^ 2)⁻¹) ≤ (k : α)⁻¹ - (n : α)⁻¹ := by

@@ -28,7 +28,7 @@ p-series, Cauchy condensation test
 -/
 
 
-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
 
 open Filter
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.p_series
-! 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.NNReal
 
+#align_import analysis.p_series from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Convergence of `p`-series
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -100,7 +100,7 @@ namespace ENNReal
 variable {f : ℕ → ℝ≥0∞}
 
 theorem le_tsum_condensed (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
-    (∑' k, f k) ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) := by
+    ∑' k, f k ≤ f 0 + ∑' k : ℕ, 2 ^ k * f (2 ^ k) := by
   rw [ENNReal.tsum_eq_iSup_nat' (Nat.tendsto_pow_atTop_atTop_of_one_lt _root_.one_lt_two)]
   refine' iSup_le fun n => (Finset.le_sum_condensed hf n).trans (add_le_add_left _ _)
   simp only [nsmul_eq_mul, Nat.cast_pow, Nat.cast_two]

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

@@ -31,6 +31,8 @@ p-series, Cauchy condensation test
 -/
 
 
+local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+
 open Filter
 
 open BigOperators ENNReal NNReal Topology
@@ -122,7 +124,7 @@ namespace NNReal
 
 /-- Cauchy condensation test for a series of `NNReal` version. -/
 theorem summable_condensed_iff {f : ℕ → ℝ≥0} (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
-    (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f := by
+    (Summable fun k : ℕ => (2 : ℝ≥0) ^ k * f (2 ^ k)) ↔ Summable f := by
   simp only [← ENNReal.tsum_coe_ne_top_iff_summable, Ne.def, not_iff_not, ENNReal.coe_mul,
     ENNReal.coe_pow, ENNReal.coe_two]
   constructor <;> intro h
@@ -139,7 +141,7 @@ end NNReal
 /-- Cauchy condensation test for series of nonnegative real numbers. -/
 theorem summable_condensed_iff_of_nonneg {f : ℕ → ℝ} (h_nonneg : ∀ n, 0 ≤ f n)
     (h_mono : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m) :
-    (Summable fun k : ℕ => 2 ^ k * f (2 ^ k)) ↔ Summable f := by
+    (Summable fun k : ℕ => (2 : ℝ) ^ k * f (2 ^ k)) ↔ Summable f := by
   lift f to ℕ → ℝ≥0 using h_nonneg
   simp only [NNReal.coe_le_coe] at *
   exact_mod_cast NNReal.summable_condensed_iff h_mono
@@ -160,7 +162,8 @@ common ratio `2 ^ {1 - p}`. -/
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, (n ^ p)⁻¹` converges
 if and only if `1 < p`. -/
 @[simp]
-theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
+theorem Real.summable_nat_rpow_inv {p : ℝ} :
+    Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
   cases' le_or_lt 0 p with hp hp
   /- Cauchy condensation test applies only to antitone sequences, so we consider the
     cases `0 ≤ p` and `p < 0` separately. -/
@@ -179,11 +182,11 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
         inv_le_inv_of_le (rpow_pos_of_pos (Nat.cast_pos.2 hm) _)
           (rpow_le_rpow m.cast_nonneg (Nat.cast_le.2 hmn) hp)
   -- If `p < 0`, then `1 / n ^ p` tends to infinity, thus the series diverges.
-  · suffices ¬Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ) by
+  · suffices ¬Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) by
       have : ¬1 < p := fun hp₁ => hp.not_le (zero_le_one.trans hp₁.le)
       simpa only [this, iff_false]
     · intro h
-      obtain ⟨k : ℕ, hk₁ : ((k ^ p)⁻¹ : ℝ) < 1, hk₀ : k ≠ 0⟩ :=
+      obtain ⟨k : ℕ, hk₁ : ((k : ℝ) ^ p)⁻¹ < 1, hk₀ : k ≠ 0⟩ :=
         ((h.tendsto_cofinite_zero.eventually (gt_mem_nhds zero_lt_one)).and
             (eventually_cofinite_ne 0)).exists
       apply hk₀
@@ -193,14 +196,15 @@ theorem Real.summable_nat_rpow_inv {p : ℝ} : Summable (fun n => (n ^ p)⁻¹ :
 #align real.summable_nat_rpow_inv Real.summable_nat_rpow_inv
 
 @[simp]
-theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => n ^ p : ℕ → ℝ) ↔ p < -1 := by
+theorem Real.summable_nat_rpow {p : ℝ} : Summable (fun n => (n : ℝ) ^ p : ℕ → ℝ) ↔ p < -1 := by
   rcases neg_surjective p with ⟨p, rfl⟩
   simp [rpow_neg]
 #align real.summable_nat_rpow Real.summable_nat_rpow
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
-theorem Real.summable_one_div_nat_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
+theorem Real.summable_one_div_nat_rpow {p : ℝ} :
+    Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
   simp
 #align real.summable_one_div_nat_rpow Real.summable_one_div_nat_rpow
 
@@ -208,14 +212,17 @@ theorem Real.summable_one_div_nat_rpow {p : ℝ} : Summable (fun n => 1 / n ^ p
 if and only if `1 < p`. -/
 -- porting note: temporarily remove `@[simp]` because of a problem with `simp`
 -- see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/looping.20in.20.60simp.60.20set/near/361134234
-theorem Real.summable_nat_pow_inv {p : ℕ} : Summable (fun n => (n ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
+theorem Real.summable_nat_pow_inv {p : ℕ} :
+    Summable (fun n => ((n : ℝ) ^ p)⁻¹ : ℕ → ℝ) ↔ 1 < p := by
   simp only [← rpow_nat_cast, Real.summable_nat_rpow_inv, Nat.one_lt_cast]
 #align real.summable_nat_pow_inv Real.summable_nat_pow_inv
 
 /-- Test for convergence of the `p`-series: the real-valued series `∑' n : ℕ, 1 / n ^ p` converges
 if and only if `1 < p`. -/
-theorem Real.summable_one_div_nat_pow {p : ℕ} : Summable (fun n => 1 / n ^ p : ℕ → ℝ) ↔ 1 < p := by
-  simp only [one_div, Real.summable_nat_pow_inv] --simp
+theorem Real.summable_one_div_nat_pow {p : ℕ} :
+    Summable (fun n => 1 / (n : ℝ) ^ p : ℕ → ℝ) ↔ 1 < p := by
+  -- Porting note: was `simp`
+  simp only [one_div, Real.summable_nat_pow_inv]
 #align real.summable_one_div_nat_pow Real.summable_one_div_nat_pow
 
 /-- Summability of the `p`-series over `ℤ`. -/
@@ -226,30 +233,32 @@ theorem Real.summable_one_div_int_pow {p : ℕ} :
       summable_int_of_summable_nat (Real.summable_one_div_nat_pow.mpr h)
         (((Real.summable_one_div_nat_pow.mpr h).mul_left <| 1 / (-1 : ℝ) ^ p).congr fun n => _)⟩
   conv_rhs =>
-    rw [Int.cast_neg, neg_eq_neg_one_mul, Real.rpow_nat_cast, mul_pow, ← div_div]
+    rw [Int.cast_neg, neg_eq_neg_one_mul, mul_pow, ← div_div]
   conv_lhs => rw [mul_div, mul_one]
-  -- Porting note: proof was `rfl`
-  norm_cast
 #align real.summable_one_div_int_pow Real.summable_one_div_int_pow
 
 theorem Real.summable_abs_int_rpow {b : ℝ} (hb : 1 < b) :
     Summable fun n : ℤ => |(n : ℝ)| ^ (-b) := by
-  refine'
-    summable_int_of_summable_nat (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
-      (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
-  on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
+  -- Porting note: was
+  -- refine'
+  --   summable_int_of_summable_nat (_ : Summable fun n : ℕ => |(n : ℝ)| ^ _)
+  --     (_ : Summable fun n : ℕ => |((-n : ℤ) : ℝ)| ^ _)
+  -- on_goal 2 => simp_rw [Int.cast_neg, Int.cast_ofNat, abs_neg]
+  -- all_goals
+  --   simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
+  --   rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
+  apply summable_int_of_summable_nat
+  on_goal 2 => simp_rw [Int.cast_neg, abs_neg]
   all_goals
-    simp_rw [fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
+    simp_rw [Int.cast_ofNat, fun n : ℕ => abs_of_nonneg (n.cast_nonneg : 0 ≤ (n : ℝ))]
     rwa [Real.summable_nat_rpow, neg_lt_neg_iff]
 #align real.summable_abs_int_rpow Real.summable_abs_int_rpow
 
 /-- Harmonic series is not unconditionally summable. -/
 theorem Real.not_summable_nat_cast_inv : ¬Summable (fun n => n⁻¹ : ℕ → ℝ) := by
-  have : ¬Summable (fun n => ((n : ℝ) ^ ((1 : ℕ) : ℝ))⁻¹ : ℕ → ℝ) :=
+  have : ¬Summable (fun n => ((n : ℝ) ^ 1)⁻¹ : ℕ → ℝ) :=
     mt (Real.summable_nat_pow_inv (p := 1)).1 (lt_irrefl 1)
-  -- porting note: I can't figure out why `simp` can't apply `pow_one` (even after `Nat.cast_one`)
-  convert this
-  simp
+  simpa
 #align real.not_summable_nat_cast_inv Real.not_summable_nat_cast_inv
 
 /-- Harmonic series is not unconditionally summable. -/
@@ -265,11 +274,6 @@ theorem Real.tendsto_sum_range_one_div_nat_succ_atTop :
   · exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le
 #align real.tendsto_sum_range_one_div_nat_succ_at_top Real.tendsto_sum_range_one_div_nat_succ_atTop
 
-section pow_macro
--- porting note: without these local macro rules Lean fails to elaborate `^` properly.
--- See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.234085
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y)
-
 @[simp]
 theorem NNReal.summable_rpow_inv {p : ℝ} :
     Summable (fun n => ((n : ℝ≥0) ^ p)⁻¹ : ℕ → ℝ≥0) ↔ 1 < p := by
@@ -286,8 +290,6 @@ theorem NNReal.summable_one_div_rpow {p : ℝ} :
   simp
 #align nnreal.summable_one_div_rpow NNReal.summable_one_div_rpow
 
-end pow_macro
-
 section
 
 open Finset
@@ -295,7 +297,7 @@ open Finset
 variable {α : Type _} [LinearOrderedField α]
 
 theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
-    (∑ i in Ioc k n, ((i ^ 2 : ℕ) : α)⁻¹) ≤ (k : α)⁻¹ - (n : α)⁻¹ := by
+    (∑ i in Ioc k n, ((i : α) ^ 2)⁻¹) ≤ (k : α)⁻¹ - (n : α)⁻¹ := by
   refine' Nat.le_induction _ _ n h
   · simp only [Ioc_self, sum_empty, sub_self, le_refl]
   intro n hn IH
@@ -310,22 +312,23 @@ theorem sum_Ioc_inv_sq_le_sub {k n : ℕ} (hk : k ≠ 0) (h : k ≤ n) :
   · ring_nf
     rw [add_comm]
     exact B.le
-  · nlinarith
+  · -- Porting note: was `nlinarith`
+    positivity
 #align sum_Ioc_inv_sq_le_sub sum_Ioc_inv_sq_le_sub
 
-theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i ^ 2 : ℕ) : α)⁻¹) ≤ 2 / (k + 1) :=
+theorem sum_Ioo_inv_sq_le (k n : ℕ) : (∑ i in Ioo k n, ((i : α) ^ 2)⁻¹) ≤ 2 / (k + 1) :=
   calc
-    (∑ i in Ioo k n, ((i ^ 2 : ℕ) : α)⁻¹) ≤ ∑ i in Ioc k (max (k + 1) n), ((i ^ 2 : ℕ) : α)⁻¹ := by
+    (∑ i in Ioo k n, ((i : α) ^ 2)⁻¹) ≤ ∑ i in Ioc k (max (k + 1) n), ((i : α) ^ 2)⁻¹ := by
       apply sum_le_sum_of_subset_of_nonneg
       · intro x hx
         simp only [mem_Ioo] at hx
         simp only [hx, hx.2.le, mem_Ioc, le_max_iff, or_true_iff, and_self_iff]
       · intro i _hi _hident
         positivity
-    _ ≤ ((k + 1 : α) ^ 2)⁻¹ + ∑ i in Ioc k.succ (max (k + 1) n), ((i ^ 2 : ℕ) : α)⁻¹ := by
+    _ ≤ ((k + 1 : α) ^ 2)⁻¹ + ∑ i in Ioc k.succ (max (k + 1) n), ((i : α) ^ 2)⁻¹ := by
       rw [← Nat.Icc_succ_left, ← Nat.Ico_succ_right, sum_eq_sum_Ico_succ_bot]
       swap; · exact Nat.succ_lt_succ ((Nat.lt_succ_self k).trans_le (le_max_left _ _))
-      rw [Nat.Ico_succ_right, Nat.Icc_succ_left, Nat.cast_pow, Nat.cast_succ]
+      rw [Nat.Ico_succ_right, Nat.Icc_succ_left, Nat.cast_succ]
     _ ≤ ((k + 1 : α) ^ 2)⁻¹ + (k + 1 : α)⁻¹ := by
       refine' add_le_add le_rfl ((sum_Ioc_inv_sq_le_sub _ (le_max_left _ _)).trans _)
       · simp only [Ne.def, Nat.succ_ne_zero, not_false_iff]

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -56,7 +56,7 @@ theorem le_sum_condensed' (hf : ∀ ⦃m n⦄, 0 < m → m ≤ n → f n ≤ f m
   suffices (∑ k in Ico (2 ^ n) (2 ^ (n + 1)), f k) ≤ 2 ^ n • f (2 ^ n) by
     rw [sum_range_succ, ← sum_Ico_consecutive]
     exact add_le_add ihn this
-    exacts[n.one_le_two_pow, Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ]
+    exacts [n.one_le_two_pow, Nat.pow_le_pow_of_le_right zero_lt_two n.le_succ]
   have : ∀ k ∈ Ico (2 ^ n) (2 ^ (n + 1)), f k ≤ f (2 ^ n) := fun k hk =>
     hf (pow_pos zero_lt_two _) (mem_Ico.mp hk).1
   convert sum_le_sum this

Removed the simp attribute on one lemma because simpNF was timing out trying to reduce the LHS. See Zulip for the problem. Once this error is corrected with simp, we should be able to add the attribute again.

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>