analysis.specific_limits.normed ⟷ Mathlib.Analysis.SpecificLimits.Normed

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

@@ -71,7 +71,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
   rcases neg_surjective m with ⟨m, rfl⟩
-  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
+  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.natCast_pos] at hm
   simp only [norm_pow, zpow_neg, zpow_natCast, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
@@ -804,7 +804,7 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
   calc
     ‖x ^ (n + 1) / (n + 1)!‖ = ‖x‖ / (n + 1) * ‖x ^ n / n !‖ := by
       rw [pow_succ', Nat.factorial_succ, Nat.cast_mul, ← div_mul_div_comm, norm_mul, norm_div,
-        Real.norm_coe_nat, Nat.cast_succ]
+        Real.norm_natCast, Nat.cast_succ]
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / n !‖ := by
       mono* with 0 ≤ ‖x ^ n / n !‖, 0 ≤ ‖x‖ <;> apply norm_nonneg
 #align real.summable_pow_div_factorial Real.summable_pow_div_factorial

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

@@ -72,7 +72,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
   by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
-  simp only [norm_pow, zpow_neg, zpow_coe_nat, ← inv_pow]
+  simp only [norm_pow, zpow_neg, zpow_natCast, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 -/
@@ -251,7 +251,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
   have A : (fun n => n ^ k : ℕ → R) =o[at_top] fun n => (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n => r₁ ^ n) =O[at_top] fun n => ‖r₁‖ ^ n by
-    simpa [div_mul_cancel _ (pow_pos h0 _).ne'] using A.mul_is_O this
+    simpa [div_mul_cancel₀ _ (pow_pos h0 _).ne'] using A.mul_is_O this
   exact is_O.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
 #align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
 -/
@@ -422,12 +422,12 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type _} [NormedField 
   have hr' : r ≠ 1 := by rintro rfl; simpa [lt_irrefl] using hr
   set s : 𝕜 := ∑' n : ℕ, n * r ^ n
   calc
-    s = (1 - r) * s / (1 - r) := (mul_div_cancel_left _ (sub_ne_zero.2 hr'.symm)).symm
+    s = (1 - r) * s / (1 - r) := (mul_div_cancel_left₀ _ (sub_ne_zero.2 hr'.symm)).symm
     _ = (s - r * s) / (1 - r) := by rw [sub_mul, one_mul]
     _ = ((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1) - r * s) / (1 - r) := by
       rw [← tsum_eq_zero_add A]
     _ = (r * ∑' n : ℕ, (n + 1) * r ^ n - r * s) / (1 - r) := by
-      simp [pow_succ, mul_left_comm _ r, tsum_mul_left]
+      simp [pow_succ', mul_left_comm _ r, tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
@@ -458,7 +458,7 @@ theorem SeminormedAddCommGroup.cauchySeq_of_le_geometric {C : ℝ} {r : ℝ} (hr
 theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) (n : ℕ) :
     dist (∑ i in range n, f i) (∑ i in range (n + 1), f i) ≤ C * r ^ n :=
   by
-  rw [sum_range_succ, dist_eq_norm, ← norm_neg, neg_sub, add_sub_cancel']
+  rw [sum_range_succ, dist_eq_norm, ← norm_neg, neg_sub, add_sub_cancel_left]
   exact hf n
 #align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometric
 -/
@@ -803,7 +803,7 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
   intro n hn
   calc
     ‖x ^ (n + 1) / (n + 1)!‖ = ‖x‖ / (n + 1) * ‖x ^ n / n !‖ := by
-      rw [pow_succ, Nat.factorial_succ, Nat.cast_mul, ← div_mul_div_comm, norm_mul, norm_div,
+      rw [pow_succ', Nat.factorial_succ, Nat.cast_mul, ← div_mul_div_comm, norm_mul, norm_div,
         Real.norm_coe_nat, Nat.cast_succ]
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / n !‖ := by
       mono* with 0 ≤ ‖x ^ n / n !‖, 0 ≤ ‖x‖ <;> apply norm_nonneg

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

@@ -71,7 +71,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
   rcases neg_surjective m with ⟨m, rfl⟩
-  rw [neg_lt_zero] at hm ; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm 
+  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
   simp only [norm_pow, zpow_neg, zpow_coe_nat, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
@@ -189,7 +189,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     rcases sign_cases_of_C_mul_pow_nonneg fun n => (abs_nonneg _).trans (H n) with
       (rfl | ⟨hC₀, ha₀⟩)
     · obtain rfl : f = 0 := by ext n; simpa using H n
-      simp only [lt_irrefl, false_or_iff] at h₀ 
+      simp only [lt_irrefl, false_or_iff] at h₀
       exact ⟨0, ⟨neg_lt_zero.2 h₀, h₀⟩, is_O_zero _ _⟩
     exact
       ⟨a, A ⟨ha₀, ha⟩,
@@ -198,7 +198,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   tfae_have 2 → 8
   · rintro ⟨a, ha, H⟩
     refine' ⟨a, ha, (H.def zero_lt_one).mono fun n hn => _⟩
-    rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn 
+    rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn
   tfae_have 8 → 7; exact fun ⟨a, ha, H⟩ => ⟨a, ha.2, H⟩
   tfae_have 7 → 3
   · rintro ⟨a, ha, H⟩
@@ -247,7 +247,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
   by_cases h0 : r₁ = 0
   · refine' (is_o_zero _ _).congr' (mem_at_top_sets.2 <| ⟨1, fun n hn => _⟩) eventually_eq.rfl
     simp [zero_pow (zero_lt_one.trans_le hn), h0]
-  rw [← Ne.def, ← norm_pos_iff] at h0 
+  rw [← Ne.def, ← norm_pos_iff] at h0
   have A : (fun n => n ^ k : ℕ → R) =o[at_top] fun n => (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n => r₁ ^ n) =O[at_top] fun n => ‖r₁‖ ^ n by
@@ -382,8 +382,8 @@ theorem summable_geometric_iff_norm_lt_one : (Summable fun n : ℕ => ξ ^ n) 
   refine' ⟨fun h => _, summable_geometric_of_norm_lt_one⟩
   obtain ⟨k : ℕ, hk : dist (ξ ^ k) 0 < 1⟩ :=
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
-  simp only [norm_pow, dist_zero_right] at hk 
-  rw [← one_pow k] at hk 
+  simp only [norm_pow, dist_zero_right] at hk
+  rw [← one_pow k] at hk
   exact lt_of_pow_lt_pow_left _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_one
 -/
@@ -535,7 +535,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
   split_ifs with H H
   · rw [norm_zero]
     exact mul_nonneg hC (pow_nonneg hr₀.le _)
-  · push_neg at H 
+  · push_neg at H
     exact h _ H
 #align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''
 -/
@@ -616,7 +616,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f :=
   by
   by_cases hr₀ : 0 ≤ r
-  · rw [eventually_at_top] at h 
+  · rw [eventually_at_top] at h
     rcases h with ⟨N, hN⟩
     rw [← @summable_nat_add_iff α _ _ _ _ N]
     refine'
@@ -626,7 +626,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     refine' le_geom hr₀ n fun i _ => _
     convert hN (i + N) (N.le_add_left i) using 3
     ac_rfl
-  · push_neg at hr₀ 
+  · push_neg at hr₀
     refine' Summable.of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
     filter_upwards [h] with _ hn
@@ -652,9 +652,9 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f :=
   by
-  rw [eventually_at_top] at h 
+  rw [eventually_at_top] at h
   rcases h with ⟨N₀, hN₀⟩
-  rw [frequently_at_top] at hf 
+  rw [frequently_at_top] at hf
   rcases hf N₀ with ⟨N, hNN₀ : N₀ ≤ N, hN⟩
   rw [← @summable_nat_add_iff α _ _ _ _ N]
   refine'
@@ -664,7 +664,7 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
   · refine' lt_of_le_of_ne (norm_nonneg _) _
     intro h''
     specialize hN₀ N hNN₀
-    simp only [comp_app, zero_add] at h'' 
+    simp only [comp_app, zero_add] at h''
     exact hN h''.symm
   · intro i
     dsimp only [comp_app]
@@ -681,7 +681,7 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCo
   have key : ∀ᶠ n in at_top, ‖f n‖ ≠ 0 :=
     by
     filter_upwards [eventually_ge_of_tendsto_gt hl h] with _ hn hc
-    rw [hc, div_zero] at hn 
+    rw [hc, div_zero] at hn
     linarith
   rcases exists_between hl with ⟨r, hr₀, hr₁⟩
   refine' not_summable_of_ratio_norm_eventually_ge hr₀ key.frequently _

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

@@ -72,7 +72,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
   by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm ; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm 
-  simp only [norm_pow, zpow_neg, zpow_ofNat, ← inv_pow]
+  simp only [norm_pow, zpow_neg, zpow_coe_nat, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 -/

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

@@ -116,7 +116,8 @@ theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
   (isLittleO_of_tendsto fun n hn => False.elim <| H.ne' <| pow_eq_zero hn) <|
-    (tendsto_pow_atTop_nhds_0_of_lt_1 (div_nonneg h₁ (h₁.trans h₂.le)) ((div_lt_one H).2 h₂)).congr
+    (tendsto_pow_atTop_nhds_zero_of_lt_one (div_nonneg h₁ (h₁.trans h₂.le))
+          ((div_lt_one H).2 h₂)).congr
       fun n => div_pow _ _ _
 #align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
 -/
@@ -305,21 +306,21 @@ theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r <
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
 -/
 
-#print tendsto_pow_atTop_nhds_0_of_norm_lt_1 /-
+#print tendsto_pow_atTop_nhds_zero_of_norm_lt_one /-
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
-theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
-    Tendsto (fun n : ℕ => x ^ n) atTop (𝓝 0) :=
+theorem tendsto_pow_atTop_nhds_zero_of_norm_lt_one {R : Type _} [NormedRing R] {x : R}
+    (h : ‖x‖ < 1) : Tendsto (fun n : ℕ => x ^ n) atTop (𝓝 0) :=
   by
   apply squeeze_zero_norm' (eventually_norm_pow_le x)
-  exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
-#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1
+  exact tendsto_pow_atTop_nhds_zero_of_lt_one (norm_nonneg _) h
+#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_zero_of_norm_lt_one
 -/
 
-#print tendsto_pow_atTop_nhds_0_of_abs_lt_1 /-
-theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
+#print tendsto_pow_atTop_nhds_zero_of_abs_lt_one /-
+theorem tendsto_pow_atTop_nhds_zero_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
-  tendsto_pow_atTop_nhds_0_of_norm_lt_1 h
-#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_0_of_abs_lt_1
+  tendsto_pow_atTop_nhds_zero_of_norm_lt_one h
+#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_zero_of_abs_lt_one
 -/
 
 /-! ### Geometric series-/
@@ -329,94 +330,94 @@ section Geometric
 
 variable {K : Type _} [NormedField K] {ξ : K}
 
-#print hasSum_geometric_of_norm_lt_1 /-
-theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
+#print hasSum_geometric_of_norm_lt_one /-
+theorem hasSum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
   have xi_ne_one : ξ ≠ 1 := by contrapose! h; simp [h]
   have A : tendsto (fun n => (ξ ^ n - 1) * (ξ - 1)⁻¹) at_top (𝓝 ((0 - 1) * (ξ - 1)⁻¹)) :=
-    ((tendsto_pow_atTop_nhds_0_of_norm_lt_1 h).sub tendsto_const_nhds).mul tendsto_const_nhds
+    ((tendsto_pow_atTop_nhds_zero_of_norm_lt_one h).sub tendsto_const_nhds).mul tendsto_const_nhds
   rw [hasSum_iff_tendsto_nat_of_summable_norm]
   · simpa [geom_sum_eq, xi_ne_one, neg_inv, div_eq_mul_inv] using A
-  · simp [norm_pow, summable_geometric_of_lt_1 (norm_nonneg _) h]
-#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1
+  · simp [norm_pow, summable_geometric_of_lt_one (norm_nonneg _) h]
+#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_one
 -/
 
-#print summable_geometric_of_norm_lt_1 /-
-theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : ℕ => ξ ^ n :=
-  ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
-#align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
+#print summable_geometric_of_norm_lt_one /-
+theorem summable_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : Summable fun n : ℕ => ξ ^ n :=
+  ⟨_, hasSum_geometric_of_norm_lt_one h⟩
+#align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_one
 -/
 
-#print tsum_geometric_of_norm_lt_1 /-
-theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
-  (hasSum_geometric_of_norm_lt_1 h).tsum_eq
-#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
+#print tsum_geometric_of_norm_lt_one /-
+theorem tsum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
+  (hasSum_geometric_of_norm_lt_one h).tsum_eq
+#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_one
 -/
 
-#print hasSum_geometric_of_abs_lt_1 /-
-theorem hasSum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
+#print hasSum_geometric_of_abs_lt_one /-
+theorem hasSum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
-  hasSum_geometric_of_norm_lt_1 h
-#align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1
+  hasSum_geometric_of_norm_lt_one h
+#align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_one
 -/
 
-#print summable_geometric_of_abs_lt_1 /-
-theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ => r ^ n :=
-  summable_geometric_of_norm_lt_1 h
-#align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
+#print summable_geometric_of_abs_lt_one /-
+theorem summable_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ => r ^ n :=
+  summable_geometric_of_norm_lt_one h
+#align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_one
 -/
 
-#print tsum_geometric_of_abs_lt_1 /-
-theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
-  tsum_geometric_of_norm_lt_1 h
-#align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
+#print tsum_geometric_of_abs_lt_one /-
+theorem tsum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+  tsum_geometric_of_norm_lt_one h
+#align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_one
 -/
 
-#print summable_geometric_iff_norm_lt_1 /-
+#print summable_geometric_iff_norm_lt_one /-
 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
 @[simp]
-theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ => ξ ^ n) ↔ ‖ξ‖ < 1 :=
+theorem summable_geometric_iff_norm_lt_one : (Summable fun n : ℕ => ξ ^ n) ↔ ‖ξ‖ < 1 :=
   by
-  refine' ⟨fun h => _, summable_geometric_of_norm_lt_1⟩
+  refine' ⟨fun h => _, summable_geometric_of_norm_lt_one⟩
   obtain ⟨k : ℕ, hk : dist (ξ ^ k) 0 < 1⟩ :=
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
   simp only [norm_pow, dist_zero_right] at hk 
   rw [← one_pow k] at hk 
   exact lt_of_pow_lt_pow_left _ zero_le_one hk
-#align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
+#align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_one
 -/
 
 end Geometric
 
 section MulGeometric
 
-#print summable_norm_pow_mul_geometric_of_norm_lt_1 /-
-theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
+#print summable_norm_pow_mul_geometric_of_norm_lt_one /-
+theorem summable_norm_pow_mul_geometric_of_norm_lt_one {R : Type _} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ => ‖(n ^ k * r ^ n : R)‖ :=
   by
   rcases exists_between hr with ⟨r', hrr', h⟩
   exact
-    summable_of_isBigO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
+    summable_of_isBigO_nat (summable_geometric_of_lt_one ((norm_nonneg _).trans hrr'.le) h)
       (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsBigO.norm_left
-#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
+#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_one
 -/
 
-#print summable_pow_mul_geometric_of_norm_lt_1 /-
-theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
+#print summable_pow_mul_geometric_of_norm_lt_one /-
+theorem summable_pow_mul_geometric_of_norm_lt_one {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
-  Summable.of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
-#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
+  Summable.of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_one _ hr
+#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_one
 -/
 
-#print hasSum_coe_mul_geometric_of_norm_lt_1 /-
+#print hasSum_coe_mul_geometric_of_norm_lt_one /-
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `has_sum` version. -/
-theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
-    (hr : ‖r‖ < 1) : HasSum (fun n => n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) :=
+theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜]
+    {r : 𝕜} (hr : ‖r‖ < 1) : HasSum (fun n => n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) :=
   by
   have A : Summable (fun n => n * r ^ n : ℕ → 𝕜) := by
-    simpa using summable_pow_mul_geometric_of_norm_lt_1 1 hr
-  have B : HasSum (pow r : ℕ → 𝕜) (1 - r)⁻¹ := hasSum_geometric_of_norm_lt_1 hr
+    simpa using summable_pow_mul_geometric_of_norm_lt_one 1 hr
+  have B : HasSum (pow r : ℕ → 𝕜) (1 - r)⁻¹ := hasSum_geometric_of_norm_lt_one hr
   refine' A.has_sum_iff.2 _
   have hr' : r ≠ 1 := by rintro rfl; simpa [lt_irrefl] using hr
   set s : 𝕜 := ∑' n : ℕ, n * r ^ n
@@ -429,15 +430,15 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
       simp [pow_succ, mul_left_comm _ r, tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
-#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
+#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
 -/
 
-#print tsum_coe_mul_geometric_of_norm_lt_1 /-
+#print tsum_coe_mul_geometric_of_norm_lt_one /-
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
-theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
+theorem tsum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
-  (hasSum_coe_mul_geometric_of_norm_lt_1 hr).tsum_eq
-#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1
+  (hasSum_coe_mul_geometric_of_norm_lt_one hr).tsum_eq
+#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_one
 -/
 
 end MulGeometric
@@ -547,44 +548,44 @@ variable {R : Type _} [NormedRing R] [CompleteSpace R]
 
 open NormedSpace
 
-#print NormedRing.summable_geometric_of_norm_lt_1 /-
+#print NormedRing.summable_geometric_of_norm_lt_one /-
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
-theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
+theorem NormedRing.summable_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     Summable fun n : ℕ => x ^ n :=
   by
-  have h1 : Summable fun n : ℕ => ‖x‖ ^ n := summable_geometric_of_lt_1 (norm_nonneg _) h
+  have h1 : Summable fun n : ℕ => ‖x‖ ^ n := summable_geometric_of_lt_one (norm_nonneg _) h
   refine' Summable.of_norm_bounded_eventually _ h1 _
   rw [Nat.cofinite_eq_atTop]
   exact eventually_norm_pow_le x
-#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
+#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_one
 -/
 
-#print NormedRing.tsum_geometric_of_norm_lt_1 /-
+#print NormedRing.tsum_geometric_of_norm_lt_one /-
 /-- Bound for the sum of a geometric series in a normed ring.  This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
-theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
+theorem NormedRing.tsum_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     ‖∑' n : ℕ, x ^ n‖ ≤ ‖(1 : R)‖ - 1 + (1 - ‖x‖)⁻¹ :=
   by
-  rw [tsum_eq_zero_add (NormedRing.summable_geometric_of_norm_lt_1 x h)]
+  rw [tsum_eq_zero_add (NormedRing.summable_geometric_of_norm_lt_one x h)]
   simp only [pow_zero]
   refine' le_trans (norm_add_le _ _) _
   have : ‖∑' b : ℕ, (fun n => x ^ (n + 1)) b‖ ≤ (1 - ‖x‖)⁻¹ - 1 :=
     by
     refine' tsum_of_norm_bounded _ fun b => norm_pow_le' _ (Nat.succ_pos b)
-    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
+    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_one (norm_nonneg x) h)
     simp
   linarith
-#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
+#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_one
 -/
 
 #print geom_series_mul_neg /-
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 :=
   by
-  have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_right (1 - x)
+  have := (NormedRing.summable_geometric_of_norm_lt_one x h).HasSum.mul_right (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (𝓝 1) := by
-    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
+    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_norm_lt_one h)
   convert ← this
   ext n
   rw [← geom_sum_mul_neg, Finset.sum_mul]
@@ -594,10 +595,10 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
 #print mul_neg_geom_series /-
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : (1 - x) * ∑' i : ℕ, x ^ i = 1 :=
   by
-  have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_left (1 - x)
+  have := (NormedRing.summable_geometric_of_norm_lt_one x h).HasSum.mul_left (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (nhds 1) := by
-    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
+    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_norm_lt_one h)
   convert ← this
   ext n
   rw [← mul_neg_geom_sum, Finset.mul_sum]
@@ -620,7 +621,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     rw [← @summable_nat_add_iff α _ _ _ _ N]
     refine'
       Summable.of_norm_bounded (fun n => ‖f N‖ * r ^ n)
-        (Summable.mul_left _ <| summable_geometric_of_lt_1 hr₀ hr₁) fun n => _
+        (Summable.mul_left _ <| summable_geometric_of_lt_one hr₀ hr₁) fun n => _
     conv_rhs => rw [mul_comm, ← zero_add N]
     refine' le_geom hr₀ n fun i _ => _
     convert hN (i + N) (N.le_add_left i) using 3

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

@@ -522,7 +522,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
   by
   set v : ℕ → α := fun n => if n < N then 0 else u n
   have hC : 0 ≤ C :=
-    (zero_le_mul_right <| pow_pos hr₀ N).mp ((norm_nonneg _).trans <| h N <| le_refl N)
+    (mul_nonneg_iff_of_pos_right <| pow_pos hr₀ N).mp ((norm_nonneg _).trans <| h N <| le_refl N)
   have : ∀ n ≥ N, u n = v n := by
     intro n hn
     simp [v, hn, if_neg (not_lt.mpr hn)]

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

@@ -383,7 +383,7 @@ theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ => ξ ^ n) ↔
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
   simp only [norm_pow, dist_zero_right] at hk 
   rw [← one_pow k] at hk 
-  exact lt_of_pow_lt_pow _ zero_le_one hk
+  exact lt_of_pow_lt_pow_left _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
 -/
 

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

@@ -629,7 +629,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     refine' Summable.of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
     filter_upwards [h] with _ hn
-    by_contra' h
+    by_contra! h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
 -/

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

@@ -41,7 +41,7 @@ theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     (∃ r, Tendsto (fun n => ∑ i in range n, |f i|) atTop (𝓝 r)) → Summable f
   | ⟨r, hr⟩ =>
     by
-    refine' summable_of_summable_norm ⟨r, (hasSum_iff_tendsto_nat_of_nonneg _ _).2 _⟩
+    refine' Summable.of_norm ⟨r, (hasSum_iff_tendsto_nat_of_nonneg _ _).2 _⟩
     exact fun i => norm_nonneg _
     simpa only using hr
 #align summable_of_absolute_convergence_real summable_of_absolute_convergence_real
@@ -405,7 +405,7 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
 #print summable_pow_mul_geometric_of_norm_lt_1 /-
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
-  summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
+  Summable.of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 -/
 
@@ -554,7 +554,7 @@ theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
     Summable fun n : ℕ => x ^ n :=
   by
   have h1 : Summable fun n : ℕ => ‖x‖ ^ n := summable_geometric_of_lt_1 (norm_nonneg _) h
-  refine' summable_of_norm_bounded_eventually _ h1 _
+  refine' Summable.of_norm_bounded_eventually _ h1 _
   rw [Nat.cofinite_eq_atTop]
   exact eventually_norm_pow_le x
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
@@ -619,14 +619,14 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     rcases h with ⟨N, hN⟩
     rw [← @summable_nat_add_iff α _ _ _ _ N]
     refine'
-      summable_of_norm_bounded (fun n => ‖f N‖ * r ^ n)
+      Summable.of_norm_bounded (fun n => ‖f N‖ * r ^ n)
         (Summable.mul_left _ <| summable_geometric_of_lt_1 hr₀ hr₁) fun n => _
     conv_rhs => rw [mul_comm, ← zero_add N]
     refine' le_geom hr₀ n fun i _ => _
     convert hN (i + N) (N.le_add_left i) using 3
     ac_rfl
   · push_neg at hr₀ 
-    refine' summable_of_norm_bounded_eventually 0 summable_zero _
+    refine' Summable.of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
     filter_upwards [h] with _ hn
     by_contra' h

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
 -/
-import Mathbin.Algebra.Order.Field.Basic
-import Mathbin.Analysis.Asymptotics.Asymptotics
-import Mathbin.Analysis.SpecificLimits.Basic
+import Algebra.Order.Field.Basic
+import Analysis.Asymptotics.Asymptotics
+import Analysis.SpecificLimits.Basic
 
 #align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.specific_limits.normed
-! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Field.Basic
 import Mathbin.Analysis.Asymptotics.Asymptotics
 import Mathbin.Analysis.SpecificLimits.Basic
 
+#align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
+
 /-!
 # A collection of specific limit computations
 

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

@@ -275,7 +275,7 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
     exact
       tendsto_const_nhds.congr'
         (mem_at_top_sets.2 ⟨1, fun n hn => by simp [zero_lt_one.trans_le hn, h0]⟩)
-  have hr' : 1 < (|r|)⁻¹ := one_lt_inv (abs_pos.2 h0) hr
+  have hr' : 1 < |r|⁻¹ := one_lt_inv (abs_pos.2 h0) hr
   rw [tendsto_zero_iff_norm_tendsto_zero]
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'
 #align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_one

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

@@ -33,10 +33,13 @@ open scoped Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
+#print tendsto_norm_atTop_atTop /-
 theorem tendsto_norm_atTop_atTop : Tendsto (norm : ℝ → ℝ) atTop atTop :=
   tendsto_abs_atTop_atTop
 #align tendsto_norm_at_top_at_top tendsto_norm_atTop_atTop
+-/
 
+#print summable_of_absolute_convergence_real /-
 theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     (∃ r, Tendsto (fun n => ∑ i in range n, |f i|) atTop (𝓝 r)) → Summable f
   | ⟨r, hr⟩ =>
@@ -45,22 +48,28 @@ theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     exact fun i => norm_nonneg _
     simpa only using hr
 #align summable_of_absolute_convergence_real summable_of_absolute_convergence_real
+-/
 
 /-! ### Powers -/
 
 
+#print tendsto_norm_zero' /-
 theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
     Tendsto (norm : 𝕜 → ℝ) (𝓝[≠] 0) (𝓝[>] 0) :=
   tendsto_norm_zero.inf <| tendsto_principal_principal.2 fun x hx => norm_pos_iff.2 hx
 #align tendsto_norm_zero' tendsto_norm_zero'
+-/
 
 namespace NormedField
 
+#print NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop /-
 theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] :
     Tendsto (fun x : 𝕜 => ‖x⁻¹‖) (𝓝[≠] 0) atTop :=
   (tendsto_inv_zero_atTop.comp tendsto_norm_zero').congr fun x => (norm_inv x).symm
 #align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
+-/
 
+#print NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop /-
 theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
@@ -69,7 +78,9 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
   simp only [norm_pow, zpow_neg, zpow_ofNat, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
+-/
 
+#print NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded /-
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
 theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [NormedField 𝕜]
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
@@ -78,7 +89,9 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
   rw [← is_o_one_iff 𝕜] at hε ⊢
   simpa using is_o.smul_is_O hε (hf.is_O_const (one_ne_zero : (1 : 𝕜) ≠ 0))
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
+-/
 
+#print NormedField.continuousAt_zpow /-
 @[simp]
 theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : ℤ} {x : 𝕜} :
     ContinuousAt (fun x => x ^ m) x ↔ x ≠ 0 ∨ 0 ≤ m :=
@@ -89,15 +102,19 @@ theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : 
     not_tendsto_atTop_of_tendsto_nhds (hc.tendsto.mono_left nhdsWithin_le_nhds).norm
       (tendsto_norm_zpow_nhds_within_0_at_top hm)
 #align normed_field.continuous_at_zpow NormedField.continuousAt_zpow
+-/
 
+#print NormedField.continuousAt_inv /-
 @[simp]
 theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 𝕜} :
     ContinuousAt Inv.inv x ↔ x ≠ 0 := by
   simpa [(zero_lt_one' ℤ).not_le] using @continuousAt_zpow _ _ (-1) x
 #align normed_field.continuous_at_inv NormedField.continuousAt_inv
+-/
 
 end NormedField
 
+#print isLittleO_pow_pow_of_lt_left /-
 theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ < r₂) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
@@ -105,20 +122,26 @@ theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂
     (tendsto_pow_atTop_nhds_0_of_lt_1 (div_nonneg h₁ (h₁.trans h₂.le)) ((div_lt_one H).2 h₂)).congr
       fun n => div_pow _ _ _
 #align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
+-/
 
+#print isBigO_pow_pow_of_le_left /-
 theorem isBigO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
     (fun n : ℕ => r₁ ^ n) =O[atTop] fun n => r₂ ^ n :=
   h₂.eq_or_lt.elim (fun h => h ▸ isBigO_refl _ _) fun h =>
     (isLittleO_pow_pow_of_lt_left h₁ h).IsBigO
 #align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_left
+-/
 
+#print isLittleO_pow_pow_of_abs_lt_left /-
 theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   by
   refine' (is_o.of_norm_left _).of_norm_right
   exact (isLittleO_pow_pow_of_lt_left (abs_nonneg r₁) h).congr (pow_abs r₁) (pow_abs r₂)
 #align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_left
+-/
 
+#print TFAE_exists_lt_isLittleO_pow /-
 /-- Various statements equivalent to the fact that `f n` grows exponentially slower than `R ^ n`.
 
 * 0: $f n = o(a ^ n)$ for some $-R < a < R$;
@@ -186,7 +209,9 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     simpa only [Real.norm_eq_abs, one_mul, abs_pow, abs_of_nonneg this]
   tfae_finish
 #align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_pow
+-/
 
+#print isLittleO_pow_const_const_pow_of_one_lt /-
 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
     (hr : 1 < r) : (fun n => n ^ k : ℕ → R) =o[atTop] fun n => r ^ n :=
@@ -205,13 +230,17 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
   refine' n.norm_cast_le.trans (mul_le_mul_of_nonneg_right _ (norm_nonneg _))
   simpa [div_eq_inv_mul, Real.norm_eq_abs, abs_of_nonneg h0] using n.cast_le_pow_div_sub h1
 #align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
+-/
 
+#print isLittleO_coe_const_pow_of_one_lt /-
 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
     (coe : ℕ → R) =o[atTop] fun n => r ^ n := by
   simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
 #align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
+-/
 
+#print isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt /-
 /-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
@@ -227,12 +256,16 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
     simpa [div_mul_cancel _ (pow_pos h0 _).ne'] using A.mul_is_O this
   exact is_O.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
 #align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
+-/
 
+#print tendsto_pow_const_div_const_pow_of_one_lt /-
 theorem tendsto_pow_const_div_const_pow_of_one_lt (k : ℕ) {r : ℝ} (hr : 1 < r) :
     Tendsto (fun n => n ^ k / r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   (isLittleO_pow_const_const_pow_of_one_lt k hr).tendsto_div_nhds_zero
 #align tendsto_pow_const_div_const_pow_of_one_lt tendsto_pow_const_div_const_pow_of_one_lt
+-/
 
+#print tendsto_pow_const_mul_const_pow_of_abs_lt_one /-
 /-- If `|r| < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`. -/
 theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n ^ k * r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
@@ -246,7 +279,9 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
   rw [tendsto_zero_iff_norm_tendsto_zero]
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'
 #align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_one
+-/
 
+#print tendsto_pow_const_mul_const_pow_of_lt_one /-
 /-- If `0 ≤ r < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`.
 This is a specialized version of `tendsto_pow_const_mul_const_pow_of_abs_lt_one`, singled out
 for ease of application. -/
@@ -254,20 +289,26 @@ theorem tendsto_pow_const_mul_const_pow_of_lt_one (k : ℕ) {r : ℝ} (hr : 0 
     Tendsto (fun n => n ^ k * r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_pow_const_mul_const_pow_of_abs_lt_one k (abs_lt.2 ⟨neg_one_lt_zero.trans_le hr, h'r⟩)
 #align tendsto_pow_const_mul_const_pow_of_lt_one tendsto_pow_const_mul_const_pow_of_lt_one
+-/
 
+#print tendsto_self_mul_const_pow_of_abs_lt_one /-
 /-- If `|r| < 1`, then `n * r ^ n` tends to zero. -/
 theorem tendsto_self_mul_const_pow_of_abs_lt_one {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n * r ^ n : ℕ → ℝ) atTop (𝓝 0) := by
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_abs_lt_one 1 hr
 #align tendsto_self_mul_const_pow_of_abs_lt_one tendsto_self_mul_const_pow_of_abs_lt_one
+-/
 
+#print tendsto_self_mul_const_pow_of_lt_one /-
 /-- If `0 ≤ r < 1`, then `n * r ^ n` tends to zero. This is a specialized version of
 `tendsto_self_mul_const_pow_of_abs_lt_one`, singled out for ease of application. -/
 theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r < 1) :
     Tendsto (fun n => n * r ^ n : ℕ → ℝ) atTop (𝓝 0) := by
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_lt_one 1 hr h'r
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
+-/
 
+#print tendsto_pow_atTop_nhds_0_of_norm_lt_1 /-
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
 theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
     Tendsto (fun n : ℕ => x ^ n) atTop (𝓝 0) :=
@@ -275,11 +316,14 @@ theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R
   apply squeeze_zero_norm' (eventually_norm_pow_le x)
   exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
 #align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1
+-/
 
+#print tendsto_pow_atTop_nhds_0_of_abs_lt_1 /-
 theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   tendsto_pow_atTop_nhds_0_of_norm_lt_1 h
 #align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_0_of_abs_lt_1
+-/
 
 /-! ### Geometric series-/
 
@@ -288,6 +332,7 @@ section Geometric
 
 variable {K : Type _} [NormedField K] {ξ : K}
 
+#print hasSum_geometric_of_norm_lt_1 /-
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
   have xi_ne_one : ξ ≠ 1 := by contrapose! h; simp [h]
@@ -297,28 +342,40 @@ theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ =
   · simpa [geom_sum_eq, xi_ne_one, neg_inv, div_eq_mul_inv] using A
   · simp [norm_pow, summable_geometric_of_lt_1 (norm_nonneg _) h]
 #align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1
+-/
 
+#print summable_geometric_of_norm_lt_1 /-
 theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : ℕ => ξ ^ n :=
   ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
+-/
 
+#print tsum_geometric_of_norm_lt_1 /-
 theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
+-/
 
+#print hasSum_geometric_of_abs_lt_1 /-
 theorem hasSum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   hasSum_geometric_of_norm_lt_1 h
 #align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1
+-/
 
+#print summable_geometric_of_abs_lt_1 /-
 theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ => r ^ n :=
   summable_geometric_of_norm_lt_1 h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
+-/
 
+#print tsum_geometric_of_abs_lt_1 /-
 theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_1 h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
+-/
 
+#print summable_geometric_iff_norm_lt_1 /-
 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
 @[simp]
@@ -331,11 +388,13 @@ theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ => ξ ^ n) ↔
   rw [← one_pow k] at hk 
   exact lt_of_pow_lt_pow _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
+-/
 
 end Geometric
 
 section MulGeometric
 
+#print summable_norm_pow_mul_geometric_of_norm_lt_1 /-
 theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ => ‖(n ^ k * r ^ n : R)‖ :=
   by
@@ -344,12 +403,16 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
     summable_of_isBigO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
       (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
+-/
 
+#print summable_pow_mul_geometric_of_norm_lt_1 /-
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
   summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
+-/
 
+#print hasSum_coe_mul_geometric_of_norm_lt_1 /-
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `has_sum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : HasSum (fun n => n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) :=
@@ -370,12 +433,15 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
+-/
 
+#print tsum_coe_mul_geometric_of_norm_lt_1 /-
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
 theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
   (hasSum_coe_mul_geometric_of_norm_lt_1 hr).tsum_eq
 #align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1
+-/
 
 end MulGeometric
 
@@ -383,18 +449,23 @@ section SummableLeGeometric
 
 variable [SeminormedAddCommGroup α] {r C : ℝ} {f : ℕ → α}
 
+#print SeminormedAddCommGroup.cauchySeq_of_le_geometric /-
 theorem SeminormedAddCommGroup.cauchySeq_of_le_geometric {C : ℝ} {r : ℝ} (hr : r < 1) {u : ℕ → α}
     (h : ∀ n, ‖u n - u (n + 1)‖ ≤ C * r ^ n) : CauchySeq u :=
   cauchySeq_of_le_geometric r C hr (by simpa [dist_eq_norm] using h)
 #align seminormed_add_comm_group.cauchy_seq_of_le_geometric SeminormedAddCommGroup.cauchySeq_of_le_geometric
+-/
 
+#print dist_partial_sum_le_of_le_geometric /-
 theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) (n : ℕ) :
     dist (∑ i in range n, f i) (∑ i in range (n + 1), f i) ≤ C * r ^ n :=
   by
   rw [sum_range_succ, dist_eq_norm, ← norm_neg, neg_sub, add_sub_cancel']
   exact hf n
 #align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometric
+-/
 
+#print cauchySeq_finset_of_geometric_bound /-
 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` form a
 Cauchy sequence. This lemma does not assume `0 ≤ r` or `0 ≤ C`. -/
 theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) :
@@ -402,7 +473,9 @@ theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖
   cauchySeq_finset_of_norm_bounded _
     (aux_hasSum_of_le_geometric hr (dist_partial_sum_le_of_le_geometric hf)).Summable hf
 #align cauchy_seq_finset_of_geometric_bound cauchySeq_finset_of_geometric_bound
+-/
 
+#print norm_sub_le_of_geometric_bound_of_hasSum /-
 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` are within
 distance `C * r ^ n / (1 - r)` of the sum of the series. This lemma does not assume `0 ≤ r` or
 `0 ≤ C`. -/
@@ -413,6 +486,7 @@ theorem norm_sub_le_of_geometric_bound_of_hasSum (hr : r < 1) (hf : ∀ n, ‖f
   apply dist_le_of_le_geometric_of_tendsto r C hr (dist_partial_sum_le_of_le_geometric hf)
   exact ha.tendsto_sum_nat
 #align norm_sub_le_of_geometric_bound_of_has_sum norm_sub_le_of_geometric_bound_of_hasSum
+-/
 
 #print dist_partial_sum /-
 @[simp]
@@ -430,16 +504,21 @@ theorem dist_partial_sum' (u : ℕ → α) (n : ℕ) :
 #align dist_partial_sum' dist_partial_sum'
 -/
 
+#print cauchy_series_of_le_geometric /-
 theorem cauchy_series_of_le_geometric {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range n, u k :=
   cauchySeq_of_le_geometric r C hr (by simp [h])
 #align cauchy_series_of_le_geometric cauchy_series_of_le_geometric
+-/
 
+#print NormedAddCommGroup.cauchy_series_of_le_geometric' /-
 theorem NormedAddCommGroup.cauchy_series_of_le_geometric' {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range (n + 1), u k :=
   (cauchy_series_of_le_geometric hr h).comp_tendsto <| tendsto_add_atTop_nat 1
 #align normed_add_comm_group.cauchy_series_of_le_geometric' NormedAddCommGroup.cauchy_series_of_le_geometric'
+-/
 
+#print NormedAddCommGroup.cauchy_series_of_le_geometric'' /-
 theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ → α} {N : ℕ} {r : ℝ}
     (hr₀ : 0 < r) (hr₁ : r < 1) (h : ∀ n ≥ N, ‖u n‖ ≤ C * r ^ n) :
     CauchySeq fun n => ∑ k in range (n + 1), u k :=
@@ -461,6 +540,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
   · push_neg at H 
     exact h _ H
 #align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''
+-/
 
 end SummableLeGeometric
 
@@ -470,6 +550,7 @@ variable {R : Type _} [NormedRing R] [CompleteSpace R]
 
 open NormedSpace
 
+#print NormedRing.summable_geometric_of_norm_lt_1 /-
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
 theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -480,7 +561,9 @@ theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   rw [Nat.cofinite_eq_atTop]
   exact eventually_norm_pow_le x
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
+-/
 
+#print NormedRing.tsum_geometric_of_norm_lt_1 /-
 /-- Bound for the sum of a geometric series in a normed ring.  This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
 theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -496,7 +579,9 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
     simp
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
+-/
 
+#print geom_series_mul_neg /-
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_right (1 - x)
@@ -507,7 +592,9 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   ext n
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
+-/
 
+#print mul_neg_geom_series /-
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : (1 - x) * ∑' i : ℕ, x ^ i = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_left (1 - x)
@@ -518,12 +605,14 @@ theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : (1 - x) * ∑' i : ℕ,
   ext n
   rw [← mul_neg_geom_sum, Finset.mul_sum]
 #align mul_neg_geom_series mul_neg_geom_series
+-/
 
 end NormedRingGeometric
 
 /-! ### Summability tests based on comparison with geometric series -/
 
 
+#print summable_of_ratio_norm_eventually_le /-
 theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGroup α]
     [CompleteSpace α] {f : ℕ → α} {r : ℝ} (hr₁ : r < 1)
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f :=
@@ -546,7 +635,9 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     by_contra' h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
+-/
 
+#print summable_of_ratio_test_tendsto_lt_one /-
 theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup α] [CompleteSpace α]
     {f : ℕ → α} {l : ℝ} (hl₁ : l < 1) (hf : ∀ᶠ n in atTop, f n ≠ 0)
     (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) : Summable f :=
@@ -556,7 +647,9 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup
   filter_upwards [eventually_le_of_tendsto_lt hr₀ h, hf] with _ _ h₁
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
+-/
 
+#print not_summable_of_ratio_norm_eventually_ge /-
 theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCommGroup α] {f : ℕ → α}
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f :=
@@ -580,7 +673,9 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     convert hN₀ (i + N) (hNN₀.trans (N.le_add_left i)) using 3
     ac_rfl
 #align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_ge
+-/
 
+#print not_summable_of_ratio_test_tendsto_gt_one /-
 theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCommGroup α]
     {f : ℕ → α} {l : ℝ} (hl : 1 < l) (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) :
     ¬Summable f :=
@@ -595,6 +690,7 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCo
   filter_upwards [eventually_ge_of_tendsto_gt hr₁ h, key] with _ _ h₁
   rwa [← le_div_iff (lt_of_le_of_ne (norm_nonneg _) h₁.symm)]
 #align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_one
+-/
 
 section
 
@@ -605,6 +701,7 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
 
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 
+#print Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded /-
 /-- **Dirichlet's Test** for monotone sequences. -/
 theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hgb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -623,7 +720,9 @@ theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone
   · rw [norm_smul, mul_comm]
     exact mul_le_mul_of_nonneg_right (hgb _) (abs_nonneg _)
 #align monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
+-/
 
+#print Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded /-
 /-- **Dirichlet's test** for antitone sequences. -/
 theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hzb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -635,11 +734,15 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
   funext
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
+-/
 
+#print norm_sum_neg_one_pow_le /-
 theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 := by
   rw [neg_one_geom_sum]; split_ifs <;> norm_num
 #align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_le
+-/
 
+#print Monotone.cauchySeq_alternating_series_of_tendsto_zero /-
 /-- The **alternating series test** for monotone sequences.
 See also `tendsto_alternating_series_of_monotone_tendsto_zero`. -/
 theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
@@ -648,14 +751,18 @@ theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
   simp_rw [mul_comm]
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zero
+-/
 
+#print Monotone.tendsto_alternating_series_of_tendsto_zero /-
 /-- The **alternating series test** for monotone sequences. -/
 theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
     ∃ l, Tendsto (fun n => ∑ i in range (n + 1), (-1) ^ i * f i) atTop (𝓝 l) :=
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zero
+-/
 
+#print Antitone.cauchySeq_alternating_series_of_tendsto_zero /-
 /-- The **alternating series test** for antitone sequences.
 See also `tendsto_alternating_series_of_antitone_tendsto_zero`. -/
 theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
@@ -664,13 +771,16 @@ theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
   simp_rw [mul_comm]
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zero
+-/
 
+#print Antitone.tendsto_alternating_series_of_tendsto_zero /-
 /-- The **alternating series test** for antitone sequences. -/
 theorem Antitone.tendsto_alternating_series_of_tendsto_zero (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
     ∃ l, Tendsto (fun n => ∑ i in range (n + 1), (-1) ^ i * f i) atTop (𝓝 l) :=
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align antitone.tendsto_alternating_series_of_tendsto_zero Antitone.tendsto_alternating_series_of_tendsto_zero
+-/
 
 end
 
@@ -679,6 +789,7 @@ end
 -/
 
 
+#print Real.summable_pow_div_factorial /-
 /-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `exp_series_div_summable`
 for a version that also works in `ℂ`, and `exp_series_summable'` for a version that works in
 any normed algebra over `ℝ` or `ℂ`. -/
@@ -699,9 +810,12 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / n !‖ := by
       mono* with 0 ≤ ‖x ^ n / n !‖, 0 ≤ ‖x‖ <;> apply norm_nonneg
 #align real.summable_pow_div_factorial Real.summable_pow_div_factorial
+-/
 
+#print Real.tendsto_pow_div_factorial_atTop /-
 theorem Real.tendsto_pow_div_factorial_atTop (x : ℝ) :
     Tendsto (fun n => x ^ n / n ! : ℕ → ℝ) atTop (𝓝 0) :=
   (Real.summable_pow_div_factorial x).tendsto_atTop_zero
 #align real.tendsto_pow_div_factorial_at_top Real.tendsto_pow_div_factorial_atTop
+-/
 

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

@@ -302,7 +302,7 @@ theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : 
   ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
 
-theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : (∑' n : ℕ, ξ ^ n) = (1 - ξ)⁻¹ :=
+theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
 
@@ -315,7 +315,7 @@ theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n
   summable_geometric_of_norm_lt_1 h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
 
-theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_1 h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
 
@@ -363,9 +363,9 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
   calc
     s = (1 - r) * s / (1 - r) := (mul_div_cancel_left _ (sub_ne_zero.2 hr'.symm)).symm
     _ = (s - r * s) / (1 - r) := by rw [sub_mul, one_mul]
-    _ = (((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1)) - r * s) / (1 - r) := by
+    _ = ((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1) - r * s) / (1 - r) := by
       rw [← tsum_eq_zero_add A]
-    _ = ((r * ∑' n : ℕ, (n + 1) * r ^ n) - r * s) / (1 - r) := by
+    _ = (r * ∑' n : ℕ, (n + 1) * r ^ n - r * s) / (1 - r) := by
       simp [pow_succ, mul_left_comm _ r, tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
@@ -407,7 +407,7 @@ theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖
 distance `C * r ^ n / (1 - r)` of the sum of the series. This lemma does not assume `0 ≤ r` or
 `0 ≤ C`. -/
 theorem norm_sub_le_of_geometric_bound_of_hasSum (hr : r < 1) (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) {a : α}
-    (ha : HasSum f a) (n : ℕ) : ‖(∑ x in Finset.range n, f x) - a‖ ≤ C * r ^ n / (1 - r) :=
+    (ha : HasSum f a) (n : ℕ) : ‖∑ x in Finset.range n, f x - a‖ ≤ C * r ^ n / (1 - r) :=
   by
   rw [← dist_eq_norm]
   apply dist_le_of_le_geometric_of_tendsto r C hr (dist_partial_sum_le_of_le_geometric hf)
@@ -508,7 +508,7 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
 
-theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 :=
+theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : (1 - x) * ∑' i : ℕ, x ^ i = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_left (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _

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

@@ -369,7 +369,6 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
       simp [pow_succ, mul_left_comm _ r, tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
-    
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
@@ -699,7 +698,6 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
         Real.norm_coe_nat, Nat.cast_succ]
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / n !‖ := by
       mono* with 0 ≤ ‖x ^ n / n !‖, 0 ≤ ‖x‖ <;> apply norm_nonneg
-    
 #align real.summable_pow_div_factorial Real.summable_pow_div_factorial
 
 theorem Real.tendsto_pow_div_factorial_atTop (x : ℝ) :

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

@@ -459,7 +459,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
   split_ifs with H H
   · rw [norm_zero]
     exact mul_nonneg hC (pow_nonneg hr₀.le _)
-  · push_neg  at H 
+  · push_neg at H 
     exact h _ H
 #align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''
 
@@ -493,7 +493,7 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   have : ‖∑' b : ℕ, (fun n => x ^ (n + 1)) b‖ ≤ (1 - ‖x‖)⁻¹ - 1 :=
     by
     refine' tsum_of_norm_bounded _ fun b => norm_pow_le' _ (Nat.succ_pos b)
-    convert(hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
+    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
     simp
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
@@ -504,7 +504,7 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (𝓝 1) := by
     simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
-  convert← this
+  convert ← this
   ext n
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
@@ -515,7 +515,7 @@ theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ,
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (nhds 1) := by
     simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
-  convert← this
+  convert ← this
   ext n
   rw [← mul_neg_geom_sum, Finset.mul_sum]
 #align mul_neg_geom_series mul_neg_geom_series
@@ -540,10 +540,10 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     refine' le_geom hr₀ n fun i _ => _
     convert hN (i + N) (N.le_add_left i) using 3
     ac_rfl
-  · push_neg  at hr₀ 
+  · push_neg at hr₀ 
     refine' summable_of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
-    filter_upwards [h]with _ hn
+    filter_upwards [h] with _ hn
     by_contra' h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
@@ -554,7 +554,7 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup
   by
   rcases exists_between hl₁ with ⟨r, hr₀, hr₁⟩
   refine' summable_of_ratio_norm_eventually_le hr₁ _
-  filter_upwards [eventually_le_of_tendsto_lt hr₀ h, hf]with _ _ h₁
+  filter_upwards [eventually_le_of_tendsto_lt hr₀ h, hf] with _ _ h₁
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
 
@@ -588,12 +588,12 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCo
   by
   have key : ∀ᶠ n in at_top, ‖f n‖ ≠ 0 :=
     by
-    filter_upwards [eventually_ge_of_tendsto_gt hl h]with _ hn hc
+    filter_upwards [eventually_ge_of_tendsto_gt hl h] with _ hn hc
     rw [hc, div_zero] at hn 
     linarith
   rcases exists_between hl with ⟨r, hr₀, hr₁⟩
   refine' not_summable_of_ratio_norm_eventually_ge hr₀ key.frequently _
-  filter_upwards [eventually_ge_of_tendsto_gt hr₁ h, key]with _ _ h₁
+  filter_upwards [eventually_ge_of_tendsto_gt hr₁ h, key] with _ _ h₁
   rwa [← le_div_iff (lt_of_le_of_ne (norm_nonneg _) h₁.symm)]
 #align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_one
 
@@ -632,7 +632,7 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
   by
   have hfa' : Monotone fun n => -f n := fun _ _ hab => neg_le_neg <| hfa hab
   have hf0' : tendsto (fun n => -f n) at_top (𝓝 0) := by convert hf0.neg; norm_num
-  convert(hfa'.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
+  convert (hfa'.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
   funext
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded

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

@@ -65,7 +65,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
   rcases neg_surjective m with ⟨m, rfl⟩
-  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
+  rw [neg_lt_zero] at hm ; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm 
   simp only [norm_pow, zpow_neg, zpow_ofNat, ← inv_pow]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
@@ -75,7 +75,7 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
     (hε : Tendsto ε l (𝓝 0)) (hf : Filter.IsBoundedUnder (· ≤ ·) l (norm ∘ f)) :
     Tendsto (ε • f) l (𝓝 0) := by
-  rw [← is_o_one_iff 𝕜] at hε⊢
+  rw [← is_o_one_iff 𝕜] at hε ⊢
   simpa using is_o.smul_is_O hε (hf.is_O_const (one_ne_zero : (1 : 𝕜) ≠ 0))
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
 
@@ -137,7 +137,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     TFAE
       [∃ a ∈ Ioo (-R) R, f =o[atTop] pow a, ∃ a ∈ Ioo 0 R, f =o[atTop] pow a,
         ∃ a ∈ Ioo (-R) R, f =O[atTop] pow a, ∃ a ∈ Ioo 0 R, f =O[atTop] pow a,
-        ∃ a < R, ∃ (C : _)(h₀ : 0 < C ∨ 0 < R), ∀ n, |f n| ≤ C * a ^ n,
+        ∃ a < R, ∃ (C : _) (h₀ : 0 < C ∨ 0 < R), ∀ n, |f n| ≤ C * a ^ n,
         ∃ a ∈ Ioo 0 R, ∃ C > 0, ∀ n, |f n| ≤ C * a ^ n, ∃ a < R, ∀ᶠ n in atTop, |f n| ≤ a ^ n,
         ∃ a ∈ Ioo 0 R, ∀ᶠ n in atTop, |f n| ≤ a ^ n] :=
   by
@@ -168,7 +168,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     rcases sign_cases_of_C_mul_pow_nonneg fun n => (abs_nonneg _).trans (H n) with
       (rfl | ⟨hC₀, ha₀⟩)
     · obtain rfl : f = 0 := by ext n; simpa using H n
-      simp only [lt_irrefl, false_or_iff] at h₀
+      simp only [lt_irrefl, false_or_iff] at h₀ 
       exact ⟨0, ⟨neg_lt_zero.2 h₀, h₀⟩, is_O_zero _ _⟩
     exact
       ⟨a, A ⟨ha₀, ha⟩,
@@ -177,7 +177,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   tfae_have 2 → 8
   · rintro ⟨a, ha, H⟩
     refine' ⟨a, ha, (H.def zero_lt_one).mono fun n hn => _⟩
-    rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn
+    rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn 
   tfae_have 8 → 7; exact fun ⟨a, ha, H⟩ => ⟨a, ha.2, H⟩
   tfae_have 7 → 3
   · rintro ⟨a, ha, H⟩
@@ -220,7 +220,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
   by_cases h0 : r₁ = 0
   · refine' (is_o_zero _ _).congr' (mem_at_top_sets.2 <| ⟨1, fun n hn => _⟩) eventually_eq.rfl
     simp [zero_pow (zero_lt_one.trans_le hn), h0]
-  rw [← Ne.def, ← norm_pos_iff] at h0
+  rw [← Ne.def, ← norm_pos_iff] at h0 
   have A : (fun n => n ^ k : ℕ → R) =o[at_top] fun n => (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n => r₁ ^ n) =O[at_top] fun n => ‖r₁‖ ^ n by
@@ -327,8 +327,8 @@ theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ => ξ ^ n) ↔
   refine' ⟨fun h => _, summable_geometric_of_norm_lt_1⟩
   obtain ⟨k : ℕ, hk : dist (ξ ^ k) 0 < 1⟩ :=
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
-  simp only [norm_pow, dist_zero_right] at hk
-  rw [← one_pow k] at hk
+  simp only [norm_pow, dist_zero_right] at hk 
+  rw [← one_pow k] at hk 
   exact lt_of_pow_lt_pow _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
 
@@ -459,7 +459,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
   split_ifs with H H
   · rw [norm_zero]
     exact mul_nonneg hC (pow_nonneg hr₀.le _)
-  · push_neg  at H
+  · push_neg  at H 
     exact h _ H
 #align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''
 
@@ -530,7 +530,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f :=
   by
   by_cases hr₀ : 0 ≤ r
-  · rw [eventually_at_top] at h
+  · rw [eventually_at_top] at h 
     rcases h with ⟨N, hN⟩
     rw [← @summable_nat_add_iff α _ _ _ _ N]
     refine'
@@ -540,7 +540,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     refine' le_geom hr₀ n fun i _ => _
     convert hN (i + N) (N.le_add_left i) using 3
     ac_rfl
-  · push_neg  at hr₀
+  · push_neg  at hr₀ 
     refine' summable_of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
     filter_upwards [h]with _ hn
@@ -562,9 +562,9 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f :=
   by
-  rw [eventually_at_top] at h
+  rw [eventually_at_top] at h 
   rcases h with ⟨N₀, hN₀⟩
-  rw [frequently_at_top] at hf
+  rw [frequently_at_top] at hf 
   rcases hf N₀ with ⟨N, hNN₀ : N₀ ≤ N, hN⟩
   rw [← @summable_nat_add_iff α _ _ _ _ N]
   refine'
@@ -574,7 +574,7 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
   · refine' lt_of_le_of_ne (norm_nonneg _) _
     intro h''
     specialize hN₀ N hNN₀
-    simp only [comp_app, zero_add] at h''
+    simp only [comp_app, zero_add] at h'' 
     exact hN h''.symm
   · intro i
     dsimp only [comp_app]
@@ -589,7 +589,7 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCo
   have key : ∀ᶠ n in at_top, ‖f n‖ ≠ 0 :=
     by
     filter_upwards [eventually_ge_of_tendsto_gt hl h]with _ hn hc
-    rw [hc, div_zero] at hn
+    rw [hc, div_zero] at hn 
     linarith
   rcases exists_between hl with ⟨r, hr₀, hr₁⟩
   refine' not_summable_of_ratio_norm_eventually_ge hr₀ key.frequently _

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

@@ -29,7 +29,7 @@ noncomputable section
 
 open Classical Set Function Filter Finset Metric Asymptotics
 
-open Classical Topology Nat BigOperators uniformity NNReal ENNReal
+open scoped Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 

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

@@ -33,22 +33,10 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
-/- warning: tendsto_norm_at_top_at_top -> tendsto_norm_atTop_atTop is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Real Real (Norm.norm.{0} Real Real.hasNorm) (Filter.atTop.{0} Real Real.preorder) (Filter.atTop.{0} Real Real.preorder)
-but is expected to have type
-  Filter.Tendsto.{0, 0} Real Real (Norm.norm.{0} Real Real.norm) (Filter.atTop.{0} Real Real.instPreorderReal) (Filter.atTop.{0} Real Real.instPreorderReal)
-Case conversion may be inaccurate. Consider using '#align tendsto_norm_at_top_at_top tendsto_norm_atTop_atTopₓ'. -/
 theorem tendsto_norm_atTop_atTop : Tendsto (norm : ℝ → ℝ) atTop atTop :=
   tendsto_abs_atTop_atTop
 #align tendsto_norm_at_top_at_top tendsto_norm_atTop_atTop
 
-/- warning: summable_of_absolute_convergence_real -> summable_of_absolute_convergence_real is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (Exists.{1} Real (fun (r : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))) -> (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}, (Exists.{1} Real (fun (r : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))) -> (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_of_absolute_convergence_real summable_of_absolute_convergence_realₓ'. -/
 theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     (∃ r, Tendsto (fun n => ∑ i in range n, |f i|) atTop (𝓝 r)) → Summable f
   | ⟨r, hr⟩ =>
@@ -61,12 +49,6 @@ theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
 /-! ### Powers -/
 
 
-/- warning: tendsto_norm_zero' -> tendsto_norm_zero' is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} 𝕜], Filter.Tendsto.{u1, 0} 𝕜 Real (Norm.norm.{u1} 𝕜 (NormedAddCommGroup.toNorm.{u1} 𝕜 _inst_1)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1)))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.instBooleanAlgebraSet.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instSingletonSet.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1))))))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
-Case conversion may be inaccurate. Consider using '#align tendsto_norm_zero' tendsto_norm_zero'ₓ'. -/
 theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
     Tendsto (norm : 𝕜 → ℝ) (𝓝[≠] 0) (𝓝[>] 0) :=
   tendsto_norm_zero.inf <| tendsto_principal_principal.2 fun x hx => norm_pos_iff.2 hx
@@ -74,23 +56,11 @@ theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
 
 namespace NormedField
 
-/- warning: normed_field.tendsto_norm_inverse_nhds_within_0_at_top -> NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTopₓ'. -/
 theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] :
     Tendsto (fun x : 𝕜 => ‖x⁻¹‖) (𝓝[≠] 0) atTop :=
   (tendsto_inv_zero_atTop.comp tendsto_norm_zero').congr fun x => (norm_inv x).symm
 #align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 
-/- warning: normed_field.tendsto_norm_zpow_nhds_within_0_at_top -> NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop is a dubious translation:
-lean 3 declaration is
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-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] {m : Int}, (LT.lt.{0} Int Int.instLTInt m (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Filter.Tendsto.{u1, 0} 𝕜 Real (fun (x : 𝕜) => Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) (HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) x m)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.instBooleanAlgebraSet.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instSingletonSet.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))))) (Filter.atTop.{0} Real Real.instPreorderReal))
-Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTopₓ'. -/
 theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
@@ -100,9 +70,6 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 
-/- warning: normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded -> NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_boundedₓ'. -/
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
 theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [NormedField 𝕜]
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
@@ -112,12 +79,6 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
   simpa using is_o.smul_is_O hε (hf.is_O_const (one_ne_zero : (1 : 𝕜) ≠ 0))
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
 
-/- warning: normed_field.continuous_at_zpow -> NormedField.continuousAt_zpow is a dubious translation:
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-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {m : Int} {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) x m) x) (Or (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) m))
-Case conversion may be inaccurate. Consider using '#align normed_field.continuous_at_zpow NormedField.continuousAt_zpowₓ'. -/
 @[simp]
 theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : ℤ} {x : 𝕜} :
     ContinuousAt (fun x => x ^ m) x ↔ x ≠ 0 ∨ 0 ≤ m :=
@@ -129,12 +90,6 @@ theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : 
       (tendsto_norm_zpow_nhds_within_0_at_top hm)
 #align normed_field.continuous_at_zpow NormedField.continuousAt_zpow
 
-/- warning: normed_field.continuous_at_inv -> NormedField.continuousAt_inv is a dubious translation:
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-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Inv.inv.{u1} 𝕜 (DivInvMonoid.toHasInv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) x) (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))))))
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-  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Inv.inv.{u1} 𝕜 (Field.toInv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) x) (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))
-Case conversion may be inaccurate. Consider using '#align normed_field.continuous_at_inv NormedField.continuousAt_invₓ'. -/
 @[simp]
 theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 𝕜} :
     ContinuousAt Inv.inv x ↔ x ≠ 0 := by
@@ -143,12 +98,6 @@ theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 
 
 end NormedField
 
-/- warning: is_o_pow_pow_of_lt_left -> isLittleO_pow_pow_of_lt_left is a dubious translation:
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-  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r₁) -> (LT.lt.{0} Real Real.instLTReal r₁ r₂) -> (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
-Case conversion may be inaccurate. Consider using '#align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_leftₓ'. -/
 theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ < r₂) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
@@ -157,24 +106,12 @@ theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂
       fun n => div_pow _ _ _
 #align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
 
-/- warning: is_O_pow_pow_of_le_left -> isBigO_pow_pow_of_le_left is a dubious translation:
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-  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r₁) -> (LE.le.{0} Real Real.instLEReal r₁ r₂) -> (Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
-Case conversion may be inaccurate. Consider using '#align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_leftₓ'. -/
 theorem isBigO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
     (fun n : ℕ => r₁ ^ n) =O[atTop] fun n => r₂ ^ n :=
   h₂.eq_or_lt.elim (fun h => h ▸ isBigO_refl _ _) fun h =>
     (isLittleO_pow_pow_of_lt_left h₁ h).IsBigO
 #align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_left
 
-/- warning: is_o_pow_pow_of_abs_lt_left -> isLittleO_pow_pow_of_abs_lt_left is a dubious translation:
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 theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   by
@@ -182,9 +119,6 @@ theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|)
   exact (isLittleO_pow_pow_of_lt_left (abs_nonneg r₁) h).congr (pow_abs r₁) (pow_abs r₂)
 #align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_left
 
-/- warning: tfae_exists_lt_is_o_pow -> TFAE_exists_lt_isLittleO_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_powₓ'. -/
 /-- Various statements equivalent to the fact that `f n` grows exponentially slower than `R ^ n`.
 
 * 0: $f n = o(a ^ n)$ for some $-R < a < R$;
@@ -253,12 +187,6 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   tfae_finish
 #align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_pow
 
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 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
     (hr : 1 < r) : (fun n => n ^ k : ℕ → R) =o[atTop] fun n => r ^ n :=
@@ -278,24 +206,12 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
   simpa [div_eq_inv_mul, Real.norm_eq_abs, abs_of_nonneg h0] using n.cast_le_pow_div_sub h1
 #align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
 
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 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
     (coe : ℕ → R) =o[atTop] fun n => r ^ n := by
   simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
 #align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
 
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 /-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
@@ -312,23 +228,11 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
   exact is_O.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
 #align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
 
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 theorem tendsto_pow_const_div_const_pow_of_one_lt (k : ℕ) {r : ℝ} (hr : 1 < r) :
     Tendsto (fun n => n ^ k / r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   (isLittleO_pow_const_const_pow_of_one_lt k hr).tendsto_div_nhds_zero
 #align tendsto_pow_const_div_const_pow_of_one_lt tendsto_pow_const_div_const_pow_of_one_lt
 
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 /-- If `|r| < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`. -/
 theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n ^ k * r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
@@ -343,12 +247,6 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'
 #align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_one
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_pow_const_mul_const_pow_of_lt_one tendsto_pow_const_mul_const_pow_of_lt_oneₓ'. -/
 /-- If `0 ≤ r < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`.
 This is a specialized version of `tendsto_pow_const_mul_const_pow_of_abs_lt_one`, singled out
 for ease of application. -/
@@ -357,24 +255,12 @@ theorem tendsto_pow_const_mul_const_pow_of_lt_one (k : ℕ) {r : ℝ} (hr : 0 
   tendsto_pow_const_mul_const_pow_of_abs_lt_one k (abs_lt.2 ⟨neg_one_lt_zero.trans_le hr, h'r⟩)
 #align tendsto_pow_const_mul_const_pow_of_lt_one tendsto_pow_const_mul_const_pow_of_lt_one
 
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 /-- If `|r| < 1`, then `n * r ^ n` tends to zero. -/
 theorem tendsto_self_mul_const_pow_of_abs_lt_one {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n * r ^ n : ℕ → ℝ) atTop (𝓝 0) := by
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_abs_lt_one 1 hr
 #align tendsto_self_mul_const_pow_of_abs_lt_one tendsto_self_mul_const_pow_of_abs_lt_one
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_oneₓ'. -/
 /-- If `0 ≤ r < 1`, then `n * r ^ n` tends to zero. This is a specialized version of
 `tendsto_self_mul_const_pow_of_abs_lt_one`, singled out for ease of application. -/
 theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r < 1) :
@@ -382,12 +268,6 @@ theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r <
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_lt_one 1 hr h'r
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1ₓ'. -/
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
 theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
     Tendsto (fun n : ℕ => x ^ n) atTop (𝓝 0) :=
@@ -396,12 +276,6 @@ theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R
   exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
 #align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_0_of_abs_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   tendsto_pow_atTop_nhds_0_of_norm_lt_1 h
@@ -414,12 +288,6 @@ section Geometric
 
 variable {K : Type _} [NormedField K] {ξ : K}
 
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-Case conversion may be inaccurate. Consider using '#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1ₓ'. -/
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
   have xi_ne_one : ξ ≠ 1 := by contrapose! h; simp [h]
@@ -430,63 +298,27 @@ theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ =
   · simp [norm_pow, summable_geometric_of_lt_1 (norm_nonneg _) h]
 #align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1
 
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 theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : ℕ => ξ ^ n :=
   ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
 
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 theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : (∑' n : ℕ, ξ ^ n) = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
 
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 theorem hasSum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   hasSum_geometric_of_norm_lt_1 h
 #align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1
 
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 theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ => r ^ n :=
   summable_geometric_of_norm_lt_1 h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
 
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 theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_1 h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
 
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 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
 @[simp]
@@ -504,12 +336,6 @@ end Geometric
 
 section MulGeometric
 
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 theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ => ‖(n ^ k * r ^ n : R)‖ :=
   by
@@ -519,23 +345,11 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
       (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
 
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-Case conversion may be inaccurate. Consider using '#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
   summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 
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-Case conversion may be inaccurate. Consider using '#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `has_sum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : HasSum (fun n => n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) :=
@@ -558,12 +372,6 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
     
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
 
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-Case conversion may be inaccurate. Consider using '#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
 theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
@@ -576,23 +384,11 @@ section SummableLeGeometric
 
 variable [SeminormedAddCommGroup α] {r C : ℝ} {f : ℕ → α}
 
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-Case conversion may be inaccurate. Consider using '#align seminormed_add_comm_group.cauchy_seq_of_le_geometric SeminormedAddCommGroup.cauchySeq_of_le_geometricₓ'. -/
 theorem SeminormedAddCommGroup.cauchySeq_of_le_geometric {C : ℝ} {r : ℝ} (hr : r < 1) {u : ℕ → α}
     (h : ∀ n, ‖u n - u (n + 1)‖ ≤ C * r ^ n) : CauchySeq u :=
   cauchySeq_of_le_geometric r C hr (by simpa [dist_eq_norm] using h)
 #align seminormed_add_comm_group.cauchy_seq_of_le_geometric SeminormedAddCommGroup.cauchySeq_of_le_geometric
 
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-Case conversion may be inaccurate. Consider using '#align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometricₓ'. -/
 theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) (n : ℕ) :
     dist (∑ i in range n, f i) (∑ i in range (n + 1), f i) ≤ C * r ^ n :=
   by
@@ -600,12 +396,6 @@ theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n
   exact hf n
 #align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometric
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_geometric_bound cauchySeq_finset_of_geometric_boundₓ'. -/
 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` form a
 Cauchy sequence. This lemma does not assume `0 ≤ r` or `0 ≤ C`. -/
 theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) :
@@ -614,12 +404,6 @@ theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖
     (aux_hasSum_of_le_geometric hr (dist_partial_sum_le_of_le_geometric hf)).Summable hf
 #align cauchy_seq_finset_of_geometric_bound cauchySeq_finset_of_geometric_bound
 
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 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` are within
 distance `C * r ^ n / (1 - r)` of the sum of the series. This lemma does not assume `0 ≤ r` or
 `0 ≤ C`. -/
@@ -647,34 +431,16 @@ theorem dist_partial_sum' (u : ℕ → α) (n : ℕ) :
 #align dist_partial_sum' dist_partial_sum'
 -/
 
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 theorem cauchy_series_of_le_geometric {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range n, u k :=
   cauchySeq_of_le_geometric r C hr (by simp [h])
 #align cauchy_series_of_le_geometric cauchy_series_of_le_geometric
 
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 theorem NormedAddCommGroup.cauchy_series_of_le_geometric' {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range (n + 1), u k :=
   (cauchy_series_of_le_geometric hr h).comp_tendsto <| tendsto_add_atTop_nat 1
 #align normed_add_comm_group.cauchy_series_of_le_geometric' NormedAddCommGroup.cauchy_series_of_le_geometric'
 
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-Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''ₓ'. -/
 theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ → α} {N : ℕ} {r : ℝ}
     (hr₀ : 0 < r) (hr₁ : r < 1) (h : ∀ n ≥ N, ‖u n‖ ≤ C * r ^ n) :
     CauchySeq fun n => ∑ k in range (n + 1), u k :=
@@ -705,12 +471,6 @@ variable {R : Type _} [NormedRing R] [CompleteSpace R]
 
 open NormedSpace
 
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-Case conversion may be inaccurate. Consider using '#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1ₓ'. -/
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
 theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -722,12 +482,6 @@ theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   exact eventually_norm_pow_le x
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
 
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-Case conversion may be inaccurate. Consider using '#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1ₓ'. -/
 /-- Bound for the sum of a geometric series in a normed ring.  This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
 theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -744,12 +498,6 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
 
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 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_right (1 - x)
@@ -761,12 +509,6 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
 
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 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_left (1 - x)
@@ -783,12 +525,6 @@ end NormedRingGeometric
 /-! ### Summability tests based on comparison with geometric series -/
 
 
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-Case conversion may be inaccurate. Consider using '#align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_leₓ'. -/
 theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGroup α]
     [CompleteSpace α] {f : ℕ → α} {r : ℝ} (hr₁ : r < 1)
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f :=
@@ -812,12 +548,6 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
 
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-Case conversion may be inaccurate. Consider using '#align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_oneₓ'. -/
 theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup α] [CompleteSpace α]
     {f : ℕ → α} {l : ℝ} (hl₁ : l < 1) (hf : ∀ᶠ n in atTop, f n ≠ 0)
     (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) : Summable f :=
@@ -828,12 +558,6 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
 
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-Case conversion may be inaccurate. Consider using '#align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_geₓ'. -/
 theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCommGroup α] {f : ℕ → α}
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f :=
@@ -858,12 +582,6 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     ac_rfl
 #align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_ge
 
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-Case conversion may be inaccurate. Consider using '#align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_oneₓ'. -/
 theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCommGroup α]
     {f : ℕ → α} {l : ℝ} (hl : 1 < l) (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) :
     ¬Summable f :=
@@ -888,12 +606,6 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
 
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 
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-Case conversion may be inaccurate. Consider using '#align monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Monotone.cauchySeq_series_mul_of_tendsto_zero_of_boundedₓ'. -/
 /-- **Dirichlet's Test** for monotone sequences. -/
 theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hgb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -913,12 +625,6 @@ theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone
     exact mul_le_mul_of_nonneg_right (hgb _) (abs_nonneg _)
 #align monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
 
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-Case conversion may be inaccurate. Consider using '#align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_boundedₓ'. -/
 /-- **Dirichlet's test** for antitone sequences. -/
 theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hzb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -931,22 +637,10 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
 
-/- warning: norm_sum_neg_one_pow_le -> norm_sum_neg_one_pow_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_leₓ'. -/
 theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 := by
   rw [neg_one_geom_sum]; split_ifs <;> norm_num
 #align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_le
 
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-Case conversion may be inaccurate. Consider using '#align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for monotone sequences.
 See also `tendsto_alternating_series_of_monotone_tendsto_zero`. -/
 theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
@@ -956,12 +650,6 @@ theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zero
 
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-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for monotone sequences. -/
 theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
@@ -969,12 +657,6 @@ theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zero
 
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-Case conversion may be inaccurate. Consider using '#align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for antitone sequences.
 See also `tendsto_alternating_series_of_antitone_tendsto_zero`. -/
 theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
@@ -984,12 +666,6 @@ theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zero
 
-/- warning: antitone.tendsto_alternating_series_of_tendsto_zero -> Antitone.tendsto_alternating_series_of_tendsto_zero is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (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 (i : 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)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
-but is expected to have type
-  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
-Case conversion may be inaccurate. Consider using '#align antitone.tendsto_alternating_series_of_tendsto_zero Antitone.tendsto_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for antitone sequences. -/
 theorem Antitone.tendsto_alternating_series_of_tendsto_zero (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
@@ -1004,12 +680,6 @@ end
 -/
 
 
-/- warning: real.summable_pow_div_factorial -> Real.summable_pow_div_factorial is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x n) ((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))) (Nat.factorial n)))
-but is expected to have type
-  forall (x : Real), 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)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x n) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)))
-Case conversion may be inaccurate. Consider using '#align real.summable_pow_div_factorial Real.summable_pow_div_factorialₓ'. -/
 /-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `exp_series_div_summable`
 for a version that also works in `ℂ`, and `exp_series_summable'` for a version that works in
 any normed algebra over `ℝ` or `ℂ`. -/
@@ -1032,12 +702,6 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
     
 #align real.summable_pow_div_factorial Real.summable_pow_div_factorial
 
-/- warning: real.tendsto_pow_div_factorial_at_top -> Real.tendsto_pow_div_factorial_atTop is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x n) ((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))) (Nat.factorial n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall (x : Real), Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x n) (Nat.cast.{0} Real Real.natCast (Nat.factorial n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align real.tendsto_pow_div_factorial_at_top Real.tendsto_pow_div_factorial_atTopₓ'. -/
 theorem Real.tendsto_pow_div_factorial_atTop (x : ℝ) :
     Tendsto (fun n => x ^ n / n ! : ℕ → ℝ) atTop (𝓝 0) :=
   (Real.summable_pow_div_factorial x).tendsto_atTop_zero

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

@@ -211,35 +211,29 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     ⟨(neg_lt_zero.2 (hx.1.trans_lt hx.2)).trans_le hx.1, hx.2⟩
   have B : Ioo 0 R ⊆ Ioo (-R) R := subset.trans Ioo_subset_Ico_self A
   -- First we prove that 1-4 are equivalent using 2 → 3 → 4, 1 → 3, and 2 → 1
-  tfae_have 1 → 3
+  tfae_have 1 → 3;
   exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsBigO⟩
-  tfae_have 2 → 1
-  exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
+  tfae_have 2 → 1; exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
   tfae_have 3 → 2
   · rintro ⟨a, ha, H⟩
     rcases exists_between (abs_lt.2 ha) with ⟨b, hab, hbR⟩
     exact
       ⟨b, ⟨(abs_nonneg a).trans_lt hab, hbR⟩,
         H.trans_is_o (isLittleO_pow_pow_of_abs_lt_left (hab.trans_le (le_abs_self b)))⟩
-  tfae_have 2 → 4
-  exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsBigO⟩
-  tfae_have 4 → 3
-  exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
+  tfae_have 2 → 4; exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsBigO⟩
+  tfae_have 4 → 3; exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
   -- Add 5 and 6 using 4 → 6 → 5 → 3
   tfae_have 4 → 6
   · rintro ⟨a, ha, H⟩
     rcases bound_of_is_O_nat_at_top H with ⟨C, hC₀, hC⟩
     refine' ⟨a, ha, C, hC₀, fun n => _⟩
     simpa only [Real.norm_eq_abs, abs_pow, abs_of_nonneg ha.1.le] using hC (pow_ne_zero n ha.1.ne')
-  tfae_have 6 → 5
-  exact fun ⟨a, ha, C, H₀, H⟩ => ⟨a, ha.2, C, Or.inl H₀, H⟩
+  tfae_have 6 → 5; exact fun ⟨a, ha, C, H₀, H⟩ => ⟨a, ha.2, C, Or.inl H₀, H⟩
   tfae_have 5 → 3
   · rintro ⟨a, ha, C, h₀, H⟩
     rcases sign_cases_of_C_mul_pow_nonneg fun n => (abs_nonneg _).trans (H n) with
       (rfl | ⟨hC₀, ha₀⟩)
-    · obtain rfl : f = 0 := by
-        ext n
-        simpa using H n
+    · obtain rfl : f = 0 := by ext n; simpa using H n
       simp only [lt_irrefl, false_or_iff] at h₀
       exact ⟨0, ⟨neg_lt_zero.2 h₀, h₀⟩, is_O_zero _ _⟩
     exact
@@ -250,8 +244,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   · rintro ⟨a, ha, H⟩
     refine' ⟨a, ha, (H.def zero_lt_one).mono fun n hn => _⟩
     rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn
-  tfae_have 8 → 7
-  exact fun ⟨a, ha, H⟩ => ⟨a, ha.2, H⟩
+  tfae_have 8 → 7; exact fun ⟨a, ha, H⟩ => ⟨a, ha.2, H⟩
   tfae_have 7 → 3
   · rintro ⟨a, ha, H⟩
     have : 0 ≤ a := nonneg_of_eventually_pow_nonneg (H.mono fun n => (abs_nonneg _).trans)
@@ -280,8 +273,7 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
   conv in (r' ^ _) ^ _ => rw [← pow_mul, mul_comm, pow_mul]
   suffices : ∀ n : ℕ, ‖(n : R)‖ ≤ (r' - 1)⁻¹ * ‖(1 : R)‖ * ‖r' ^ n‖
   exact (is_O_of_le' _ this).pow _
-  intro n
-  rw [mul_right_comm]
+  intro n; rw [mul_right_comm]
   refine' n.norm_cast_le.trans (mul_le_mul_of_nonneg_right _ (norm_nonneg _))
   simpa [div_eq_inv_mul, Real.norm_eq_abs, abs_of_nonneg h0] using n.cast_le_pow_div_sub h1
 #align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
@@ -430,9 +422,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1ₓ'. -/
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
-  have xi_ne_one : ξ ≠ 1 := by
-    contrapose! h
-    simp [h]
+  have xi_ne_one : ξ ≠ 1 := by contrapose! h; simp [h]
   have A : tendsto (fun n => (ξ ^ n - 1) * (ξ - 1)⁻¹) at_top (𝓝 ((0 - 1) * (ξ - 1)⁻¹)) :=
     ((tendsto_pow_atTop_nhds_0_of_norm_lt_1 h).sub tendsto_const_nhds).mul tendsto_const_nhds
   rw [hasSum_iff_tendsto_nat_of_summable_norm]
@@ -554,9 +544,7 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
     simpa using summable_pow_mul_geometric_of_norm_lt_1 1 hr
   have B : HasSum (pow r : ℕ → 𝕜) (1 - r)⁻¹ := hasSum_geometric_of_norm_lt_1 hr
   refine' A.has_sum_iff.2 _
-  have hr' : r ≠ 1 := by
-    rintro rfl
-    simpa [lt_irrefl] using hr
+  have hr' : r ≠ 1 := by rintro rfl; simpa [lt_irrefl] using hr
   set s : 𝕜 := ∑' n : ℕ, n * r ^ n
   calc
     s = (1 - r) * s / (1 - r) := (mul_div_cancel_left _ (sub_ne_zero.2 hr'.symm)).symm
@@ -937,10 +925,7 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
     CauchySeq fun n => ∑ i in range (n + 1), f i • z i :=
   by
   have hfa' : Monotone fun n => -f n := fun _ _ hab => neg_le_neg <| hfa hab
-  have hf0' : tendsto (fun n => -f n) at_top (𝓝 0) :=
-    by
-    convert hf0.neg
-    norm_num
+  have hf0' : tendsto (fun n => -f n) at_top (𝓝 0) := by convert hf0.neg; norm_num
   convert(hfa'.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
   funext
   simp
@@ -952,10 +937,8 @@ lean 3 declaration is
 but is expected to have type
   forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} Real Real.norm (Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_leₓ'. -/
-theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 :=
-  by
-  rw [neg_one_geom_sum]
-  split_ifs <;> norm_num
+theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 := by
+  rw [neg_one_geom_sum]; split_ifs <;> norm_num
 #align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_le
 
 /- warning: monotone.cauchy_seq_alternating_series_of_tendsto_zero -> Monotone.cauchySeq_alternating_series_of_tendsto_zero is a dubious translation:

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

@@ -101,10 +101,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 
 /- warning: normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded -> NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {𝕜 : Type.{u2}} {𝔸 : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} 𝔸] [_inst_3 : NormedSpace.{u2, u3} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)] {l : Filter.{u1} ι} {ε : ι -> 𝕜} {f : ι -> 𝔸}, (Filter.Tendsto.{u1, u2} ι 𝕜 ε l (nhds.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))))))))) -> (Filter.IsBoundedUnder.{0, u1} Real ι (LE.le.{0} Real Real.hasLe) l (Function.comp.{succ u1, succ u3, 1} ι 𝔸 Real (Norm.norm.{u3} 𝔸 (NormedAddCommGroup.toHasNorm.{u3} 𝔸 _inst_2)) f)) -> (Filter.Tendsto.{u1, u3} ι 𝔸 (SMul.smul.{max u1 u2, max u1 u3} (ι -> 𝕜) (ι -> 𝔸) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => 𝕜) (fun (ᾰ : ι) => 𝔸) (fun (i : ι) => SMulZeroClass.toHasSmul.{u2, u3} 𝕜 𝔸 (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 𝔸 (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 𝔸 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 𝔸 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2))) (NormedSpace.toModule.{u2, u3} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2) _inst_3)))))) ε f) l (nhds.{u3} 𝔸 (UniformSpace.toTopologicalSpace.{u3} 𝔸 (PseudoMetricSpace.toUniformSpace.{u3} 𝔸 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))) (OfNat.ofNat.{u3} 𝔸 0 (OfNat.mk.{u3} 𝔸 0 (Zero.zero.{u3} 𝔸 (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (SubNegMonoid.toAddMonoid.{u3} 𝔸 (AddGroup.toSubNegMonoid.{u3} 𝔸 (NormedAddGroup.toAddGroup.{u3} 𝔸 (NormedAddCommGroup.toNormedAddGroup.{u3} 𝔸 _inst_2)))))))))))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_boundedₓ'. -/
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
 theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [NormedField 𝕜]
@@ -186,10 +183,7 @@ theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|)
 #align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_left
 
 /- warning: tfae_exists_lt_is_o_pow -> TFAE_exists_lt_isLittleO_pow is a dubious translation:
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-  forall (f : Nat -> Real) (R : Real), List.TFAE (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal R) R)) (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5493 : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5493)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real 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x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5583)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5623 : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5623)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (LT.lt.{0} Real Real.instLTReal a R) (Exists.{1} Real (fun (C : Real) => Exists.{0} (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5666 : Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) => forall (n : Nat), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Exists.{1} Real (fun (C : Real) => And (GT.gt.{0} Real Real.instLTReal C (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (LT.lt.{0} Real Real.instLTReal a R) (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))) (List.nil.{0} Prop)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_powₓ'. -/
 /-- Various statements equivalent to the fact that `f n` grows exponentially slower than `R ^ n`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
 
 ! This file was ported from Lean 3 source module analysis.specific_limits.normed
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.SpecificLimits.Basic
 /-!
 # A collection of specific limit computations
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains important specific limit computations in (semi-)normed groups/rings/spaces, as
 as well as such computations in `ℝ` when the natural proof passes through a fact about normed
 spaces.

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -267,7 +267,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
 Case conversion may be inaccurate. Consider using '#align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_ltₓ'. -/
 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
@@ -293,7 +293,7 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
 Case conversion may be inaccurate. Consider using '#align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_ltₓ'. -/
 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
@@ -305,7 +305,7 @@ theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r₁ : R} {r₂ : Real}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r₁) r₂) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r₁ n)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₂ n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r₁ : R} {r₂ : Real}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r₁) r₂) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r₁ n)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r₁ : R} {r₂ : Real}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r₁) r₂) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r₁ n)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
 Case conversion may be inaccurate. Consider using '#align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_ltₓ'. -/
 /-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
@@ -429,7 +429,7 @@ variable {K : Type _} [NormedField K] {ξ : K}
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSum.{u1, 0} K Nat (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K _inst_1)))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))))))) ξ)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} K Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) ξ)))
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} K Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1))))))) ξ)))
 Case conversion may be inaccurate. Consider using '#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1ₓ'. -/
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
@@ -457,7 +457,7 @@ theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : 
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} K (tsum.{u1, 0} K (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K _inst_1)))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))))))) ξ)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} K (tsum.{u1, 0} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) ξ)))
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} K (tsum.{u1, 0} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1))))))) ξ)))
 Case conversion may be inaccurate. Consider using '#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1ₓ'. -/
 theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : (∑' n : ℕ, ξ ^ n) = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
@@ -521,7 +521,7 @@ section MulGeometric
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : R}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r n))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n))))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n))))
 Case conversion may be inaccurate. Consider using '#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ => ‖(n ^ k * r ^ n : R)‖ :=
@@ -536,7 +536,7 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (k : Nat) {r : R}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r n)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n)))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n)))
 Case conversion may be inaccurate. Consider using '#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
@@ -547,7 +547,7 @@ theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [Com
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSum.{u1, 0} 𝕜 Nat (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat 𝕜 (HasLiftT.mk.{1, succ u1} Nat 𝕜 (CoeTCₓ.coe.{1, succ u1} Nat 𝕜 (Nat.castCoe.{u1} 𝕜 (AddMonoidWithOne.toNatCast.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) r n)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) r) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} 𝕜 Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} 𝕜 Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `has_sum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
@@ -577,7 +577,7 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} 𝕜 (tsum.{u1, 0} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) Nat (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat 𝕜 (HasLiftT.mk.{1, succ u1} Nat 𝕜 (CoeTCₓ.coe.{1, succ u1} Nat 𝕜 (Nat.castCoe.{u1} 𝕜 (AddMonoidWithOne.toNatCast.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) r n))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) r) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} 𝕜 (tsum.{u1, 0} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) Nat (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} 𝕜 (tsum.{u1, 0} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) Nat (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
 Case conversion may be inaccurate. Consider using '#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
 theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
@@ -741,7 +741,7 @@ theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (tsum.{u1, 0} R (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x n))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Inv.inv.{0} Real Real.hasInv (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x n))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Inv.inv.{0} Real Real.instInvReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x)))))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x n))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Inv.inv.{0} Real Real.instInvReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x)))))
 Case conversion may be inaccurate. Consider using '#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1ₓ'. -/
 /-- Bound for the sum of a geometric series in a normed ring.  This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
@@ -763,7 +763,7 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (tsum.{u1, 0} R (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x i)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (NormedAddGroup.toAddGroup.{u1} R (NormedAddCommGroup.toNormedAddGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) x)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align geom_series_mul_neg geom_series_mul_negₓ'. -/
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 :=
   by
@@ -780,7 +780,7 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (NormedAddGroup.toAddGroup.{u1} R (NormedAddCommGroup.toNormedAddGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) x) (tsum.{u1, 0} R (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x i))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mul_neg_geom_series mul_neg_geom_seriesₓ'. -/
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -30,10 +30,22 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
+/- warning: tendsto_norm_at_top_at_top -> tendsto_norm_atTop_atTop is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Real Real (Norm.norm.{0} Real Real.hasNorm) (Filter.atTop.{0} Real Real.preorder) (Filter.atTop.{0} Real Real.preorder)
+but is expected to have type
+  Filter.Tendsto.{0, 0} Real Real (Norm.norm.{0} Real Real.norm) (Filter.atTop.{0} Real Real.instPreorderReal) (Filter.atTop.{0} Real Real.instPreorderReal)
+Case conversion may be inaccurate. Consider using '#align tendsto_norm_at_top_at_top tendsto_norm_atTop_atTopₓ'. -/
 theorem tendsto_norm_atTop_atTop : Tendsto (norm : ℝ → ℝ) atTop atTop :=
   tendsto_abs_atTop_atTop
 #align tendsto_norm_at_top_at_top tendsto_norm_atTop_atTop
 
+/- warning: summable_of_absolute_convergence_real -> summable_of_absolute_convergence_real is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Exists.{1} Real (fun (r : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))) -> (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}, (Exists.{1} Real (fun (r : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))) -> (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_of_absolute_convergence_real summable_of_absolute_convergence_realₓ'. -/
 theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     (∃ r, Tendsto (fun n => ∑ i in range n, |f i|) atTop (𝓝 r)) → Summable f
   | ⟨r, hr⟩ =>
@@ -46,6 +58,12 @@ theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
 /-! ### Powers -/
 
 
+/- warning: tendsto_norm_zero' -> tendsto_norm_zero' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} 𝕜], Filter.Tendsto.{u1, 0} 𝕜 Real (Norm.norm.{u1} 𝕜 (NormedAddCommGroup.toHasNorm.{u1} 𝕜 _inst_1)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 _inst_1))))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.booleanAlgebra.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasSingleton.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 _inst_1)))))))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} 𝕜], Filter.Tendsto.{u1, 0} 𝕜 Real (Norm.norm.{u1} 𝕜 (NormedAddCommGroup.toNorm.{u1} 𝕜 _inst_1)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝕜 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1)))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.instBooleanAlgebraSet.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instSingletonSet.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (NegZeroClass.toZero.{u1} 𝕜 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝕜 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝕜 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝕜 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 _inst_1))))))))))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_norm_zero' tendsto_norm_zero'ₓ'. -/
 theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
     Tendsto (norm : 𝕜 → ℝ) (𝓝[≠] 0) (𝓝[>] 0) :=
   tendsto_norm_zero.inf <| tendsto_principal_principal.2 fun x hx => norm_pos_iff.2 hx
@@ -53,11 +71,23 @@ theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
 
 namespace NormedField
 
+/- warning: normed_field.tendsto_norm_inverse_nhds_within_0_at_top -> NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜], Filter.Tendsto.{u1, 0} 𝕜 Real (fun (x : 𝕜) => Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (Inv.inv.{u1} 𝕜 (DivInvMonoid.toHasInv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1)))) x)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.booleanAlgebra.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasSingleton.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))))) (Filter.atTop.{0} Real Real.preorder)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜], Filter.Tendsto.{u1, 0} 𝕜 Real (fun (x : 𝕜) => Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) (Inv.inv.{u1} 𝕜 (Field.toInv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)) x)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.instBooleanAlgebraSet.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instSingletonSet.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))))) (Filter.atTop.{0} Real Real.instPreorderReal)
+Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTopₓ'. -/
 theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] :
     Tendsto (fun x : 𝕜 => ‖x⁻¹‖) (𝓝[≠] 0) atTop :=
   (tendsto_inv_zero_atTop.comp tendsto_norm_zero').congr fun x => (norm_inv x).symm
 #align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 
+/- warning: normed_field.tendsto_norm_zpow_nhds_within_0_at_top -> NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] {m : Int}, (LT.lt.{0} Int Int.hasLt m (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Filter.Tendsto.{u1, 0} 𝕜 Real (fun (x : 𝕜) => Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) x m)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.booleanAlgebra.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasSingleton.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))))) (Filter.atTop.{0} Real Real.preorder))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] {m : Int}, (LT.lt.{0} Int Int.instLTInt m (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Filter.Tendsto.{u1, 0} 𝕜 Real (fun (x : 𝕜) => Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) (HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) x m)) (nhdsWithin.{u1} 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) (HasCompl.compl.{u1} (Set.{u1} 𝕜) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} 𝕜) (Set.instBooleanAlgebraSet.{u1} 𝕜)) (Singleton.singleton.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instSingletonSet.{u1} 𝕜) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))))) (Filter.atTop.{0} Real Real.instPreorderReal))
+Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTopₓ'. -/
 theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
     Tendsto (fun x : 𝕜 => ‖x ^ m‖) (𝓝[≠] 0) atTop :=
   by
@@ -67,6 +97,12 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
   exact (tendsto_pow_at_top hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 
+/- warning: normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded -> NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {𝕜 : Type.{u2}} {𝔸 : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} 𝔸] [_inst_3 : NormedSpace.{u2, u3} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)] {l : Filter.{u1} ι} {ε : ι -> 𝕜} {f : ι -> 𝔸}, (Filter.Tendsto.{u1, u2} ι 𝕜 ε l (nhds.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))))))))))) -> (Filter.IsBoundedUnder.{0, u1} Real ι (LE.le.{0} Real Real.hasLe) l (Function.comp.{succ u1, succ u3, 1} ι 𝔸 Real (Norm.norm.{u3} 𝔸 (NormedAddCommGroup.toHasNorm.{u3} 𝔸 _inst_2)) f)) -> (Filter.Tendsto.{u1, u3} ι 𝔸 (SMul.smul.{max u1 u2, max u1 u3} (ι -> 𝕜) (ι -> 𝔸) (Pi.smul'.{u1, u2, u3} ι (fun (ᾰ : ι) => 𝕜) (fun (ᾰ : ι) => 𝔸) (fun (i : ι) => SMulZeroClass.toHasSmul.{u2, u3} 𝕜 𝔸 (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕜 𝔸 (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 𝔸 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (AddCommMonoid.toAddMonoid.{u3} 𝔸 (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 𝔸 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝔸 (SeminormedAddCommGroup.toAddCommGroup.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2))) (NormedSpace.toModule.{u2, u3} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2) _inst_3)))))) ε f) l (nhds.{u3} 𝔸 (UniformSpace.toTopologicalSpace.{u3} 𝔸 (PseudoMetricSpace.toUniformSpace.{u3} 𝔸 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} 𝔸 _inst_2)))) (OfNat.ofNat.{u3} 𝔸 0 (OfNat.mk.{u3} 𝔸 0 (Zero.zero.{u3} 𝔸 (AddZeroClass.toHasZero.{u3} 𝔸 (AddMonoid.toAddZeroClass.{u3} 𝔸 (SubNegMonoid.toAddMonoid.{u3} 𝔸 (AddGroup.toSubNegMonoid.{u3} 𝔸 (NormedAddGroup.toAddGroup.{u3} 𝔸 (NormedAddCommGroup.toNormedAddGroup.{u3} 𝔸 _inst_2)))))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {𝕜 : Type.{u2}} {𝔸 : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} 𝔸] [_inst_3 : NormedSpace.{u2, u1} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝔸 _inst_2)] {l : Filter.{u3} ι} {ε : ι -> 𝕜} {f : ι -> 𝔸}, (Filter.Tendsto.{u3, u2} ι 𝕜 ε l (nhds.{u2} 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))))))) -> (Filter.IsBoundedUnder.{0, u3} Real ι (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4948 : Real) (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4950 : Real) => LE.le.{0} Real Real.instLEReal x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4948 x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4950) l (Function.comp.{succ u3, succ u1, 1} ι 𝔸 Real (Norm.norm.{u1} 𝔸 (NormedAddCommGroup.toNorm.{u1} 𝔸 _inst_2)) f)) -> (Filter.Tendsto.{u3, u1} ι 𝔸 (HSMul.hSMul.{max u3 u2, max u3 u1, max u3 u1} (ι -> 𝕜) (ι -> 𝔸) (ι -> 𝔸) (instHSMul.{max u3 u2, max u3 u1} (ι -> 𝕜) (ι -> 𝔸) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4928 : ι) => 𝕜) (fun (a._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.4931 : ι) => 𝔸) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕜 𝔸 (NegZeroClass.toZero.{u1} 𝔸 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝔸 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝔸 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝔸 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝔸 (NormedAddCommGroup.toAddCommGroup.{u1} 𝔸 _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 𝔸 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} 𝔸 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝔸 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝔸 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝔸 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝔸 (NormedAddCommGroup.toAddCommGroup.{u1} 𝔸 _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 𝔸 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} 𝔸 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝔸 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝔸 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝔸 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝔸 (NormedAddCommGroup.toAddCommGroup.{u1} 𝔸 _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 𝔸 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝔸 (NormedAddCommGroup.toAddCommGroup.{u1} 𝔸 _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 𝔸 _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝔸 _inst_2) _inst_3))))))) ε f) l (nhds.{u1} 𝔸 (UniformSpace.toTopologicalSpace.{u1} 𝔸 (PseudoMetricSpace.toUniformSpace.{u1} 𝔸 (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} 𝔸 (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} 𝔸 _inst_2)))) (OfNat.ofNat.{u1} 𝔸 0 (Zero.toOfNat0.{u1} 𝔸 (NegZeroClass.toZero.{u1} 𝔸 (SubNegZeroMonoid.toNegZeroClass.{u1} 𝔸 (SubtractionMonoid.toSubNegZeroMonoid.{u1} 𝔸 (SubtractionCommMonoid.toSubtractionMonoid.{u1} 𝔸 (AddCommGroup.toDivisionAddCommMonoid.{u1} 𝔸 (NormedAddCommGroup.toAddCommGroup.{u1} 𝔸 _inst_2))))))))))
+Case conversion may be inaccurate. Consider using '#align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_boundedₓ'. -/
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
 theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [NormedField 𝕜]
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
@@ -76,6 +112,12 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
   simpa using is_o.smul_is_O hε (hf.is_O_const (one_ne_zero : (1 : 𝕜) ≠ 0))
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
 
+/- warning: normed_field.continuous_at_zpow -> NormedField.continuousAt_zpow is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {m : Int} {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) x m) x) (Or (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))))))) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) m))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {m : Int} {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (fun (x : 𝕜) => HPow.hPow.{u1, 0, u1} 𝕜 Int 𝕜 (instHPow.{u1, 0} 𝕜 Int (DivInvMonoid.Pow.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) x m) x) (Or (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) m))
+Case conversion may be inaccurate. Consider using '#align normed_field.continuous_at_zpow NormedField.continuousAt_zpowₓ'. -/
 @[simp]
 theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : ℤ} {x : 𝕜} :
     ContinuousAt (fun x => x ^ m) x ↔ x ≠ 0 ∨ 0 ≤ m :=
@@ -87,6 +129,12 @@ theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : 
       (tendsto_norm_zpow_nhds_within_0_at_top hm)
 #align normed_field.continuous_at_zpow NormedField.continuousAt_zpow
 
+/- warning: normed_field.continuous_at_inv -> NormedField.continuousAt_inv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Inv.inv.{u1} 𝕜 (DivInvMonoid.toHasInv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) x) (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] {x : 𝕜}, Iff (ContinuousAt.{u1, u1} 𝕜 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Inv.inv.{u1} 𝕜 (Field.toInv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) x) (Ne.{succ u1} 𝕜 x (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align normed_field.continuous_at_inv NormedField.continuousAt_invₓ'. -/
 @[simp]
 theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 𝕜} :
     ContinuousAt Inv.inv x ↔ x ≠ 0 := by
@@ -95,6 +143,12 @@ theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 
 
 end NormedField
 
+/- warning: is_o_pow_pow_of_lt_left -> isLittleO_pow_pow_of_lt_left is a dubious translation:
+lean 3 declaration is
+  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r₁) -> (LT.lt.{0} Real Real.hasLt r₁ r₂) -> (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.hasNorm Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₂ n))
+but is expected to have type
+  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r₁) -> (LT.lt.{0} Real Real.instLTReal r₁ r₂) -> (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
+Case conversion may be inaccurate. Consider using '#align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_leftₓ'. -/
 theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ < r₂) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
@@ -103,12 +157,24 @@ theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂
       fun n => div_pow _ _ _
 #align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
 
+/- warning: is_O_pow_pow_of_le_left -> isBigO_pow_pow_of_le_left is a dubious translation:
+lean 3 declaration is
+  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r₁) -> (LE.le.{0} Real Real.hasLe r₁ r₂) -> (Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.hasNorm Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₂ n))
+but is expected to have type
+  forall {r₁ : Real} {r₂ : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r₁) -> (LE.le.{0} Real Real.instLEReal r₁ r₂) -> (Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
+Case conversion may be inaccurate. Consider using '#align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_leftₓ'. -/
 theorem isBigO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
     (fun n : ℕ => r₁ ^ n) =O[atTop] fun n => r₂ ^ n :=
   h₂.eq_or_lt.elim (fun h => h ▸ isBigO_refl _ _) fun h =>
     (isLittleO_pow_pow_of_lt_left h₁ h).IsBigO
 #align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_left
 
+/- warning: is_o_pow_pow_of_abs_lt_left -> isLittleO_pow_pow_of_abs_lt_left is a dubious translation:
+lean 3 declaration is
+  forall {r₁ : Real} {r₂ : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r₁) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r₂)) -> (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.hasNorm Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₂ n))
+but is expected to have type
+  forall {r₁ : Real} {r₂ : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r₁) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r₂)) -> (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₁ n) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
+Case conversion may be inaccurate. Consider using '#align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_leftₓ'. -/
 theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   by
@@ -116,6 +182,12 @@ theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|)
   exact (isLittleO_pow_pow_of_lt_left (abs_nonneg r₁) h).congr (pow_abs r₁) (pow_abs r₂)
 #align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_left
 
+/- warning: tfae_exists_lt_is_o_pow -> TFAE_exists_lt_isLittleO_pow is a dubious translation:
+lean 3 declaration is
+  forall (f : Nat -> Real) (R : Real), List.TFAE (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg R) R)) (fun (H : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg R) R)) => Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.hasNorm Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} 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Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) (fun (H : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) => Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.hasNorm Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt a R) (fun (H : LT.lt.{0} Real Real.hasLt a R) => Exists.{1} Real (fun (C : Real) => Exists.{0} (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) (fun (h₀ : Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) => forall (n : Nat), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) (fun (H : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) => Exists.{1} Real (fun (C : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt C (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt C (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => forall (n : Nat), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (LT.lt.{0} Real Real.hasLt a R) (fun (H : LT.lt.{0} Real Real.hasLt a R) => Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => Exists.{0} (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) (fun (H : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) a (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) R)) => Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))))) (List.nil.{0} Prop)))))))))
+but is expected to have type
+  forall (f : Nat -> Real) (R : Real), List.TFAE (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal R) R)) (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5493 : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5493)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Asymptotics.IsLittleO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5533 : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5533)))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal R) R)) (Asymptotics.IsBigO.{0, 0, 0} Nat Real Real Real.norm Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5583 : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a 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Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (fun (x._@.Mathlib.Analysis.SpecificLimits.Normed._hyg.5666 : Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) => forall (n : Nat), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Exists.{1} Real (fun (C : Real) => And (GT.gt.{0} Real Real.instLTReal C (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n))))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (LT.lt.{0} Real Real.instLTReal a R) (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))) (List.cons.{0} Prop (Exists.{1} Real (fun (a : Real) => And (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) a (Set.Ioo.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) R)) (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (f n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) a n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))) (List.nil.{0} Prop)))))))))
+Case conversion may be inaccurate. Consider using '#align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_powₓ'. -/
 /-- Various statements equivalent to the fact that `f n` grows exponentially slower than `R ^ n`.
 
 * 0: $f n = o(a ^ n)$ for some $-R < a < R$;
@@ -130,7 +202,7 @@ theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|)
 
 NB: For backwards compatibility, if you add more items to the list, please append them at the end of
 the list. -/
-theorem tFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
+theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     TFAE
       [∃ a ∈ Ioo (-R) R, f =o[atTop] pow a, ∃ a ∈ Ioo 0 R, f =o[atTop] pow a,
         ∃ a ∈ Ioo (-R) R, f =O[atTop] pow a, ∃ a ∈ Ioo 0 R, f =O[atTop] pow a,
@@ -189,8 +261,14 @@ theorem tFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     refine' ⟨a, A ⟨this, ha⟩, is_O.of_bound 1 _⟩
     simpa only [Real.norm_eq_abs, one_mul, abs_pow, abs_of_nonneg this]
   tfae_finish
-#align tfae_exists_lt_is_o_pow tFAE_exists_lt_isLittleO_pow
-
+#align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_pow
+
+/- warning: is_o_pow_const_const_pow_of_one_lt -> isLittleO_pow_const_const_pow_of_one_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
+Case conversion may be inaccurate. Consider using '#align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_ltₓ'. -/
 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
     (hr : 1 < r) : (fun n => n ^ k : ℕ → R) =o[atTop] fun n => r ^ n :=
@@ -211,12 +289,24 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
   simpa [div_eq_inv_mul, Real.norm_eq_abs, abs_of_nonneg h0] using n.cast_le_pow_div_sub h1
 #align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
 
+/- warning: is_o_coe_const_pow_of_one_lt -> isLittleO_coe_const_pow_of_one_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
+Case conversion may be inaccurate. Consider using '#align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_ltₓ'. -/
 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
 theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
     (coe : ℕ → R) =o[atTop] fun n => r ^ n := by
   simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
 #align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
 
+/- warning: is_o_pow_const_mul_const_pow_const_pow_of_norm_lt -> isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r₁ : R} {r₂ : Real}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r₁) r₂) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toHasNorm.{u1} R _inst_1) Real.hasNorm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r₁ n)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r₂ n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r₁ : R} {r₂ : Real}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r₁) r₂) -> (Asymptotics.IsLittleO.{0, u1, 0} Nat R Real (NormedRing.toNorm.{u1} R _inst_1) Real.norm (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r₁ n)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r₂ n))
+Case conversion may be inaccurate. Consider using '#align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_ltₓ'. -/
 /-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
@@ -233,11 +323,23 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Nor
   exact is_O.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
 #align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
 
+/- warning: tendsto_pow_const_div_const_pow_of_one_lt -> tendsto_pow_const_div_const_pow_of_one_lt is a dubious translation:
+lean 3 declaration is
+  forall (k : Nat) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (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) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall (k : Nat) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast n) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_const_div_const_pow_of_one_lt tendsto_pow_const_div_const_pow_of_one_ltₓ'. -/
 theorem tendsto_pow_const_div_const_pow_of_one_lt (k : ℕ) {r : ℝ} (hr : 1 < r) :
     Tendsto (fun n => n ^ k / r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   (isLittleO_pow_const_const_pow_of_one_lt k hr).tendsto_div_nhds_zero
 #align tendsto_pow_const_div_const_pow_of_one_lt tendsto_pow_const_div_const_pow_of_one_lt
 
+/- warning: tendsto_pow_const_mul_const_pow_of_abs_lt_one -> tendsto_pow_const_mul_const_pow_of_abs_lt_one is a dubious translation:
+lean 3 declaration is
+  forall (k : Nat) {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : 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)) ((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) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall (k : Nat) {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast n) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_oneₓ'. -/
 /-- If `|r| < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`. -/
 theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n ^ k * r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
@@ -252,6 +354,12 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'
 #align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_one
 
+/- warning: tendsto_pow_const_mul_const_pow_of_lt_one -> tendsto_pow_const_mul_const_pow_of_lt_one is a dubious translation:
+lean 3 declaration is
+  forall (k : Nat) {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : 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)) ((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) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall (k : Nat) {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Nat.cast.{0} Real Real.natCast n) k) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_const_mul_const_pow_of_lt_one tendsto_pow_const_mul_const_pow_of_lt_oneₓ'. -/
 /-- If `0 ≤ r < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`.
 This is a specialized version of `tendsto_pow_const_mul_const_pow_of_abs_lt_one`, singled out
 for ease of application. -/
@@ -260,12 +368,24 @@ theorem tendsto_pow_const_mul_const_pow_of_lt_one (k : ℕ) {r : ℝ} (hr : 0 
   tendsto_pow_const_mul_const_pow_of_abs_lt_one k (abs_lt.2 ⟨neg_one_lt_zero.trans_le hr, h'r⟩)
 #align tendsto_pow_const_mul_const_pow_of_lt_one tendsto_pow_const_mul_const_pow_of_lt_one
 
+/- warning: tendsto_self_mul_const_pow_of_abs_lt_one -> tendsto_self_mul_const_pow_of_abs_lt_one is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((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) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast n) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_self_mul_const_pow_of_abs_lt_one tendsto_self_mul_const_pow_of_abs_lt_oneₓ'. -/
 /-- If `|r| < 1`, then `n * r ^ n` tends to zero. -/
 theorem tendsto_self_mul_const_pow_of_abs_lt_one {r : ℝ} (hr : |r| < 1) :
     Tendsto (fun n => n * r ^ n : ℕ → ℝ) atTop (𝓝 0) := by
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_abs_lt_one 1 hr
 #align tendsto_self_mul_const_pow_of_abs_lt_one tendsto_self_mul_const_pow_of_abs_lt_one
 
+/- warning: tendsto_self_mul_const_pow_of_lt_one -> tendsto_self_mul_const_pow_of_lt_one is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((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) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast n) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_oneₓ'. -/
 /-- If `0 ≤ r < 1`, then `n * r ^ n` tends to zero. This is a specialized version of
 `tendsto_self_mul_const_pow_of_abs_lt_one`, singled out for ease of application. -/
 theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r < 1) :
@@ -273,6 +393,12 @@ theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r <
   simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_lt_one 1 hr h'r
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
 
+/- warning: tendsto_pow_at_top_nhds_0_of_norm_lt_1 -> tendsto_pow_atTop_nhds_0_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {x : R}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, u1} Nat R (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} R (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] {x : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, u1} Nat R (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} R (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1ₓ'. -/
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
 theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
     Tendsto (fun n : ℕ => x ^ n) atTop (𝓝 0) :=
@@ -281,6 +407,12 @@ theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R
   exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
 #align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1
 
+/- warning: tendsto_pow_at_top_nhds_0_of_abs_lt_1 -> tendsto_pow_atTop_nhds_0_of_abs_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_0_of_abs_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   tendsto_pow_atTop_nhds_0_of_norm_lt_1 h
@@ -293,6 +425,12 @@ section Geometric
 
 variable {K : Type _} [NormedField K] {ξ : K}
 
+/- warning: has_sum_geometric_of_norm_lt_1 -> hasSum_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSum.{u1, 0} K Nat (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K _inst_1)))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))))))) ξ)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} K Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) ξ)))
+Case conversion may be inaccurate. Consider using '#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1ₓ'. -/
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ => ξ ^ n) (1 - ξ)⁻¹ :=
   by
   have xi_ne_one : ξ ≠ 1 := by
@@ -305,27 +443,63 @@ theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ =
   · simp [norm_pow, summable_geometric_of_lt_1 (norm_nonneg _) h]
 #align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1
 
+/- warning: summable_geometric_of_norm_lt_1 -> summable_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{u1, 0} K Nat (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{u1, 0} K Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n))
+Case conversion may be inaccurate. Consider using '#align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : ℕ => ξ ^ n :=
   ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
 
+/- warning: tsum_geometric_of_norm_lt_1 -> tsum_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} K (tsum.{u1, 0} K (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n)) (Inv.inv.{u1} K (DivInvMonoid.toHasInv.{u1} K (DivisionRing.toDivInvMonoid.{u1} K (NormedDivisionRing.toDivisionRing.{u1} K (NormedField.toNormedDivisionRing.{u1} K _inst_1)))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (SubNegMonoid.toHasSub.{u1} K (AddGroup.toSubNegMonoid.{u1} K (NormedAddGroup.toAddGroup.{u1} K (NormedAddCommGroup.toNormedAddGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))))))) ξ)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} K (tsum.{u1, 0} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n)) (Inv.inv.{u1} K (Field.toInv.{u1} K (NormedField.toField.{u1} K _inst_1)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) ξ)))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1ₓ'. -/
 theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : (∑' n : ℕ, ξ ^ n) = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
 
+/- warning: has_sum_geometric_of_abs_lt_1 -> hasSum_geometric_of_abs_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSum.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n) (Inv.inv.{0} Real Real.hasInv (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r)))
+but is expected to have type
+  forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n) (Inv.inv.{0} Real Real.instInvReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r)))
+Case conversion may be inaccurate. Consider using '#align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1ₓ'. -/
 theorem hasSum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   hasSum_geometric_of_norm_lt_1 h
 #align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1
 
+/- warning: summable_geometric_of_abs_lt_1 -> summable_geometric_of_abs_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))
+but is expected to have type
+  forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))
+Case conversion may be inaccurate. Consider using '#align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1ₓ'. -/
 theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ => r ^ n :=
   summable_geometric_of_norm_lt_1 h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
 
+/- warning: tsum_geometric_of_abs_lt_1 -> tsum_geometric_of_abs_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{1} Real (tsum.{0, 0} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (Inv.inv.{0} Real Real.hasInv (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r)))
+but is expected to have type
+  forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{1} Real (tsum.{0, 0} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (Inv.inv.{0} Real Real.instInvReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r)))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1ₓ'. -/
 theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_1 h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
 
+/- warning: summable_geometric_iff_norm_lt_1 -> summable_geometric_iff_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, Iff (Summable.{u1, 0} K Nat (AddCommGroup.toAddCommMonoid.{u1} K (NormedAddCommGroup.toAddCommGroup.{u1} K (NonUnitalNormedRing.toNormedAddCommGroup.{u1} K (NormedRing.toNonUnitalNormedRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSemiNormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) ξ n)) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} K (NormedField.toHasNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : NormedField.{u1} K] {ξ : K}, Iff (Summable.{u1, 0} K Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (NormedRing.toRing.{u1} K (NormedCommRing.toNormedRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} K (PseudoMetricSpace.toUniformSpace.{u1} K (SeminormedRing.toPseudoMetricSpace.{u1} K (SeminormedCommRing.toSeminormedRing.{u1} K (NormedCommRing.toSeminormedCommRing.{u1} K (NormedField.toNormedCommRing.{u1} K _inst_1)))))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K (NormedField.toField.{u1} K _inst_1)))))))) ξ n)) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} K (NormedField.toNorm.{u1} K _inst_1) ξ) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1ₓ'. -/
 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
 @[simp]
@@ -343,6 +517,12 @@ end Geometric
 
 section MulGeometric
 
+/- warning: summable_norm_pow_mul_geometric_of_norm_lt_1 -> summable_norm_pow_mul_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : R}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r n))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n))))
+Case conversion may be inaccurate. Consider using '#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ => ‖(n ^ k * r ^ n : R)‖ :=
   by
@@ -352,11 +532,23 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
       (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
 
+/- warning: summable_pow_mul_geometric_of_norm_lt_1 -> summable_pow_mul_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (k : Nat) {r : R}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) r n)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (k : Nat) {r : R}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))) n) k) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) r n)))
+Case conversion may be inaccurate. Consider using '#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1ₓ'. -/
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n => n ^ k * r ^ n : ℕ → R) :=
   summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 
+/- warning: has_sum_coe_mul_geometric_of_norm_lt_1 -> hasSum_coe_mul_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSum.{u1, 0} 𝕜 Nat (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat 𝕜 (HasLiftT.mk.{1, succ u1} Nat 𝕜 (CoeTCₓ.coe.{1, succ u1} Nat 𝕜 (Nat.castCoe.{u1} 𝕜 (AddMonoidWithOne.toNatCast.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) r n)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) r) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSum.{u1, 0} 𝕜 Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `has_sum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : HasSum (fun n => n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) :=
@@ -381,6 +573,12 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
     
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
 
+/- warning: tsum_coe_mul_geometric_of_norm_lt_1 -> tsum_coe_mul_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} 𝕜 (tsum.{u1, 0} 𝕜 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) Nat (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat 𝕜 (HasLiftT.mk.{1, succ u1} Nat 𝕜 (CoeTCₓ.coe.{1, succ u1} Nat 𝕜 (Nat.castCoe.{u1} 𝕜 (AddMonoidWithOne.toNatCast.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) r n))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 _inst_1))))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))) r) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : CompleteSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} 𝕜 (tsum.{u1, 0} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) Nat (fun (n : Nat) => HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) n) (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) r n))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (Field.toDiv.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) r (HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) r) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1ₓ'. -/
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
 theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
@@ -393,11 +591,23 @@ section SummableLeGeometric
 
 variable [SeminormedAddCommGroup α] {r C : ℝ} {f : ℕ → α}
 
+/- warning: seminormed_add_comm_group.cauchy_seq_of_le_geometric -> SeminormedAddCommGroup.cauchySeq_of_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall {u : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α _inst_1))))) (u n) (u (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))))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) u))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {u : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α _inst_1))))) (u n) (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) u))
+Case conversion may be inaccurate. Consider using '#align seminormed_add_comm_group.cauchy_seq_of_le_geometric SeminormedAddCommGroup.cauchySeq_of_le_geometricₓ'. -/
 theorem SeminormedAddCommGroup.cauchySeq_of_le_geometric {C : ℝ} {r : ℝ} (hr : r < 1) {u : ℕ → α}
     (h : ∀ n, ‖u n - u (n + 1)‖ ≤ C * r ^ n) : CauchySeq u :=
   cauchySeq_of_le_geometric r C hr (by simpa [dist_eq_norm] using h)
 #align seminormed_add_comm_group.cauchy_seq_of_le_geometric SeminormedAddCommGroup.cauchySeq_of_le_geometric
 
+/- warning: dist_partial_sum_le_of_le_geometric -> dist_partial_sum_le_of_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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 (i : Nat) => f i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (i : Nat) => f i)) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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 (i : Nat) => f i))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)))
+Case conversion may be inaccurate. Consider using '#align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometricₓ'. -/
 theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) (n : ℕ) :
     dist (∑ i in range n, f i) (∑ i in range (n + 1), f i) ≤ C * r ^ n :=
   by
@@ -405,6 +615,12 @@ theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n
   exact hf n
 #align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometric
 
+/- warning: cauchy_seq_finset_of_geometric_bound -> cauchySeq_finset_of_geometric_bound is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (CauchySeq.{u1, 0} α (Finset.{0} Nat) (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} (Finset.{0} Nat) (Finset.lattice.{0} Nat (fun (a : Nat) (b : Nat) => Nat.decidableEq a b))) (fun (s : Finset.{0} Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) s (fun (x : Nat) => f x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (CauchySeq.{u1, 0} α (Finset.{0} Nat) (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} (Finset.{0} Nat) (Finset.instLatticeFinset.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b))) (fun (s : Finset.{0} Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) s (fun (x : Nat) => f x)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_geometric_bound cauchySeq_finset_of_geometric_boundₓ'. -/
 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` form a
 Cauchy sequence. This lemma does not assume `0 ≤ r` or `0 ≤ C`. -/
 theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) :
@@ -413,6 +629,12 @@ theorem cauchySeq_finset_of_geometric_bound (hr : r < 1) (hf : ∀ n, ‖f n‖
     (aux_hasSum_of_le_geometric hr (dist_partial_sum_le_of_le_geometric hf)).Summable hf
 #align cauchy_seq_finset_of_geometric_bound cauchySeq_finset_of_geometric_bound
 
+/- warning: norm_sub_le_of_geometric_bound_of_has_sum -> norm_sub_le_of_geometric_bound_of_hasSum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (forall {a : α}, (HasSum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f a) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α _inst_1))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (x : Nat) => f x)) a)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {r : Real} {C : Real} {f : Nat -> α}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (forall {a : α}, (HasSum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f a) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (SeminormedAddGroup.toAddGroup.{u1} α (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} α _inst_1))))) (Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (x : Nat) => f x)) a)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r))))
+Case conversion may be inaccurate. Consider using '#align norm_sub_le_of_geometric_bound_of_has_sum norm_sub_le_of_geometric_bound_of_hasSumₓ'. -/
 /-- If `‖f n‖ ≤ C * r ^ n` for all `n : ℕ` and some `r < 1`, then the partial sums of `f` are within
 distance `C * r ^ n / (1 - r)` of the sum of the series. This lemma does not assume `0 ≤ r` or
 `0 ≤ C`. -/
@@ -424,28 +646,50 @@ theorem norm_sub_le_of_geometric_bound_of_hasSum (hr : r < 1) (hf : ∀ n, ‖f
   exact ha.tendsto_sum_nat
 #align norm_sub_le_of_geometric_bound_of_has_sum norm_sub_le_of_geometric_bound_of_hasSum
 
+#print dist_partial_sum /-
 @[simp]
 theorem dist_partial_sum (u : ℕ → α) (n : ℕ) :
     dist (∑ k in range (n + 1), u k) (∑ k in range n, u k) = ‖u n‖ := by
   simp [dist_eq_norm, sum_range_succ]
 #align dist_partial_sum dist_partial_sum
+-/
 
+#print dist_partial_sum' /-
 @[simp]
 theorem dist_partial_sum' (u : ℕ → α) (n : ℕ) :
     dist (∑ k in range n, u k) (∑ k in range (n + 1), u k) = ‖u n‖ := by
   simp [dist_eq_norm', sum_range_succ]
 #align dist_partial_sum' dist_partial_sum'
+-/
 
+/- warning: cauchy_series_of_le_geometric -> cauchy_series_of_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (k : Nat) => u k)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (Finset.range n) (fun (k : Nat) => u k)))
+Case conversion may be inaccurate. Consider using '#align cauchy_series_of_le_geometric cauchy_series_of_le_geometricₓ'. -/
 theorem cauchy_series_of_le_geometric {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range n, u k :=
   cauchySeq_of_le_geometric r C hr (by simp [h])
 #align cauchy_series_of_le_geometric cauchy_series_of_le_geometric
 
+/- warning: normed_add_comm_group.cauchy_series_of_le_geometric' -> NormedAddCommGroup.cauchy_series_of_le_geometric' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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) => u k)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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) => u k)))
+Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.cauchy_series_of_le_geometric' NormedAddCommGroup.cauchy_series_of_le_geometric'ₓ'. -/
 theorem NormedAddCommGroup.cauchy_series_of_le_geometric' {C : ℝ} {u : ℕ → α} {r : ℝ} (hr : r < 1)
     (h : ∀ n, ‖u n‖ ≤ C * r ^ n) : CauchySeq fun n => ∑ k in range (n + 1), u k :=
   (cauchy_series_of_le_geometric hr h).comp_tendsto <| tendsto_add_atTop_nat 1
 #align normed_add_comm_group.cauchy_series_of_le_geometric' NormedAddCommGroup.cauchy_series_of_le_geometric'
 
+/- warning: normed_add_comm_group.cauchy_series_of_le_geometric'' -> NormedAddCommGroup.cauchy_series_of_le_geometric'' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {N : Nat} {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall (n : Nat), (GE.ge.{0} Nat Nat.hasLe n N) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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) => u k)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {C : Real} {u : Nat -> α} {N : Nat} {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall (n : Nat), (GE.ge.{0} Nat instLENat n N) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (u n)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _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) => u k)))
+Case conversion may be inaccurate. Consider using '#align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''ₓ'. -/
 theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ → α} {N : ℕ} {r : ℝ}
     (hr₀ : 0 < r) (hr₁ : r < 1) (h : ∀ n ≥ N, ‖u n‖ ≤ C * r ^ n) :
     CauchySeq fun n => ∑ k in range (n + 1), u k :=
@@ -476,6 +720,12 @@ variable {R : Type _} [NormedRing R] [CompleteSpace R]
 
 open NormedSpace
 
+/- warning: normed_ring.summable_geometric_of_norm_lt_1 -> NormedRing.summable_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Summable.{u1, 0} R Nat (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Summable.{u1, 0} R Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x n))
+Case conversion may be inaccurate. Consider using '#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1ₓ'. -/
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
 theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -487,6 +737,12 @@ theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   exact eventually_norm_pow_le x
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
 
+/- warning: normed_ring.tsum_geometric_of_norm_lt_1 -> NormedRing.tsum_geometric_of_norm_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (tsum.{u1, 0} R (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x n))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Inv.inv.{0} Real Real.hasInv (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (n : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x n))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Inv.inv.{0} Real Real.instInvReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x)))))
+Case conversion may be inaccurate. Consider using '#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1ₓ'. -/
 /-- Bound for the sum of a geometric series in a normed ring.  This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
 theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
@@ -503,6 +759,12 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
 
+/- warning: geom_series_mul_neg -> geom_series_mul_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (NormedRing.toHasNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) (tsum.{u1, 0} R (AddCommGroup.toAddCommMonoid.{u1} R (NormedAddCommGroup.toAddCommGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1)))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (NormedRing.toRing.{u1} R _inst_1)))) x i)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (NormedAddGroup.toAddGroup.{u1} R (NormedAddCommGroup.toNormedAddGroup.{u1} R (NonUnitalNormedRing.toNormedAddCommGroup.{u1} R (NormedRing.toNonUnitalNormedRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))) x)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))))))
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+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align geom_series_mul_neg geom_series_mul_negₓ'. -/
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_right (1 - x)
@@ -514,6 +776,12 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
 
+/- warning: mul_neg_geom_series -> mul_neg_geom_series is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : NormedRing.{u1} R] [_inst_2 : CompleteSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))] (x : R), (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (NormedRing.toNorm.{u1} R _inst_1) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (NormedRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) x) (tsum.{u1, 0} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))) (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (NormedRing.toSeminormedRing.{u1} R _inst_1)))) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R _inst_1)))))) x i))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align mul_neg_geom_series mul_neg_geom_seriesₓ'. -/
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 :=
   by
   have := (NormedRing.summable_geometric_of_norm_lt_1 x h).HasSum.mul_left (1 - x)
@@ -530,6 +798,12 @@ end NormedRingGeometric
 /-! ### Summability tests based on comparison with geometric series -/
 
 
+/- warning: summable_of_ratio_norm_eventually_le -> summable_of_ratio_norm_eventually_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] [_inst_2 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))] {f : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f (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)))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) -> (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] [_inst_2 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))] {f : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) -> (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_leₓ'. -/
 theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGroup α]
     [CompleteSpace α] {f : ℕ → α} {r : ℝ} (hr₁ : r < 1)
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f :=
@@ -553,6 +827,12 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
 
+/- warning: summable_of_ratio_test_tendsto_lt_one -> summable_of_ratio_test_tendsto_lt_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] [_inst_2 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))] {f : Nat -> α} {l : Real}, (LT.lt.{0} Real Real.hasLt l (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => Ne.{succ u1} α (f n) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (NormedAddGroup.toAddGroup.{u1} α (NormedAddCommGroup.toNormedAddGroup.{u1} α _inst_1)))))))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Norm.norm.{u1} α (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f (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)))))) (Norm.norm.{u1} α (NormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} α] [_inst_2 : CompleteSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))] {f : Nat -> α} {l : Real}, (LT.lt.{0} Real Real.instLTReal l (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => Ne.{succ u1} α (f n) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Norm.norm.{u1} α (NormedAddCommGroup.toNorm.{u1} α _inst_1) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Norm.norm.{u1} α (NormedAddCommGroup.toNorm.{u1} α _inst_1) (f n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (NormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} α _inst_1)))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_oneₓ'. -/
 theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup α] [CompleteSpace α]
     {f : ℕ → α} {l : ℝ} (hl₁ : l < 1) (hf : ∀ᶠ n in atTop, f n ≠ 0)
     (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) : Summable f :=
@@ -563,6 +843,12 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
 
+/- warning: not_summable_of_ratio_norm_eventually_ge -> not_summable_of_ratio_norm_eventually_ge is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {f : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) r) -> (Filter.Frequently.{0} Nat (fun (n : Nat) => Ne.{1} Real (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n))) (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f (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))))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) -> (Not (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {f : Nat -> α} {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) r) -> (Filter.Frequently.{0} Nat (fun (n : Nat) => Ne.{1} Real (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) -> (Filter.Eventually.{0} Nat (fun (n : Nat) => LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n))) (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) -> (Not (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f))
+Case conversion may be inaccurate. Consider using '#align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_geₓ'. -/
 theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCommGroup α] {f : ℕ → α}
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f :=
@@ -587,6 +873,12 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     ac_rfl
 #align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_ge
 
+/- warning: not_summable_of_ratio_test_tendsto_gt_one -> not_summable_of_ratio_test_tendsto_gt_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {f : Nat -> α} {l : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) l) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f (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)))))) (Norm.norm.{u1} α (SeminormedAddCommGroup.toHasNorm.{u1} α _inst_1) (f n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Not (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} α] {f : Nat -> α} {l : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) l) -> (Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Norm.norm.{u1} α (SeminormedAddCommGroup.toNorm.{u1} α _inst_1) (f n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)) -> (Not (Summable.{u1, 0} α Nat (AddCommGroup.toAddCommMonoid.{u1} α (SeminormedAddCommGroup.toAddCommGroup.{u1} α _inst_1)) (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} α _inst_1))) f))
+Case conversion may be inaccurate. Consider using '#align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_oneₓ'. -/
 theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCommGroup α]
     {f : ℕ → α} {l : ℝ} (hl : 1 < l) (h : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) :
     ¬Summable f :=
@@ -611,6 +903,12 @@ variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
 
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 
+/- warning: monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded -> Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {b : Real} {f : Nat -> Real} {z : Nat -> E}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} E (NormedAddCommGroup.toHasNorm.{u1} E _inst_1) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => z i))) b) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _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 (i : Nat) => SMul.smul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (f i) (z i))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {b : Real} {f : Nat -> Real} {z : Nat -> E}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (NormedAddCommGroup.toNorm.{u1} E _inst_1) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => z i))) b) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _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 (i : Nat) => HSMul.hSMul.{0, u1, u1} Real E E (instHSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)))))) (f i) (z i))))
+Case conversion may be inaccurate. Consider using '#align monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Monotone.cauchySeq_series_mul_of_tendsto_zero_of_boundedₓ'. -/
 /-- **Dirichlet's Test** for monotone sequences. -/
 theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hgb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -630,6 +928,12 @@ theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone
     exact mul_le_mul_of_nonneg_right (hgb _) (abs_nonneg _)
 #align monotone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
 
+/- warning: antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded -> Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {b : Real} {f : Nat -> Real} {z : Nat -> E}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} E (NormedAddCommGroup.toHasNorm.{u1} E _inst_1) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => z i))) b) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _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 (i : Nat) => SMul.smul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E (Ring.toSemiring.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2))))) (f i) (z i))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] {b : Real} {f : Nat -> Real} {z : Nat -> E}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (NormedAddCommGroup.toNorm.{u1} E _inst_1) (Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => z i))) b) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1))) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _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 (i : Nat) => HSMul.hSMul.{0, u1, u1} Real E E (instHSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)))))) (f i) (z i))))
+Case conversion may be inaccurate. Consider using '#align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_boundedₓ'. -/
 /-- **Dirichlet's test** for antitone sequences. -/
 theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hzb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
@@ -645,12 +949,24 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
 
+/- warning: norm_sum_neg_one_pow_le -> norm_sum_neg_one_pow_le is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{0} Real Real.hasNorm (Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall (n : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{0} Real Real.norm (Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_leₓ'. -/
 theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 :=
   by
   rw [neg_one_geom_sum]
   split_ifs <;> norm_num
 #align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_le
 
+/- warning: monotone.cauchy_seq_alternating_series_of_tendsto_zero -> Monotone.cauchySeq_alternating_series_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (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 (i : 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)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i) (f i))))
+but is expected to have type
+  forall {f : Nat -> Real}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i) (f i))))
+Case conversion may be inaccurate. Consider using '#align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for monotone sequences.
 See also `tendsto_alternating_series_of_monotone_tendsto_zero`. -/
 theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
@@ -660,6 +976,12 @@ theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zero
 
+/- warning: monotone.tendsto_alternating_series_of_tendsto_zero -> Monotone.tendsto_alternating_series_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (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 (i : 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)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
+but is expected to have type
+  forall {f : Nat -> Real}, (Monotone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
+Case conversion may be inaccurate. Consider using '#align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for monotone sequences. -/
 theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
@@ -667,6 +989,12 @@ theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zero
 
+/- warning: antitone.cauchy_seq_alternating_series_of_tendsto_zero -> Antitone.cauchySeq_alternating_series_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (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 (i : 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)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i) (f i))))
+but is expected to have type
+  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i) (f i))))
+Case conversion may be inaccurate. Consider using '#align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for antitone sequences.
 See also `tendsto_alternating_series_of_antitone_tendsto_zero`. -/
 theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
@@ -676,6 +1004,12 @@ theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
   exact hfa.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zero
 
+/- warning: antitone.tendsto_alternating_series_of_tendsto_zero -> Antitone.tendsto_alternating_series_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Real.preorder f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (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 (i : 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)) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
+but is expected to have type
+  forall {f : Nat -> Real}, (Antitone.{0, 0} Nat Real (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) Real.instPreorderReal f) -> (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Exists.{1} Real (fun (l : Real) => Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Neg.neg.{0} Real Real.instNegReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) i) (f i))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) l)))
+Case conversion may be inaccurate. Consider using '#align antitone.tendsto_alternating_series_of_tendsto_zero Antitone.tendsto_alternating_series_of_tendsto_zeroₓ'. -/
 /-- The **alternating series test** for antitone sequences. -/
 theorem Antitone.tendsto_alternating_series_of_tendsto_zero (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
@@ -690,6 +1024,12 @@ end
 -/
 
 
+/- warning: real.summable_pow_div_factorial -> Real.summable_pow_div_factorial is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), 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))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x n) ((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))) (Nat.factorial n)))
+but is expected to have type
+  forall (x : Real), 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)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x n) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)))
+Case conversion may be inaccurate. Consider using '#align real.summable_pow_div_factorial Real.summable_pow_div_factorialₓ'. -/
 /-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `exp_series_div_summable`
 for a version that also works in `ℂ`, and `exp_series_summable'` for a version that works in
 any normed algebra over `ℝ` or `ℂ`. -/
@@ -712,6 +1052,12 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n => x ^ n / n
     
 #align real.summable_pow_div_factorial Real.summable_pow_div_factorial
 
+/- warning: real.tendsto_pow_div_factorial_at_top -> Real.tendsto_pow_div_factorial_atTop is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x n) ((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))) (Nat.factorial n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall (x : Real), Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x n) (Nat.cast.{0} Real Real.natCast (Nat.factorial n))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align real.tendsto_pow_div_factorial_at_top Real.tendsto_pow_div_factorial_atTopₓ'. -/
 theorem Real.tendsto_pow_div_factorial_atTop (x : ℝ) :
     Tendsto (fun n => x ^ n / n ! : ℕ → ℝ) atTop (𝓝 0) :=
   (Real.summable_pow_div_factorial x).tendsto_atTop_zero

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

@@ -95,25 +95,26 @@ theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 
 
 end NormedField
 
-theorem isOCat_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ < r₂) :
+theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ < r₂) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
-  (isOCat_of_tendsto fun n hn => False.elim <| H.ne' <| pow_eq_zero hn) <|
+  (isLittleO_of_tendsto fun n hn => False.elim <| H.ne' <| pow_eq_zero hn) <|
     (tendsto_pow_atTop_nhds_0_of_lt_1 (div_nonneg h₁ (h₁.trans h₂.le)) ((div_lt_one H).2 h₂)).congr
       fun n => div_pow _ _ _
-#align is_o_pow_pow_of_lt_left isOCat_pow_pow_of_lt_left
+#align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
 
-theorem isO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
+theorem isBigO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
     (fun n : ℕ => r₁ ^ n) =O[atTop] fun n => r₂ ^ n :=
-  h₂.eq_or_lt.elim (fun h => h ▸ isO_refl _ _) fun h => (isOCat_pow_pow_of_lt_left h₁ h).IsO
-#align is_O_pow_pow_of_le_left isO_pow_pow_of_le_left
+  h₂.eq_or_lt.elim (fun h => h ▸ isBigO_refl _ _) fun h =>
+    (isLittleO_pow_pow_of_lt_left h₁ h).IsBigO
+#align is_O_pow_pow_of_le_left isBigO_pow_pow_of_le_left
 
-theorem isOCat_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
+theorem isLittleO_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
     (fun n : ℕ => r₁ ^ n) =o[atTop] fun n => r₂ ^ n :=
   by
   refine' (is_o.of_norm_left _).of_norm_right
-  exact (isOCat_pow_pow_of_lt_left (abs_nonneg r₁) h).congr (pow_abs r₁) (pow_abs r₂)
-#align is_o_pow_pow_of_abs_lt_left isOCat_pow_pow_of_abs_lt_left
+  exact (isLittleO_pow_pow_of_lt_left (abs_nonneg r₁) h).congr (pow_abs r₁) (pow_abs r₂)
+#align is_o_pow_pow_of_abs_lt_left isLittleO_pow_pow_of_abs_lt_left
 
 /-- Various statements equivalent to the fact that `f n` grows exponentially slower than `R ^ n`.
 
@@ -129,7 +130,7 @@ theorem isOCat_pow_pow_of_abs_lt_left {r₁ r₂ : ℝ} (h : |r₁| < |r₂|) :
 
 NB: For backwards compatibility, if you add more items to the list, please append them at the end of
 the list. -/
-theorem tFAE_exists_lt_isOCat_pow (f : ℕ → ℝ) (R : ℝ) :
+theorem tFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     TFAE
       [∃ a ∈ Ioo (-R) R, f =o[atTop] pow a, ∃ a ∈ Ioo 0 R, f =o[atTop] pow a,
         ∃ a ∈ Ioo (-R) R, f =O[atTop] pow a, ∃ a ∈ Ioo 0 R, f =O[atTop] pow a,
@@ -142,7 +143,7 @@ theorem tFAE_exists_lt_isOCat_pow (f : ℕ → ℝ) (R : ℝ) :
   have B : Ioo 0 R ⊆ Ioo (-R) R := subset.trans Ioo_subset_Ico_self A
   -- First we prove that 1-4 are equivalent using 2 → 3 → 4, 1 → 3, and 2 → 1
   tfae_have 1 → 3
-  exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsO⟩
+  exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsBigO⟩
   tfae_have 2 → 1
   exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
   tfae_have 3 → 2
@@ -150,9 +151,9 @@ theorem tFAE_exists_lt_isOCat_pow (f : ℕ → ℝ) (R : ℝ) :
     rcases exists_between (abs_lt.2 ha) with ⟨b, hab, hbR⟩
     exact
       ⟨b, ⟨(abs_nonneg a).trans_lt hab, hbR⟩,
-        H.trans_is_o (isOCat_pow_pow_of_abs_lt_left (hab.trans_le (le_abs_self b)))⟩
+        H.trans_is_o (isLittleO_pow_pow_of_abs_lt_left (hab.trans_le (le_abs_self b)))⟩
   tfae_have 2 → 4
-  exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsO⟩
+  exact fun ⟨a, ha, H⟩ => ⟨a, ha, H.IsBigO⟩
   tfae_have 4 → 3
   exact fun ⟨a, ha, H⟩ => ⟨a, B ha, H⟩
   -- Add 5 and 6 using 4 → 6 → 5 → 3
@@ -188,10 +189,10 @@ theorem tFAE_exists_lt_isOCat_pow (f : ℕ → ℝ) (R : ℝ) :
     refine' ⟨a, A ⟨this, ha⟩, is_O.of_bound 1 _⟩
     simpa only [Real.norm_eq_abs, one_mul, abs_pow, abs_of_nonneg this]
   tfae_finish
-#align tfae_exists_lt_is_o_pow tFAE_exists_lt_isOCat_pow
+#align tfae_exists_lt_is_o_pow tFAE_exists_lt_isLittleO_pow
 
 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
-theorem isOCat_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
+theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
     (hr : 1 < r) : (fun n => n ^ k : ℕ → R) =o[atTop] fun n => r ^ n :=
   by
   have : tendsto (fun x : ℝ => x ^ k) (𝓝[>] 1) (𝓝 1) :=
@@ -200,7 +201,7 @@ theorem isOCat_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : 
     ((this.eventually (gt_mem_nhds hr)).And self_mem_nhdsWithin).exists
   have h0 : 0 ≤ r' := zero_le_one.trans h1.le
   suffices : (fun n => n ^ k : ℕ → R) =O[at_top] fun n : ℕ => (r' ^ k) ^ n
-  exact this.trans_is_o (isOCat_pow_pow_of_lt_left (pow_nonneg h0 _) hr')
+  exact this.trans_is_o (isLittleO_pow_pow_of_lt_left (pow_nonneg h0 _) hr')
   conv in (r' ^ _) ^ _ => rw [← pow_mul, mul_comm, pow_mul]
   suffices : ∀ n : ℕ, ‖(n : R)‖ ≤ (r' - 1)⁻¹ * ‖(1 : R)‖ * ‖r' ^ n‖
   exact (is_O_of_le' _ this).pow _
@@ -208,16 +209,16 @@ theorem isOCat_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : 
   rw [mul_right_comm]
   refine' n.norm_cast_le.trans (mul_le_mul_of_nonneg_right _ (norm_nonneg _))
   simpa [div_eq_inv_mul, Real.norm_eq_abs, abs_of_nonneg h0] using n.cast_le_pow_div_sub h1
-#align is_o_pow_const_const_pow_of_one_lt isOCat_pow_const_const_pow_of_one_lt
+#align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
 
 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
-theorem isOCat_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
+theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
     (coe : ℕ → R) =o[atTop] fun n => r ^ n := by
-  simpa only [pow_one] using @isOCat_pow_const_const_pow_of_one_lt R _ 1 _ hr
-#align is_o_coe_const_pow_of_one_lt isOCat_coe_const_pow_of_one_lt
+  simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
+#align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
 
 /-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
-theorem isOCat_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
+theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
     (fun n => n ^ k * r₁ ^ n : ℕ → R) =o[atTop] fun n => r₂ ^ n :=
   by
@@ -226,15 +227,15 @@ theorem isOCat_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [Normed
     simp [zero_pow (zero_lt_one.trans_le hn), h0]
   rw [← Ne.def, ← norm_pos_iff] at h0
   have A : (fun n => n ^ k : ℕ → R) =o[at_top] fun n => (r₂ / ‖r₁‖) ^ n :=
-    isOCat_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
+    isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n => r₁ ^ n) =O[at_top] fun n => ‖r₁‖ ^ n by
     simpa [div_mul_cancel _ (pow_pos h0 _).ne'] using A.mul_is_O this
   exact is_O.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
-#align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isOCat_pow_const_mul_const_pow_const_pow_of_norm_lt
+#align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
 
 theorem tendsto_pow_const_div_const_pow_of_one_lt (k : ℕ) {r : ℝ} (hr : 1 < r) :
     Tendsto (fun n => n ^ k / r ^ n : ℕ → ℝ) atTop (𝓝 0) :=
-  (isOCat_pow_const_const_pow_of_one_lt k hr).tendsto_div_nhds_zero
+  (isLittleO_pow_const_const_pow_of_one_lt k hr).tendsto_div_nhds_zero
 #align tendsto_pow_const_div_const_pow_of_one_lt tendsto_pow_const_div_const_pow_of_one_lt
 
 /-- If `|r| < 1`, then `n ^ k r ^ n` tends to zero for any natural `k`. -/
@@ -347,8 +348,8 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R]
   by
   rcases exists_between hr with ⟨r', hrr', h⟩
   exact
-    summable_of_isO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
-      (isOCat_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsO.norm_left
+    summable_of_isBigO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
+      (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').IsBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
 
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -497,7 +497,7 @@ theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
   have : ‖∑' b : ℕ, (fun n => x ^ (n + 1)) b‖ ≤ (1 - ‖x‖)⁻¹ - 1 :=
     by
     refine' tsum_of_norm_bounded _ fun b => norm_pow_le' _ (Nat.succ_pos b)
-    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
+    convert(hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
     simp
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
@@ -508,7 +508,7 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (𝓝 1) := by
     simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
-  convert ← this
+  convert← this
   ext n
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
@@ -519,7 +519,7 @@ theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ,
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : tendsto (fun n : ℕ => 1 - x ^ n) at_top (nhds 1) := by
     simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
-  convert ← this
+  convert← this
   ext n
   rw [← mul_neg_geom_sum, Finset.mul_sum]
 #align mul_neg_geom_series mul_neg_geom_series
@@ -639,7 +639,7 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
     by
     convert hf0.neg
     norm_num
-  convert (hfa'.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
+  convert(hfa'.cauchy_seq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
   funext
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded

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

@@ -26,7 +26,7 @@ noncomputable section
 
 open Classical Set Function Filter Finset Metric Asymptotics
 
-open Classical Topology Nat BigOperators uniformity NNReal Ennreal
+open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 

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

@@ -272,15 +272,15 @@ theorem tendsto_pow_atTop_nhds_zero_of_norm_lt_one {R : Type*} [NormedRing R] {x
   apply squeeze_zero_norm' (eventually_norm_pow_le x)
   exact tendsto_pow_atTop_nhds_zero_of_lt_one (norm_nonneg _) h
 #align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_zero_of_norm_lt_one
-@[deprecated] alias tendsto_pow_atTop_nhds_0_of_norm_lt_1 :=
-  tendsto_pow_atTop_nhds_zero_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias tendsto_pow_atTop_nhds_0_of_norm_lt_1 := tendsto_pow_atTop_nhds_zero_of_norm_lt_one
 
 theorem tendsto_pow_atTop_nhds_zero_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
   tendsto_pow_atTop_nhds_zero_of_norm_lt_one h
 #align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_zero_of_abs_lt_one
-@[deprecated] alias tendsto_pow_atTop_nhds_0_of_abs_lt_1 :=
-  tendsto_pow_atTop_nhds_zero_of_abs_lt_one
+@[deprecated] -- 2024-01-31
+alias tendsto_pow_atTop_nhds_0_of_abs_lt_1 := tendsto_pow_atTop_nhds_zero_of_abs_lt_one
 
 /-! ### Geometric series-/
 
@@ -299,33 +299,35 @@ theorem hasSum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ
   · simpa [geom_sum_eq, xi_ne_one, neg_inv, div_eq_mul_inv] using A
   · simp [norm_pow, summable_geometric_of_lt_one (norm_nonneg _) h]
 #align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_one
-@[deprecated] alias hasSum_geometric_of_norm_lt_1 := hasSum_geometric_of_norm_lt_one
+@[deprecated] alias hasSum_geometric_of_norm_lt_1 := hasSum_geometric_of_norm_lt_one -- 2024-01-31
 
 theorem summable_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : Summable fun n : ℕ ↦ ξ ^ n :=
   ⟨_, hasSum_geometric_of_norm_lt_one h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_one
-@[deprecated] alias summable_geometric_of_norm_lt_1 := summable_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias summable_geometric_of_norm_lt_1 := summable_geometric_of_norm_lt_one
 
 theorem tsum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_one h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_one
-@[deprecated] alias tsum_geometric_of_norm_lt_1 := tsum_geometric_of_norm_lt_one
+@[deprecated] alias tsum_geometric_of_norm_lt_1 := tsum_geometric_of_norm_lt_one -- 2024-01-31
 
 theorem hasSum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
     HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ :=
   hasSum_geometric_of_norm_lt_one h
 #align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_one
-@[deprecated] alias hasSum_geometric_of_abs_lt_1 := hasSum_geometric_of_abs_lt_one
+@[deprecated] alias hasSum_geometric_of_abs_lt_1 := hasSum_geometric_of_abs_lt_one -- 2024-01-31
 
 theorem summable_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ ↦ r ^ n :=
   summable_geometric_of_norm_lt_one h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_one
-@[deprecated] alias summable_geometric_of_abs_lt_1 := summable_geometric_of_abs_lt_one
+@[deprecated] -- 2024-01-31
+alias summable_geometric_of_abs_lt_1 := summable_geometric_of_abs_lt_one
 
 theorem tsum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_one h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_one
-@[deprecated] alias tsum_geometric_of_abs_lt_1 := tsum_geometric_of_abs_lt_one
+@[deprecated] alias tsum_geometric_of_abs_lt_1 := tsum_geometric_of_abs_lt_one -- 2024-01-31
 
 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
@@ -338,7 +340,8 @@ theorem summable_geometric_iff_norm_lt_one : (Summable fun n : ℕ ↦ ξ ^ n) 
   rw [← one_pow k] at hk
   exact lt_of_pow_lt_pow_left _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_one
-@[deprecated] alias summable_geometric_iff_norm_lt_1 := summable_geometric_iff_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias summable_geometric_iff_norm_lt_1 := summable_geometric_iff_norm_lt_one
 
 end Geometric
 
@@ -350,15 +353,15 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_one {R : Type*} [NormedRing R
   exact summable_of_isBigO_nat (summable_geometric_of_lt_one ((norm_nonneg _).trans hrr'.le) h)
     (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').isBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_one
-@[deprecated] alias summable_norm_pow_mul_geometric_of_norm_lt_1 :=
-  summable_norm_pow_mul_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias summable_norm_pow_mul_geometric_of_norm_lt_1 := summable_norm_pow_mul_geometric_of_norm_lt_one
 
 theorem summable_pow_mul_geometric_of_norm_lt_one {R : Type*} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n ↦ (n : R) ^ k * r ^ n : ℕ → R) :=
   .of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_one _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_one
-@[deprecated] alias summable_pow_mul_geometric_of_norm_lt_1 :=
-  summable_pow_mul_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias summable_pow_mul_geometric_of_norm_lt_1 := summable_pow_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedDivisionRing 𝕜] [CompleteSpace 𝕜]
@@ -387,15 +390,16 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedDivisionRi
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq,
         div_mul_eq_div_div_swap]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
-@[deprecated] alias hasSum_coe_mul_geometric_of_norm_lt_1 :=
-  hasSum_coe_mul_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias hasSum_coe_mul_geometric_of_norm_lt_1 := hasSum_coe_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
 theorem tsum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedDivisionRing 𝕜] [CompleteSpace 𝕜]
     {r : 𝕜} (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
   (hasSum_coe_mul_geometric_of_norm_lt_one hr).tsum_eq
 #align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_one
-@[deprecated] alias tsum_coe_mul_geometric_of_norm_lt_1 := tsum_coe_mul_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias tsum_coe_mul_geometric_of_norm_lt_1 := tsum_coe_mul_geometric_of_norm_lt_one
 
 end MulGeometric
 
@@ -497,8 +501,8 @@ theorem NormedRing.summable_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
   have h1 : Summable fun n : ℕ ↦ ‖x‖ ^ n := summable_geometric_of_lt_one (norm_nonneg _) h
   h1.of_norm_bounded_eventually_nat _ (eventually_norm_pow_le x)
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_one
-@[deprecated] alias NormedRing.summable_geometric_of_norm_lt_1 :=
-  NormedRing.summable_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias NormedRing.summable_geometric_of_norm_lt_1 := NormedRing.summable_geometric_of_norm_lt_one
 
 /-- Bound for the sum of a geometric series in a normed ring. This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
@@ -513,8 +517,8 @@ theorem NormedRing.tsum_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     simp
   linarith
 #align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_one
-@[deprecated] alias NormedRing.tsum_geometric_of_norm_lt_1 :=
-  NormedRing.tsum_geometric_of_norm_lt_one
+@[deprecated] -- 2024-01-31
+alias NormedRing.tsum_geometric_of_norm_lt_1 := NormedRing.tsum_geometric_of_norm_lt_one
 
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 := by
   have := (NormedRing.summable_geometric_of_norm_lt_one x h).hasSum.mul_right (1 - x)

@@ -53,12 +53,13 @@ theorem tendsto_norm_zero' {𝕜 : Type*} [NormedAddCommGroup 𝕜] :
 
 namespace NormedField
 
-theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] :
+theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type*} [NormedDivisionRing 𝕜] :
     Tendsto (fun x : 𝕜 ↦ ‖x⁻¹‖) (𝓝[≠] 0) atTop :=
   (tendsto_inv_zero_atTop.comp tendsto_norm_zero').congr fun x ↦ (norm_inv x).symm
 #align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 
-theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
+theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedDivisionRing 𝕜] {m : ℤ}
+    (hm : m < 0) :
     Tendsto (fun x : 𝕜 ↦ ‖x ^ m‖) (𝓝[≠] 0) atTop := by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.natCast_pos] at hm
@@ -67,8 +68,8 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
-theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type*} [NormedField 𝕜]
-    [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
+theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type*} [NormedDivisionRing 𝕜]
+    [NormedAddCommGroup 𝔸] [Module 𝕜 𝔸] [BoundedSMul 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
     (hε : Tendsto ε l (𝓝 0)) (hf : Filter.IsBoundedUnder (· ≤ ·) l (norm ∘ f)) :
     Tendsto (ε • f) l (𝓝 0) := by
   rw [← isLittleO_one_iff 𝕜] at hε ⊢
@@ -286,7 +287,7 @@ theorem tendsto_pow_atTop_nhds_zero_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
 
 section Geometric
 
-variable {K : Type*} [NormedField K] {ξ : K}
+variable {K : Type*} [NormedDivisionRing K] {ξ : K}
 
 theorem hasSum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ ↦ ξ ^ n) (1 - ξ)⁻¹ := by
   have xi_ne_one : ξ ≠ 1 := by
@@ -360,7 +361,7 @@ theorem summable_pow_mul_geometric_of_norm_lt_one {R : Type*} [NormedRing R] [Co
   summable_pow_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
-theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜]
+theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedDivisionRing 𝕜] [CompleteSpace 𝕜]
     {r : 𝕜} (hr : ‖r‖ < 1) : HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by
   have A : Summable (fun n ↦ (n : 𝕜) * r ^ n : ℕ → 𝕜) := by
     simpa only [pow_one] using summable_pow_mul_geometric_of_norm_lt_one 1 hr
@@ -370,22 +371,28 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜
     rintro rfl
     simp [lt_irrefl] at hr
   set s : 𝕜 := ∑' n : ℕ, n * r ^ n
+  have : Commute (1 - r) s :=
+    .tsum_right _ fun _ =>
+      .sub_left (.one_left _) (.mul_right (Nat.commute_cast _ _) (.pow_right (.refl _) _))
   calc
-    s = (1 - r) * s / (1 - r) := (mul_div_cancel_left₀ _ (sub_ne_zero.2 hr'.symm)).symm
+    s = s * (1 - r) / (1 - r) := (mul_div_cancel_right₀ _ (sub_ne_zero.2 hr'.symm)).symm
+    _ = (1 - r) * s / (1 - r) := by rw [this.eq]
     _ = (s - r * s) / (1 - r) := by rw [_root_.sub_mul, one_mul]
     _ = (((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1)) - r * s) / (1 - r) := by
       rw [← tsum_eq_zero_add A]
-    _ = ((r * ∑' n : ℕ, (n + 1) * r ^ n) - r * s) / (1 - r) := by
-      simp [_root_.pow_succ', mul_left_comm _ r, _root_.tsum_mul_left]
+    _ = ((r * ∑' n : ℕ, ↑(n + 1) * r ^ n) - r * s) / (1 - r) := by
+      simp only [cast_zero, pow_zero, mul_one, _root_.pow_succ', (Nat.cast_commute _ r).left_comm,
+        _root_.tsum_mul_left, zero_add]
     _ = r / (1 - r) ^ 2 := by
-      simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
+      simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq,
+        div_mul_eq_div_div_swap]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
 @[deprecated] alias hasSum_coe_mul_geometric_of_norm_lt_1 :=
   hasSum_coe_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
-theorem tsum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
-    (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
+theorem tsum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedDivisionRing 𝕜] [CompleteSpace 𝕜]
+    {r : 𝕜} (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
   (hasSum_coe_mul_geometric_of_norm_lt_one hr).tsum_eq
 #align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_one
 @[deprecated] alias tsum_coe_mul_geometric_of_norm_lt_1 := tsum_coe_mul_geometric_of_norm_lt_one

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -219,7 +219,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type*} [Norm
   by_cases h0 : r₁ = 0
   · refine' (isLittleO_zero _ _).congr' (mem_atTop_sets.2 <| ⟨1, fun n hn ↦ _⟩) EventuallyEq.rfl
     simp [zero_pow (one_le_iff_ne_zero.1 hn), h0]
-  rw [← Ne.def, ← norm_pos_iff] at h0
+  rw [← Ne, ← norm_pos_iff] at h0
   have A : (fun n ↦ (n : R) ^ k : ℕ → R) =o[atTop] fun n ↦ (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n ↦ r₁ ^ n) =O[atTop] fun n ↦ ‖r₁‖ ^ n by

in doc comments. These are terms of type bool, hence should be (Bool.)true/false.

And correct a typo also caused in the same PR.

@@ -770,7 +770,7 @@ end
 
 /-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `expSeries_div_summable`
 for a version that also works in `ℂ`, and `NormedSpace.expSeries_summable'` for a version
-that works inany normed algebra over `ℝ` or `ℂ`. -/
+that works in any normed algebra over `ℝ` or `ℂ`. -/
 theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n / n ! : ℕ → ℝ) := by
   -- We start with trivial estimates
   have A : (0 : ℝ) < ⌊‖x‖⌋₊ + 1 := zero_lt_one.trans_le (by simp)

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

@@ -172,7 +172,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   -- Add 7 and 8 using 2 → 8 → 7 → 3
   tfae_have 2 → 8
   · rintro ⟨a, ha, H⟩
-    refine' ⟨a, ha, (H.definition zero_lt_one).mono fun n hn ↦ _⟩
+    refine' ⟨a, ha, (H.def zero_lt_one).mono fun n hn ↦ _⟩
     rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn
   tfae_have 8 → 7
   exact fun ⟨a, ha, H⟩ ↦ ⟨a, ha.2, H⟩

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

@@ -61,7 +61,7 @@ theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜
 theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
     Tendsto (fun x : 𝕜 ↦ ‖x ^ m‖) (𝓝[≠] 0) atTop := by
   rcases neg_surjective m with ⟨m, rfl⟩
-  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
+  rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.natCast_pos] at hm
   simp only [norm_pow, zpow_neg, zpow_natCast, ← inv_pow]
   exact (tendsto_pow_atTop hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
@@ -783,7 +783,7 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n /
   calc
     ‖x ^ (n + 1) / (n + 1)!‖ = ‖x‖ / (n + 1) * ‖x ^ n / (n !)‖ := by
       rw [_root_.pow_succ', Nat.factorial_succ, Nat.cast_mul, ← _root_.div_mul_div_comm, norm_mul,
-        norm_div, Real.norm_coe_nat, Nat.cast_succ]
+        norm_div, Real.norm_natCast, Nat.cast_succ]
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / (n !)‖ :=
       -- Porting note: this was `by mono* with 0 ≤ ‖x ^ n / (n !)‖, 0 ≤ ‖x‖ <;> apply norm_nonneg`
       -- but we can't wait on `mono`.

@@ -768,9 +768,9 @@ end
 ### Factorial
 -/
 
-/-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `exp_series_div_summable`
-for a version that also works in `ℂ`, and `exp_series_summable'` for a version that works in
-any normed algebra over `ℝ` or `ℂ`. -/
+/-- The series `∑' n, x ^ n / n!` is summable of any `x : ℝ`. See also `expSeries_div_summable`
+for a version that also works in `ℂ`, and `NormedSpace.expSeries_summable'` for a version
+that works inany normed algebra over `ℝ` or `ℂ`. -/
 theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n / n ! : ℕ → ℝ) := by
   -- We start with trivial estimates
   have A : (0 : ℝ) < ⌊‖x‖⌋₊ + 1 := zero_lt_one.trans_le (by simp)

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.

@@ -376,7 +376,7 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜
     _ = (((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1)) - r * s) / (1 - r) := by
       rw [← tsum_eq_zero_add A]
     _ = ((r * ∑' n : ℕ, (n + 1) * r ^ n) - r * s) / (1 - r) := by
-      simp [_root_.pow_succ, mul_left_comm _ r, _root_.tsum_mul_left]
+      simp [_root_.pow_succ', mul_left_comm _ r, _root_.tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
@@ -713,7 +713,7 @@ theorem Monotone.tendsto_le_alternating_series
   have ha : Antitone (fun n ↦ ∑ i in range (2 * n), (-1) ^ i * f i) := by
     refine' antitone_nat_of_succ_le (fun n ↦ _)
     rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
-    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
+    simp_rw [_root_.pow_succ', show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
       ← sub_eq_add_neg, sub_le_iff_le_add]
     gcongr
     exact hfm (by omega)
@@ -728,7 +728,7 @@ theorem Monotone.alternating_series_le_tendsto
     refine' monotone_nat_of_le_succ (fun n ↦ _)
     rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring,
       sum_range_succ _ (2 * n + 1 + 1), sum_range_succ _ (2 * n + 1)]
-    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
+    simp_rw [_root_.pow_succ', show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
       ← sub_eq_add_neg, sub_add_eq_add_sub, le_sub_iff_add_le]
     gcongr
     exact hfm (by omega)
@@ -742,7 +742,7 @@ theorem Antitone.alternating_series_le_tendsto
   have hm : Monotone (fun n ↦ ∑ i in range (2 * n), (-1) ^ i * f i) := by
     refine' monotone_nat_of_le_succ (fun n ↦ _)
     rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
-    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
+    simp_rw [_root_.pow_succ', show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
       ← sub_eq_add_neg, le_sub_iff_add_le]
     gcongr
     exact hfa (by omega)
@@ -756,7 +756,7 @@ theorem Antitone.tendsto_le_alternating_series
   have ha : Antitone (fun n ↦ ∑ i in range (2 * n + 1), (-1) ^ i * f i) := by
     refine' antitone_nat_of_succ_le (fun n ↦ _)
     rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
-    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
+    simp_rw [_root_.pow_succ', show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
       ← sub_eq_add_neg, sub_add_eq_add_sub, sub_le_iff_le_add]
     gcongr
     exact hfa (by omega)
@@ -782,7 +782,7 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n /
   intro n hn
   calc
     ‖x ^ (n + 1) / (n + 1)!‖ = ‖x‖ / (n + 1) * ‖x ^ n / (n !)‖ := by
-      rw [_root_.pow_succ, Nat.factorial_succ, Nat.cast_mul, ← _root_.div_mul_div_comm, norm_mul,
+      rw [_root_.pow_succ', Nat.factorial_succ, Nat.cast_mul, ← _root_.div_mul_div_comm, norm_mul,
         norm_div, Real.norm_coe_nat, Nat.cast_succ]
     _ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / (n !)‖ :=
       -- Porting note: this was `by mono* with 0 ≤ ‖x ^ n / (n !)‖, 0 ≤ ‖x‖ <;> apply norm_nonneg`

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

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

| Statement | New name | Old name | |

@@ -223,7 +223,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type*} [Norm
   have A : (fun n ↦ (n : R) ^ k : ℕ → R) =o[atTop] fun n ↦ (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)
   suffices (fun n ↦ r₁ ^ n) =O[atTop] fun n ↦ ‖r₁‖ ^ n by
-    simpa [div_mul_cancel _ (pow_pos h0 _).ne'] using A.mul_isBigO this
+    simpa [div_mul_cancel₀ _ (pow_pos h0 _).ne'] using A.mul_isBigO this
   exact IsBigO.of_bound 1 (by simpa using eventually_norm_pow_le r₁)
 #align is_o_pow_const_mul_const_pow_const_pow_of_norm_lt isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt
 
@@ -371,7 +371,7 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜
     simp [lt_irrefl] at hr
   set s : 𝕜 := ∑' n : ℕ, n * r ^ n
   calc
-    s = (1 - r) * s / (1 - r) := (mul_div_cancel_left _ (sub_ne_zero.2 hr'.symm)).symm
+    s = (1 - r) * s / (1 - r) := (mul_div_cancel_left₀ _ (sub_ne_zero.2 hr'.symm)).symm
     _ = (s - r * s) / (1 - r) := by rw [_root_.sub_mul, one_mul]
     _ = (((0 : ℕ) * r ^ 0 + ∑' n : ℕ, (n + 1 : ℕ) * r ^ (n + 1)) - r * s) / (1 - r) := by
       rw [← tsum_eq_zero_add A]
@@ -403,7 +403,7 @@ nonrec theorem SeminormedAddCommGroup.cauchySeq_of_le_geometric {C : ℝ} {r : 
 
 theorem dist_partial_sum_le_of_le_geometric (hf : ∀ n, ‖f n‖ ≤ C * r ^ n) (n : ℕ) :
     dist (∑ i in range n, f i) (∑ i in range (n + 1), f i) ≤ C * r ^ n := by
-  rw [sum_range_succ, dist_eq_norm, ← norm_neg, neg_sub, add_sub_cancel']
+  rw [sum_range_succ, dist_eq_norm, ← norm_neg, neg_sub, add_sub_cancel_left]
   exact hf n
 #align dist_partial_sum_le_of_le_geometric dist_partial_sum_le_of_le_geometric
 

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -172,7 +172,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
   -- Add 7 and 8 using 2 → 8 → 7 → 3
   tfae_have 2 → 8
   · rintro ⟨a, ha, H⟩
-    refine' ⟨a, ha, (H.def zero_lt_one).mono fun n hn ↦ _⟩
+    refine' ⟨a, ha, (H.definition zero_lt_one).mono fun n hn ↦ _⟩
     rwa [Real.norm_eq_abs, Real.norm_eq_abs, one_mul, abs_pow, abs_of_pos ha.1] at hn
   tfae_have 8 → 7
   exact fun ⟨a, ha, H⟩ ↦ ⟨a, ha.2, H⟩

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

@@ -62,7 +62,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {
     Tendsto (fun x : 𝕜 ↦ ‖x ^ m‖) (𝓝[≠] 0) atTop := by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
-  simp only [norm_pow, zpow_neg, zpow_coe_nat, ← inv_pow]
+  simp only [norm_pow, zpow_neg, zpow_natCast, ← inv_pow]
   exact (tendsto_pow_atTop hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -627,7 +627,6 @@ section
 
 
 variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
-
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 
 /-- **Dirichlet's test** for monotone sequences. -/

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -659,7 +659,6 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
     convert hf0.neg
     norm_num
   convert (hfa'.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0' hzb).neg
-  funext
   simp
 #align antitone.cauchy_seq_series_mul_of_tendsto_zero_of_bounded Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded
 

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

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

@@ -23,9 +23,11 @@ well as such computations in `ℝ` when the natural proof passes through a fact
 
 noncomputable section
 
-open Classical Set Function Filter Finset Metric Asymptotics
+open scoped Classical
+open Set Function Filter Finset Metric Asymptotics
 
-open Classical Topology Nat BigOperators uniformity NNReal ENNReal
+open scoped Classical
+open Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type*} {β : Type*} {ι : Type*}
 

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>

@@ -663,7 +663,7 @@ theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone
 
 theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i‖ ≤ 1 := by
   rw [neg_one_geom_sum]
-  split_ifs <;> norm_num
+  split_ifs <;> set_option tactic.skipAssignedInstances false in norm_num
 #align norm_sum_neg_one_pow_le norm_sum_neg_one_pow_le
 
 /-- The **alternating series test** for monotone sequences.
@@ -717,7 +717,7 @@ theorem Monotone.tendsto_le_alternating_series
       ← sub_eq_add_neg, sub_le_iff_le_add]
     gcongr
     exact hfm (by omega)
-  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by dsimp; omega) tendsto_id)) _
 
 /-- Partial sums of an alternating monotone series with an odd number of terms provide
 lower bounds on the limit. -/
@@ -732,7 +732,7 @@ theorem Monotone.alternating_series_le_tendsto
       ← sub_eq_add_neg, sub_add_eq_add_sub, le_sub_iff_add_le]
     gcongr
     exact hfm (by omega)
-  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by dsimp; omega) tendsto_id)) _
 
 /-- Partial sums of an alternating antitone series with an even number of terms provide
 lower bounds on the limit. -/
@@ -746,7 +746,7 @@ theorem Antitone.alternating_series_le_tendsto
       ← sub_eq_add_neg, le_sub_iff_add_le]
     gcongr
     exact hfa (by omega)
-  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by dsimp; omega) tendsto_id)) _
 
 /-- Partial sums of an alternating antitone series with an odd number of terms provide
 upper bounds on the limit. -/
@@ -760,7 +760,7 @@ theorem Antitone.tendsto_le_alternating_series
       ← sub_eq_add_neg, sub_add_eq_add_sub, sub_le_iff_le_add]
     gcongr
     exact hfa (by omega)
-  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by dsimp; omega) tendsto_id)) _
 
 end
 

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".

@@ -179,7 +179,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     have : 0 ≤ a := nonneg_of_eventually_pow_nonneg (H.mono fun n ↦ (abs_nonneg _).trans)
     refine' ⟨a, A ⟨this, ha⟩, IsBigO.of_bound 1 _⟩
     simpa only [Real.norm_eq_abs, one_mul, abs_pow, abs_of_nonneg this]
-  -- porting note: used to work without explicitly having 6 → 7
+  -- Porting note: used to work without explicitly having 6 → 7
   tfae_have 6 → 7
   · exact fun h ↦ tfae_8_to_7 <| tfae_2_to_8 <| tfae_3_to_2 <| tfae_5_to_3 <| tfae_6_to_5 h
   tfae_finish

This resolves the Zulip comment here.

@@ -628,10 +628,11 @@ variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
 
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 
-/-- **Dirichlet's Test** for monotone sequences. -/
+/-- **Dirichlet's test** for monotone sequences. -/
 theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hgb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
-    CauchySeq fun n ↦ ∑ i in range (n + 1), f i • z i := by
+    CauchySeq fun n ↦ ∑ i in range n, f i • z i := by
+  rw [← cauchySeq_shift 1]
   simp_rw [Finset.sum_range_by_parts _ _ (Nat.succ _), sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
     tsub_zero]
   apply (NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded hf0
@@ -650,7 +651,7 @@ theorem Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Monotone
 /-- **Dirichlet's test** for antitone sequences. -/
 theorem Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) (hzb : ∀ n, ‖∑ i in range n, z i‖ ≤ b) :
-    CauchySeq fun n ↦ ∑ i in range (n + 1), f i • z i := by
+    CauchySeq fun n ↦ ∑ i in range n, f i • z i := by
   have hfa' : Monotone fun n ↦ -f n := fun _ _ hab ↦ neg_le_neg <| hfa hab
   have hf0' : Tendsto (fun n ↦ -f n) atTop (𝓝 0) := by
     convert hf0.neg
@@ -668,7 +669,7 @@ theorem norm_sum_neg_one_pow_le (n : ℕ) : ‖∑ i in range n, (-1 : ℝ) ^ i
 /-- The **alternating series test** for monotone sequences.
 See also `Monotone.tendsto_alternating_series_of_tendsto_zero`. -/
 theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
-    (hf0 : Tendsto f atTop (𝓝 0)) : CauchySeq fun n ↦ ∑ i in range (n + 1), (-1) ^ i * f i := by
+    (hf0 : Tendsto f atTop (𝓝 0)) : CauchySeq fun n ↦ ∑ i in range n, (-1) ^ i * f i := by
   simp_rw [mul_comm]
   exact hfa.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align monotone.cauchy_seq_alternating_series_of_tendsto_zero Monotone.cauchySeq_alternating_series_of_tendsto_zero
@@ -676,14 +677,14 @@ theorem Monotone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Monotone f)
 /-- The **alternating series test** for monotone sequences. -/
 theorem Monotone.tendsto_alternating_series_of_tendsto_zero (hfa : Monotone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
-    ∃ l, Tendsto (fun n ↦ ∑ i in range (n + 1), (-1) ^ i * f i) atTop (𝓝 l) :=
+    ∃ l, Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l) :=
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align monotone.tendsto_alternating_series_of_tendsto_zero Monotone.tendsto_alternating_series_of_tendsto_zero
 
 /-- The **alternating series test** for antitone sequences.
 See also `Antitone.tendsto_alternating_series_of_tendsto_zero`. -/
 theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
-    (hf0 : Tendsto f atTop (𝓝 0)) : CauchySeq fun n ↦ ∑ i in range (n + 1), (-1) ^ i * f i := by
+    (hf0 : Tendsto f atTop (𝓝 0)) : CauchySeq fun n ↦ ∑ i in range n, (-1) ^ i * f i := by
   simp_rw [mul_comm]
   exact hfa.cauchySeq_series_mul_of_tendsto_zero_of_bounded hf0 norm_sum_neg_one_pow_le
 #align antitone.cauchy_seq_alternating_series_of_tendsto_zero Antitone.cauchySeq_alternating_series_of_tendsto_zero
@@ -691,7 +692,7 @@ theorem Antitone.cauchySeq_alternating_series_of_tendsto_zero (hfa : Antitone f)
 /-- The **alternating series test** for antitone sequences. -/
 theorem Antitone.tendsto_alternating_series_of_tendsto_zero (hfa : Antitone f)
     (hf0 : Tendsto f atTop (𝓝 0)) :
-    ∃ l, Tendsto (fun n ↦ ∑ i in range (n + 1), (-1) ^ i * f i) atTop (𝓝 l) :=
+    ∃ l, Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l) :=
   cauchySeq_tendsto_of_complete <| hfa.cauchySeq_alternating_series_of_tendsto_zero hf0
 #align antitone.tendsto_alternating_series_of_tendsto_zero Antitone.tendsto_alternating_series_of_tendsto_zero
 

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

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

@@ -60,7 +60,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {
     Tendsto (fun x : 𝕜 ↦ ‖x ^ m‖) (𝓝[≠] 0) atTop := by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
-  simp only [norm_pow, zpow_neg, zpow_ofNat, ← inv_pow]
+  simp only [norm_pow, zpow_neg, zpow_coe_nat, ← inv_pow]
   exact (tendsto_pow_atTop hm.ne').comp NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 

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

@@ -453,12 +453,12 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
     (mul_nonneg_iff_of_pos_right <| pow_pos hr₀ N).mp ((norm_nonneg _).trans <| h N <| le_refl N)
   have : ∀ n ≥ N, u n = v n := by
     intro n hn
-    simp [hn, if_neg (not_lt.mpr hn)]
+    simp [v, hn, if_neg (not_lt.mpr hn)]
   refine'
     cauchySeq_sum_of_eventually_eq this (NormedAddCommGroup.cauchy_series_of_le_geometric' hr₁ _)
   · exact C
   intro n
-  simp only
+  simp only [v]
   split_ifs with H
   · rw [norm_zero]
     exact mul_nonneg hC (pow_nonneg hr₀.le _)

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

This follows on from #6964.

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

@@ -193,11 +193,11 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type*} [NormedRing R] (k :
   obtain ⟨r' : ℝ, hr' : r' ^ k < r, h1 : 1 < r'⟩ :=
     ((this.eventually (gt_mem_nhds hr)).and self_mem_nhdsWithin).exists
   have h0 : 0 ≤ r' := zero_le_one.trans h1.le
-  suffices : (fun n ↦ (n : R) ^ k : ℕ → R) =O[atTop] fun n : ℕ ↦ (r' ^ k) ^ n
-  exact this.trans_isLittleO (isLittleO_pow_pow_of_lt_left (pow_nonneg h0 _) hr')
+  suffices (fun n ↦ (n : R) ^ k : ℕ → R) =O[atTop] fun n : ℕ ↦ (r' ^ k) ^ n from
+    this.trans_isLittleO (isLittleO_pow_pow_of_lt_left (pow_nonneg h0 _) hr')
   conv in (r' ^ _) ^ _ => rw [← pow_mul, mul_comm, pow_mul]
-  suffices : ∀ n : ℕ, ‖(n : R)‖ ≤ (r' - 1)⁻¹ * ‖(1 : R)‖ * ‖r' ^ n‖
-  exact (isBigO_of_le' _ this).pow _
+  suffices ∀ n : ℕ, ‖(n : R)‖ ≤ (r' - 1)⁻¹ * ‖(1 : R)‖ * ‖r' ^ n‖ from
+    (isBigO_of_le' _ this).pow _
   intro n
   rw [mul_right_comm]
   refine' n.norm_cast_le.trans (mul_le_mul_of_nonneg_right _ (norm_nonneg _))
@@ -775,8 +775,8 @@ theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n /
   have A : (0 : ℝ) < ⌊‖x‖⌋₊ + 1 := zero_lt_one.trans_le (by simp)
   have B : ‖x‖ / (⌊‖x‖⌋₊ + 1) < 1 := (div_lt_one A).2 (Nat.lt_floor_add_one _)
   -- Then we apply the ratio test. The estimate works for `n ≥ ⌊‖x‖⌋₊`.
-  suffices : ∀ n ≥ ⌊‖x‖⌋₊, ‖x ^ (n + 1) / (n + 1)!‖ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / ↑n !‖
-  exact summable_of_ratio_norm_eventually_le B (eventually_atTop.2 ⟨⌊‖x‖⌋₊, this⟩)
+  suffices ∀ n ≥ ⌊‖x‖⌋₊, ‖x ^ (n + 1) / (n + 1)!‖ ≤ ‖x‖ / (⌊‖x‖⌋₊ + 1) * ‖x ^ n / ↑n !‖ from
+    summable_of_ratio_norm_eventually_le B (eventually_atTop.2 ⟨⌊‖x‖⌋₊, this⟩)
   -- Finally, we prove the upper estimate
   intro n hn
   calc

• Rename Data.Real.CauSeq to Algebra.Order.CauSeq.Basic
• Rename Data.Real.CauSeqCompletion to Algebra.Order.CauSeq.Completion
• Move the general lemmas about CauSeq from Data.Complex.Exponential to a new file Algebra.Order.CauSeq.BigOperators
• Move the lemmas mentioning Module from Algebra.BigOperators.Intervals to a new file Algebra.BigOperators.Module
• Move a few more lemmas to earlier files
• Deprecate abv_sum_le_sum_abv as it's a duplicate of IsAbsoluteValue.abv_sum

@@ -3,6 +3,7 @@ Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
 -/
+import Mathlib.Algebra.BigOperators.Module
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic

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

The const_smul_self lemmas match the existing const_mul_self ones.

shake then reports that the imports can be reduced.

@@ -7,6 +7,7 @@ import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.List.TFAE
+import Mathlib.Analysis.NormedSpace.Basic
 
 #align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

@@ -7,7 +7,6 @@ import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.List.TFAE
-import Mathlib.Data.Real.Sqrt
 
 #align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Bounds.20on.20alternating.20convergent.20series/near/418770183

@@ -696,6 +696,72 @@ theorem Antitone.tendsto_alternating_series_of_tendsto_zero (hfa : Antitone f)
 
 end
 
+/-! ### Partial sum bounds on alternating convergent series -/
+
+section
+
+variable {E : Type*} [OrderedRing E] [TopologicalSpace E] [OrderClosedTopology E]
+  {l : E} {f : ℕ → E}
+
+/-- Partial sums of an alternating monotone series with an even number of terms provide
+upper bounds on the limit. -/
+theorem Monotone.tendsto_le_alternating_series
+    (hfl : Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l))
+    (hfm : Monotone f) (k : ℕ) : l ≤ ∑ i in range (2 * k), (-1) ^ i * f i := by
+  have ha : Antitone (fun n ↦ ∑ i in range (2 * n), (-1) ^ i * f i) := by
+    refine' antitone_nat_of_succ_le (fun n ↦ _)
+    rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
+    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
+      ← sub_eq_add_neg, sub_le_iff_le_add]
+    gcongr
+    exact hfm (by omega)
+  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+
+/-- Partial sums of an alternating monotone series with an odd number of terms provide
+lower bounds on the limit. -/
+theorem Monotone.alternating_series_le_tendsto
+    (hfl : Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l))
+    (hfm : Monotone f) (k : ℕ) : ∑ i in range (2 * k + 1), (-1) ^ i * f i ≤ l := by
+  have hm : Monotone (fun n ↦ ∑ i in range (2 * n + 1), (-1) ^ i * f i) := by
+    refine' monotone_nat_of_le_succ (fun n ↦ _)
+    rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring,
+      sum_range_succ _ (2 * n + 1 + 1), sum_range_succ _ (2 * n + 1)]
+    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
+      ← sub_eq_add_neg, sub_add_eq_add_sub, le_sub_iff_add_le]
+    gcongr
+    exact hfm (by omega)
+  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+
+/-- Partial sums of an alternating antitone series with an even number of terms provide
+lower bounds on the limit. -/
+theorem Antitone.alternating_series_le_tendsto
+    (hfl : Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l))
+    (hfa : Antitone f) (k : ℕ) : ∑ i in range (2 * k), (-1) ^ i * f i ≤ l := by
+  have hm : Monotone (fun n ↦ ∑ i in range (2 * n), (-1) ^ i * f i) := by
+    refine' monotone_nat_of_le_succ (fun n ↦ _)
+    rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
+    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, one_mul,
+      ← sub_eq_add_neg, le_sub_iff_add_le]
+    gcongr
+    exact hfa (by omega)
+  exact hm.ge_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+
+/-- Partial sums of an alternating antitone series with an odd number of terms provide
+upper bounds on the limit. -/
+theorem Antitone.tendsto_le_alternating_series
+    (hfl : Tendsto (fun n ↦ ∑ i in range n, (-1) ^ i * f i) atTop (𝓝 l))
+    (hfa : Antitone f) (k : ℕ) : l ≤ ∑ i in range (2 * k + 1), (-1) ^ i * f i := by
+  have ha : Antitone (fun n ↦ ∑ i in range (2 * n + 1), (-1) ^ i * f i) := by
+    refine' antitone_nat_of_succ_le (fun n ↦ _)
+    rw [show 2 * (n + 1) = 2 * n + 1 + 1 by ring, sum_range_succ, sum_range_succ]
+    simp_rw [_root_.pow_succ, show (-1 : E) ^ (2 * n) = 1 by simp, neg_one_mul, neg_neg, one_mul,
+      ← sub_eq_add_neg, sub_add_eq_add_sub, sub_le_iff_le_add]
+    gcongr
+    exact hfa (by omega)
+  exact ha.le_of_tendsto (hfl.comp (tendsto_atTop_mono (fun n ↦ by omega) tendsto_id)) _
+
+end
+
 /-!
 ### Factorial
 -/

Also fix GeneralizedContinuedFraction.of_convergence: it worked for the Preorder.topology only.

@@ -518,7 +518,7 @@ theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) *
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 := by
   have := (NormedRing.summable_geometric_of_norm_lt_one x h).hasSum.mul_left (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
-  have : Tendsto (fun n : ℕ ↦ 1 - x ^ n) atTop (nhds 1) := by
+  have : Tendsto (fun n : ℕ ↦ 1 - x ^ n) atTop (𝓝 1) := by
     simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_norm_lt_one h)
   convert← this
   rw [← mul_neg_geom_sum, Finset.mul_sum]

From https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Bounds.20on.20alternating.20convergent.20series/near/417504820

@@ -465,6 +465,13 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
     exact h _ H
 #align normed_add_comm_group.cauchy_series_of_le_geometric'' NormedAddCommGroup.cauchy_series_of_le_geometric''
 
+/-- The term norms of any convergent series are bounded by a constant. -/
+lemma exists_norm_le_of_cauchySeq (h : CauchySeq fun n ↦ ∑ k in range n, f k) :
+    ∃ C, ∀ n, ‖f n‖ ≤ C := by
+  obtain ⟨b, ⟨_, key, _⟩⟩ := cauchySeq_iff_le_tendsto_0.mp h
+  refine ⟨b 0, fun n ↦ ?_⟩
+  simpa only [dist_partial_sum'] using key n (n + 1) 0 (_root_.zero_le _) (_root_.zero_le _)
+
 end SummableLeGeometric
 
 section NormedRingGeometric
@@ -586,6 +593,31 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type*} [SeminormedAddCom
   rwa [← le_div_iff (lt_of_le_of_ne (norm_nonneg _) h₁.symm)]
 #align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_one
 
+section NormedDivisionRing
+
+variable [NormedDivisionRing α] [CompleteSpace α] {f : ℕ → α}
+
+/-- If a power series converges at `w`, it converges absolutely at all `z` of smaller norm. -/
+theorem summable_powerSeries_of_norm_lt {w z : α}
+    (h : CauchySeq fun n ↦ ∑ i in range n, f i * w ^ i) (hz : ‖z‖ < ‖w‖) :
+    Summable fun n ↦ f n * z ^ n := by
+  have hw : 0 < ‖w‖ := (norm_nonneg z).trans_lt hz
+  obtain ⟨C, hC⟩ := exists_norm_le_of_cauchySeq h
+  rw [summable_iff_cauchySeq_finset]
+  refine cauchySeq_finset_of_geometric_bound (r := ‖z‖ / ‖w‖) (C := C) ((div_lt_one hw).mpr hz)
+    (fun n ↦ ?_)
+  rw [norm_mul, norm_pow, div_pow, ← mul_comm_div]
+  conv at hC => enter [n]; rw [norm_mul, norm_pow, ← _root_.le_div_iff (by positivity)]
+  exact mul_le_mul_of_nonneg_right (hC n) (pow_nonneg (norm_nonneg z) n)
+
+/-- If a power series converges at 1, it converges absolutely at all `z` of smaller norm. -/
+theorem summable_powerSeries_of_norm_lt_one {z : α}
+    (h : CauchySeq fun n ↦ ∑ i in range n, f i) (hz : ‖z‖ < 1) :
+    Summable fun n ↦ f n * z ^ n :=
+  summable_powerSeries_of_norm_lt (w := 1) (by simp [h]) (by simp [hz])
+
+end NormedDivisionRing
+
 section
 
 /-! ### Dirichlet and alternating series tests -/

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.

@@ -93,8 +93,8 @@ theorem isLittleO_pow_pow_of_lt_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂
     (fun n : ℕ ↦ r₁ ^ n) =o[atTop] fun n ↦ r₂ ^ n :=
   have H : 0 < r₂ := h₁.trans_lt h₂
   (isLittleO_of_tendsto fun _ hn ↦ False.elim <| H.ne' <| pow_eq_zero hn) <|
-    (tendsto_pow_atTop_nhds_0_of_lt_1 (div_nonneg h₁ (h₁.trans h₂.le)) ((div_lt_one H).2 h₂)).congr
-      fun _ ↦ div_pow _ _ _
+    (tendsto_pow_atTop_nhds_zero_of_lt_one
+      (div_nonneg h₁ (h₁.trans h₂.le)) ((div_lt_one H).2 h₂)).congr fun _ ↦ div_pow _ _ _
 #align is_o_pow_pow_of_lt_left isLittleO_pow_pow_of_lt_left
 
 theorem isBigO_pow_pow_of_le_left {r₁ r₂ : ℝ} (h₁ : 0 ≤ r₁) (h₂ : r₁ ≤ r₂) :
@@ -262,16 +262,21 @@ theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r <
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
 
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
-theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type*} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
+theorem tendsto_pow_atTop_nhds_zero_of_norm_lt_one {R : Type*} [NormedRing R] {x : R}
+    (h : ‖x‖ < 1) :
     Tendsto (fun n : ℕ ↦ x ^ n) atTop (𝓝 0) := by
   apply squeeze_zero_norm' (eventually_norm_pow_le x)
-  exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
-#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_0_of_norm_lt_1
+  exact tendsto_pow_atTop_nhds_zero_of_lt_one (norm_nonneg _) h
+#align tendsto_pow_at_top_nhds_0_of_norm_lt_1 tendsto_pow_atTop_nhds_zero_of_norm_lt_one
+@[deprecated] alias tendsto_pow_atTop_nhds_0_of_norm_lt_1 :=
+  tendsto_pow_atTop_nhds_zero_of_norm_lt_one
 
-theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
+theorem tendsto_pow_atTop_nhds_zero_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
-  tendsto_pow_atTop_nhds_0_of_norm_lt_1 h
-#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_0_of_abs_lt_1
+  tendsto_pow_atTop_nhds_zero_of_norm_lt_one h
+#align tendsto_pow_at_top_nhds_0_of_abs_lt_1 tendsto_pow_atTop_nhds_zero_of_abs_lt_one
+@[deprecated] alias tendsto_pow_atTop_nhds_0_of_abs_lt_1 :=
+  tendsto_pow_atTop_nhds_zero_of_abs_lt_one
 
 /-! ### Geometric series-/
 
@@ -280,71 +285,83 @@ section Geometric
 
 variable {K : Type*} [NormedField K] {ξ : K}
 
-theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ ↦ ξ ^ n) (1 - ξ)⁻¹ := by
+theorem hasSum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ ↦ ξ ^ n) (1 - ξ)⁻¹ := by
   have xi_ne_one : ξ ≠ 1 := by
     contrapose! h
     simp [h]
   have A : Tendsto (fun n ↦ (ξ ^ n - 1) * (ξ - 1)⁻¹) atTop (𝓝 ((0 - 1) * (ξ - 1)⁻¹)) :=
-    ((tendsto_pow_atTop_nhds_0_of_norm_lt_1 h).sub tendsto_const_nhds).mul tendsto_const_nhds
+    ((tendsto_pow_atTop_nhds_zero_of_norm_lt_one h).sub tendsto_const_nhds).mul tendsto_const_nhds
   rw [hasSum_iff_tendsto_nat_of_summable_norm]
   · simpa [geom_sum_eq, xi_ne_one, neg_inv, div_eq_mul_inv] using A
-  · simp [norm_pow, summable_geometric_of_lt_1 (norm_nonneg _) h]
-#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_1
-
-theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : ℕ ↦ ξ ^ n :=
-  ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
-#align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
-
-theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
-  (hasSum_geometric_of_norm_lt_1 h).tsum_eq
-#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
-
-theorem hasSum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ :=
-  hasSum_geometric_of_norm_lt_1 h
-#align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_1
-
-theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ ↦ r ^ n :=
-  summable_geometric_of_norm_lt_1 h
-#align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
-
-theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
-  tsum_geometric_of_norm_lt_1 h
-#align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
+  · simp [norm_pow, summable_geometric_of_lt_one (norm_nonneg _) h]
+#align has_sum_geometric_of_norm_lt_1 hasSum_geometric_of_norm_lt_one
+@[deprecated] alias hasSum_geometric_of_norm_lt_1 := hasSum_geometric_of_norm_lt_one
+
+theorem summable_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : Summable fun n : ℕ ↦ ξ ^ n :=
+  ⟨_, hasSum_geometric_of_norm_lt_one h⟩
+#align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_one
+@[deprecated] alias summable_geometric_of_norm_lt_1 := summable_geometric_of_norm_lt_one
+
+theorem tsum_geometric_of_norm_lt_one (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
+  (hasSum_geometric_of_norm_lt_one h).tsum_eq
+#align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_one
+@[deprecated] alias tsum_geometric_of_norm_lt_1 := tsum_geometric_of_norm_lt_one
+
+theorem hasSum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) :
+    HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ :=
+  hasSum_geometric_of_norm_lt_one h
+#align has_sum_geometric_of_abs_lt_1 hasSum_geometric_of_abs_lt_one
+@[deprecated] alias hasSum_geometric_of_abs_lt_1 := hasSum_geometric_of_abs_lt_one
+
+theorem summable_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : Summable fun n : ℕ ↦ r ^ n :=
+  summable_geometric_of_norm_lt_one h
+#align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_one
+@[deprecated] alias summable_geometric_of_abs_lt_1 := summable_geometric_of_abs_lt_one
+
+theorem tsum_geometric_of_abs_lt_one {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+  tsum_geometric_of_norm_lt_one h
+#align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_one
+@[deprecated] alias tsum_geometric_of_abs_lt_1 := tsum_geometric_of_abs_lt_one
 
 /-- A geometric series in a normed field is summable iff the norm of the common ratio is less than
 one. -/
 @[simp]
-theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ ↦ ξ ^ n) ↔ ‖ξ‖ < 1 := by
-  refine' ⟨fun h ↦ _, summable_geometric_of_norm_lt_1⟩
+theorem summable_geometric_iff_norm_lt_one : (Summable fun n : ℕ ↦ ξ ^ n) ↔ ‖ξ‖ < 1 := by
+  refine' ⟨fun h ↦ _, summable_geometric_of_norm_lt_one⟩
   obtain ⟨k : ℕ, hk : dist (ξ ^ k) 0 < 1⟩ :=
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
   simp only [norm_pow, dist_zero_right] at hk
   rw [← one_pow k] at hk
   exact lt_of_pow_lt_pow_left _ zero_le_one hk
-#align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
+#align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_one
+@[deprecated] alias summable_geometric_iff_norm_lt_1 := summable_geometric_iff_norm_lt_one
 
 end Geometric
 
 section MulGeometric
 
-theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R] (k : ℕ) {r : R}
+theorem summable_norm_pow_mul_geometric_of_norm_lt_one {R : Type*} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ ↦ ‖((n : R) ^ k * r ^ n : R)‖ := by
   rcases exists_between hr with ⟨r', hrr', h⟩
-  exact summable_of_isBigO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
+  exact summable_of_isBigO_nat (summable_geometric_of_lt_one ((norm_nonneg _).trans hrr'.le) h)
     (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').isBigO.norm_left
-#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
+#align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_one
+@[deprecated] alias summable_norm_pow_mul_geometric_of_norm_lt_1 :=
+  summable_norm_pow_mul_geometric_of_norm_lt_one
 
-theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R] [CompleteSpace R]
+theorem summable_pow_mul_geometric_of_norm_lt_one {R : Type*} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n ↦ (n : R) ^ k * r ^ n : ℕ → R) :=
-  .of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
-#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
+  .of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_one _ hr
+#align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_one
+@[deprecated] alias summable_pow_mul_geometric_of_norm_lt_1 :=
+  summable_pow_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
-theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
-    (hr : ‖r‖ < 1) : HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by
+theorem hasSum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜]
+    {r : 𝕜} (hr : ‖r‖ < 1) : HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by
   have A : Summable (fun n ↦ (n : 𝕜) * r ^ n : ℕ → 𝕜) := by
-    simpa only [pow_one] using summable_pow_mul_geometric_of_norm_lt_1 1 hr
-  have B : HasSum (r ^ · : ℕ → 𝕜) (1 - r)⁻¹ := hasSum_geometric_of_norm_lt_1 hr
+    simpa only [pow_one] using summable_pow_mul_geometric_of_norm_lt_one 1 hr
+  have B : HasSum (r ^ · : ℕ → 𝕜) (1 - r)⁻¹ := hasSum_geometric_of_norm_lt_one hr
   refine' A.hasSum_iff.2 _
   have hr' : r ≠ 1 := by
     rintro rfl
@@ -359,13 +376,16 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type*} [NormedField 𝕜]
       simp [_root_.pow_succ, mul_left_comm _ r, _root_.tsum_mul_left]
     _ = r / (1 - r) ^ 2 := by
       simp [add_mul, tsum_add A B.summable, mul_add, B.tsum_eq, ← div_eq_mul_inv, sq, div_div]
-#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
+#align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_one
+@[deprecated] alias hasSum_coe_mul_geometric_of_norm_lt_1 :=
+  hasSum_coe_mul_geometric_of_norm_lt_one
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
-theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
+theorem tsum_coe_mul_geometric_of_norm_lt_one {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
-  (hasSum_coe_mul_geometric_of_norm_lt_1 hr).tsum_eq
-#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1
+  (hasSum_coe_mul_geometric_of_norm_lt_one hr).tsum_eq
+#align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_one
+@[deprecated] alias tsum_coe_mul_geometric_of_norm_lt_1 := tsum_coe_mul_geometric_of_norm_lt_one
 
 end MulGeometric
 
@@ -455,40 +475,44 @@ open NormedSpace
 
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
-theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
+theorem NormedRing.summable_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     Summable fun n : ℕ ↦ x ^ n :=
-  have h1 : Summable fun n : ℕ ↦ ‖x‖ ^ n := summable_geometric_of_lt_1 (norm_nonneg _) h
+  have h1 : Summable fun n : ℕ ↦ ‖x‖ ^ n := summable_geometric_of_lt_one (norm_nonneg _) h
   h1.of_norm_bounded_eventually_nat _ (eventually_norm_pow_le x)
-#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
+#align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_one
+@[deprecated] alias NormedRing.summable_geometric_of_norm_lt_1 :=
+  NormedRing.summable_geometric_of_norm_lt_one
 
 /-- Bound for the sum of a geometric series in a normed ring. This formula does not assume that the
 normed ring satisfies the axiom `‖1‖ = 1`. -/
-theorem NormedRing.tsum_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
+theorem NormedRing.tsum_geometric_of_norm_lt_one (x : R) (h : ‖x‖ < 1) :
     ‖∑' n : ℕ, x ^ n‖ ≤ ‖(1 : R)‖ - 1 + (1 - ‖x‖)⁻¹ := by
-  rw [tsum_eq_zero_add (NormedRing.summable_geometric_of_norm_lt_1 x h)]
+  rw [tsum_eq_zero_add (summable_geometric_of_norm_lt_one x h)]
   simp only [_root_.pow_zero]
   refine' le_trans (norm_add_le _ _) _
   have : ‖∑' b : ℕ, (fun n ↦ x ^ (n + 1)) b‖ ≤ (1 - ‖x‖)⁻¹ - 1 := by
     refine' tsum_of_norm_bounded _ fun b ↦ norm_pow_le' _ (Nat.succ_pos b)
-    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_1 (norm_nonneg x) h)
+    convert (hasSum_nat_add_iff' 1).mpr (hasSum_geometric_of_lt_one (norm_nonneg x) h)
     simp
   linarith
-#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_1
+#align normed_ring.tsum_geometric_of_norm_lt_1 NormedRing.tsum_geometric_of_norm_lt_one
+@[deprecated] alias NormedRing.tsum_geometric_of_norm_lt_1 :=
+  NormedRing.tsum_geometric_of_norm_lt_one
 
 theorem geom_series_mul_neg (x : R) (h : ‖x‖ < 1) : (∑' i : ℕ, x ^ i) * (1 - x) = 1 := by
-  have := (NormedRing.summable_geometric_of_norm_lt_1 x h).hasSum.mul_right (1 - x)
+  have := (NormedRing.summable_geometric_of_norm_lt_one x h).hasSum.mul_right (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : Tendsto (fun n : ℕ ↦ 1 - x ^ n) atTop (𝓝 1) := by
-    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
+    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_norm_lt_one h)
   convert← this
   rw [← geom_sum_mul_neg, Finset.sum_mul]
 #align geom_series_mul_neg geom_series_mul_neg
 
 theorem mul_neg_geom_series (x : R) (h : ‖x‖ < 1) : ((1 - x) * ∑' i : ℕ, x ^ i) = 1 := by
-  have := (NormedRing.summable_geometric_of_norm_lt_1 x h).hasSum.mul_left (1 - x)
+  have := (NormedRing.summable_geometric_of_norm_lt_one x h).hasSum.mul_left (1 - x)
   refine' tendsto_nhds_unique this.tendsto_sum_nat _
   have : Tendsto (fun n : ℕ ↦ 1 - x ^ n) atTop (nhds 1) := by
-    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_0_of_norm_lt_1 h)
+    simpa using tendsto_const_nhds.sub (tendsto_pow_atTop_nhds_zero_of_norm_lt_one h)
   convert← this
   rw [← mul_neg_geom_sum, Finset.mul_sum]
 #align mul_neg_geom_series mul_neg_geom_series
@@ -505,7 +529,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGrou
     rcases h with ⟨N, hN⟩
     rw [← @summable_nat_add_iff α _ _ _ _ N]
     refine .of_norm_bounded (fun n ↦ ‖f N‖ * r ^ n)
-      (Summable.mul_left _ <| summable_geometric_of_lt_1 hr₀ hr₁) fun n ↦ ?_
+      (Summable.mul_left _ <| summable_geometric_of_lt_one hr₀ hr₁) fun n ↦ ?_
     simp only
     conv_rhs => rw [mul_comm, ← zero_add N]
     refine' le_geom (u := fun n ↦ ‖f (n + N)‖) hr₀ n fun i _ ↦ _

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -215,7 +215,7 @@ theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type*} [Norm
     (fun n ↦ (n : R) ^ k * r₁ ^ n : ℕ → R) =o[atTop] fun n ↦ r₂ ^ n := by
   by_cases h0 : r₁ = 0
   · refine' (isLittleO_zero _ _).congr' (mem_atTop_sets.2 <| ⟨1, fun n hn ↦ _⟩) EventuallyEq.rfl
-    simp [zero_pow (zero_lt_one.trans_le hn), h0]
+    simp [zero_pow (one_le_iff_ne_zero.1 hn), h0]
   rw [← Ne.def, ← norm_pos_iff] at h0
   have A : (fun n ↦ (n : R) ^ k : ℕ → R) =o[atTop] fun n ↦ (r₂ / ‖r₁‖) ^ n :=
     isLittleO_pow_const_const_pow_of_one_lt k ((one_lt_div h0).2 h)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -7,6 +7,7 @@ import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.List.TFAE
+import Mathlib.Data.Real.Sqrt
 
 #align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

@@ -428,7 +428,7 @@ theorem NormedAddCommGroup.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ 
     CauchySeq fun n ↦ ∑ k in range (n + 1), u k := by
   set v : ℕ → α := fun n ↦ if n < N then 0 else u n
   have hC : 0 ≤ C :=
-    (zero_le_mul_right <| pow_pos hr₀ N).mp ((norm_nonneg _).trans <| h N <| le_refl N)
+    (mul_nonneg_iff_of_pos_right <| pow_pos hr₀ N).mp ((norm_nonneg _).trans <| h N <| le_refl N)
   have : ∀ n ≥ N, u n = v n := by
     intro n hn
     simp [hn, if_neg (not_lt.mpr hn)]

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -127,7 +127,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     TFAE
       [∃ a ∈ Ioo (-R) R, f =o[atTop] (a ^ ·), ∃ a ∈ Ioo 0 R, f =o[atTop] (a ^ ·),
         ∃ a ∈ Ioo (-R) R, f =O[atTop] (a ^ ·), ∃ a ∈ Ioo 0 R, f =O[atTop] (a ^ ·),
-        ∃ a < R, ∃ (C : _) (_ : 0 < C ∨ 0 < R), ∀ n, |f n| ≤ C * a ^ n,
+        ∃ a < R, ∃ C : ℝ, (0 < C ∨ 0 < R) ∧ ∀ n, |f n| ≤ C * a ^ n,
         ∃ a ∈ Ioo 0 R, ∃ C > 0, ∀ n, |f n| ≤ C * a ^ n, ∃ a < R, ∀ᶠ n in atTop, |f n| ≤ a ^ n,
         ∃ a ∈ Ioo 0 R, ∀ᶠ n in atTop, |f n| ≤ a ^ n] := by
   have A : Ico 0 R ⊆ Ioo (-R) R :=

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.

@@ -319,7 +319,7 @@ theorem summable_geometric_iff_norm_lt_1 : (Summable fun n : ℕ ↦ ξ ^ n) ↔
     (h.tendsto_cofinite_zero.eventually (ball_mem_nhds _ zero_lt_one)).exists
   simp only [norm_pow, dist_zero_right] at hk
   rw [← one_pow k] at hk
-  exact lt_of_pow_lt_pow _ zero_le_one hk
+  exact lt_of_pow_lt_pow_left _ zero_le_one hk
 #align summable_geometric_iff_norm_lt_1 summable_geometric_iff_norm_lt_1
 
 end Geometric

To fit with the "please try harder" convention of ! tactics.

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

@@ -513,7 +513,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGrou
   · push_neg at hr₀
     refine' .of_norm_bounded_eventually_nat 0 summable_zero _
     filter_upwards [h] with _ hn
-    by_contra' h
+    by_contra! h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
 

• Remove simp-lemma bitwise_of_ne_zero, since it wasn't used, and could cause loops in an inconsistent context.

@@ -233,7 +233,7 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
     Tendsto (fun n ↦ (n : ℝ) ^ k * r ^ n : ℕ → ℝ) atTop (𝓝 0) := by
   by_cases h0 : r = 0
   · exact tendsto_const_nhds.congr'
-      (mem_atTop_sets.2 ⟨1, fun n hn ↦ by simp [zero_lt_one.trans_le hn, h0]⟩)
+      (mem_atTop_sets.2 ⟨1, fun n hn ↦ by simp [zero_lt_one.trans_le hn |>.ne', h0]⟩)
   have hr' : 1 < |r|⁻¹ := one_lt_inv (abs_pos.2 h0) hr
   rw [tendsto_zero_iff_norm_tendsto_zero]
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'

Rename

• summable_of_norm_bounded -> Summable.of_norm_bounded;
• summable_of_norm_bounded_eventually -> Summable.of_norm_bounded_eventually;
• summable_of_nnnorm_bounded -> Summable.of_nnnorm_bounded;
• summable_of_summable_norm -> Summable.of_norm;
• summable_of_summable_nnnorm -> Summable.of_nnnorm;

New lemmas

• Summable.of_norm_bounded_eventually_nat
• Summable.norm

Misc changes

• Golf a few proofs.

@@ -34,9 +34,9 @@ theorem tendsto_norm_atTop_atTop : Tendsto (norm : ℝ → ℝ) atTop atTop :=
 theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
     (∃ r, Tendsto (fun n ↦ ∑ i in range n, |f i|) atTop (𝓝 r)) → Summable f
   | ⟨r, hr⟩ => by
-    refine' summable_of_summable_norm ⟨r, (hasSum_iff_tendsto_nat_of_nonneg _ _).2 _⟩
-    exact fun i ↦ norm_nonneg _
-    simpa only using hr
+    refine .of_norm ⟨r, (hasSum_iff_tendsto_nat_of_nonneg ?_ _).2 ?_⟩
+    · exact fun i ↦ norm_nonneg _
+    · simpa only using hr
 #align summable_of_absolute_convergence_real summable_of_absolute_convergence_real
 
 /-! ### Powers -/
@@ -335,7 +335,7 @@ theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R]
 
 theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n ↦ (n : R) ^ k * r ^ n : ℕ → R) :=
-  summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
+  .of_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
@@ -455,11 +455,9 @@ open NormedSpace
 /-- A geometric series in a complete normed ring is summable.
 Proved above (same name, different namespace) for not-necessarily-complete normed fields. -/
 theorem NormedRing.summable_geometric_of_norm_lt_1 (x : R) (h : ‖x‖ < 1) :
-    Summable fun n : ℕ ↦ x ^ n := by
+    Summable fun n : ℕ ↦ x ^ n :=
   have h1 : Summable fun n : ℕ ↦ ‖x‖ ^ n := summable_geometric_of_lt_1 (norm_nonneg _) h
-  refine' summable_of_norm_bounded_eventually _ h1 _
-  rw [Nat.cofinite_eq_atTop]
-  exact eventually_norm_pow_le x
+  h1.of_norm_bounded_eventually_nat _ (eventually_norm_pow_le x)
 #align normed_ring.summable_geometric_of_norm_lt_1 NormedRing.summable_geometric_of_norm_lt_1
 
 /-- Bound for the sum of a geometric series in a normed ring. This formula does not assume that the
@@ -498,7 +496,6 @@ end NormedRingGeometric
 
 /-! ### Summability tests based on comparison with geometric series -/
 
-
 theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGroup α]
     [CompleteSpace α] {f : ℕ → α} {r : ℝ} (hr₁ : r < 1)
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f := by
@@ -506,16 +503,15 @@ theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGrou
   · rw [eventually_atTop] at h
     rcases h with ⟨N, hN⟩
     rw [← @summable_nat_add_iff α _ _ _ _ N]
-    refine' summable_of_norm_bounded (fun n ↦ ‖f N‖ * r ^ n)
-      (Summable.mul_left _ <| summable_geometric_of_lt_1 hr₀ hr₁) fun n ↦ _
+    refine .of_norm_bounded (fun n ↦ ‖f N‖ * r ^ n)
+      (Summable.mul_left _ <| summable_geometric_of_lt_1 hr₀ hr₁) fun n ↦ ?_
     simp only
     conv_rhs => rw [mul_comm, ← zero_add N]
     refine' le_geom (u := fun n ↦ ‖f (n + N)‖) hr₀ n fun i _ ↦ _
     convert hN (i + N) (N.le_add_left i) using 3
     ac_rfl
   · push_neg at hr₀
-    refine' summable_of_norm_bounded_eventually 0 summable_zero _
-    rw [Nat.cofinite_eq_atTop]
+    refine' .of_norm_bounded_eventually_nat 0 summable_zero _
     filter_upwards [h] with _ hn
     by_contra' h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)

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

@@ -516,7 +516,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGrou
   · push_neg at hr₀
     refine' summable_of_norm_bounded_eventually 0 summable_zero _
     rw [Nat.cofinite_eq_atTop]
-    filter_upwards [h]with _ hn
+    filter_upwards [h] with _ hn
     by_contra' h
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
@@ -526,7 +526,7 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type*} [NormedAddCommGroup 
     (h : Tendsto (fun n ↦ ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) : Summable f := by
   rcases exists_between hl₁ with ⟨r, hr₀, hr₁⟩
   refine' summable_of_ratio_norm_eventually_le hr₁ _
-  filter_upwards [eventually_le_of_tendsto_lt hr₀ h, hf]with _ _ h₁
+  filter_upwards [eventually_le_of_tendsto_lt hr₀ h, hf] with _ _ h₁
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
 
@@ -556,12 +556,12 @@ theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type*} [SeminormedAddCom
     {f : ℕ → α} {l : ℝ} (hl : 1 < l) (h : Tendsto (fun n ↦ ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) :
     ¬Summable f := by
   have key : ∀ᶠ n in atTop, ‖f n‖ ≠ 0 := by
-    filter_upwards [eventually_ge_of_tendsto_gt hl h]with _ hn hc
+    filter_upwards [eventually_ge_of_tendsto_gt hl h] with _ hn hc
     rw [hc, _root_.div_zero] at hn
     linarith
   rcases exists_between hl with ⟨r, hr₀, hr₁⟩
   refine' not_summable_of_ratio_norm_eventually_ge hr₀ key.frequently _
-  filter_upwards [eventually_ge_of_tendsto_gt hr₁ h, key]with _ _ h₁
+  filter_upwards [eventually_ge_of_tendsto_gt hr₁ h, key] with _ _ h₁
   rwa [← le_div_iff (lt_of_le_of_ne (norm_nonneg _) h₁.symm)]
 #align not_summable_of_ratio_test_tendsto_gt_one not_summable_of_ratio_test_tendsto_gt_one
 

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

This has nice performance benefits.

@@ -25,7 +25,7 @@ open Classical Set Function Filter Finset Metric Asymptotics
 
 open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
-variable {α : Type _} {β : Type _} {ι : Type _}
+variable {α : Type*} {β : Type*} {ι : Type*}
 
 theorem tendsto_norm_atTop_atTop : Tendsto (norm : ℝ → ℝ) atTop atTop :=
   tendsto_abs_atTop_atTop
@@ -42,19 +42,19 @@ theorem summable_of_absolute_convergence_real {f : ℕ → ℝ} :
 /-! ### Powers -/
 
 
-theorem tendsto_norm_zero' {𝕜 : Type _} [NormedAddCommGroup 𝕜] :
+theorem tendsto_norm_zero' {𝕜 : Type*} [NormedAddCommGroup 𝕜] :
     Tendsto (norm : 𝕜 → ℝ) (𝓝[≠] 0) (𝓝[>] 0) :=
   tendsto_norm_zero.inf <| tendsto_principal_principal.2 fun _ hx ↦ norm_pos_iff.2 hx
 #align tendsto_norm_zero' tendsto_norm_zero'
 
 namespace NormedField
 
-theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] :
+theorem tendsto_norm_inverse_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] :
     Tendsto (fun x : 𝕜 ↦ ‖x⁻¹‖) (𝓝[≠] 0) atTop :=
   (tendsto_inv_zero_atTop.comp tendsto_norm_zero').congr fun x ↦ (norm_inv x).symm
 #align normed_field.tendsto_norm_inverse_nhds_within_0_at_top NormedField.tendsto_norm_inverse_nhdsWithin_0_atTop
 
-theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
+theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type*} [NormedField 𝕜] {m : ℤ} (hm : m < 0) :
     Tendsto (fun x : 𝕜 ↦ ‖x ^ m‖) (𝓝[≠] 0) atTop := by
   rcases neg_surjective m with ⟨m, rfl⟩
   rw [neg_lt_zero] at hm; lift m to ℕ using hm.le; rw [Int.coe_nat_pos] at hm
@@ -63,7 +63,7 @@ theorem tendsto_norm_zpow_nhdsWithin_0_atTop {𝕜 : Type _} [NormedField 𝕜]
 #align normed_field.tendsto_norm_zpow_nhds_within_0_at_top NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop
 
 /-- The (scalar) product of a sequence that tends to zero with a bounded one also tends to zero. -/
-theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [NormedField 𝕜]
+theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type*} [NormedField 𝕜]
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
     (hε : Tendsto ε l (𝓝 0)) (hf : Filter.IsBoundedUnder (· ≤ ·) l (norm ∘ f)) :
     Tendsto (ε • f) l (𝓝 0) := by
@@ -72,7 +72,7 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
 
 @[simp]
-theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : ℤ} {x : 𝕜} :
+theorem continuousAt_zpow {𝕜 : Type*} [NontriviallyNormedField 𝕜] {m : ℤ} {x : 𝕜} :
     ContinuousAt (fun x ↦ x ^ m) x ↔ x ≠ 0 ∨ 0 ≤ m := by
   refine' ⟨_, continuousAt_zpow₀ _ _⟩
   contrapose!; rintro ⟨rfl, hm⟩ hc
@@ -81,7 +81,7 @@ theorem continuousAt_zpow {𝕜 : Type _} [NontriviallyNormedField 𝕜] {m : 
 #align normed_field.continuous_at_zpow NormedField.continuousAt_zpow
 
 @[simp]
-theorem continuousAt_inv {𝕜 : Type _} [NontriviallyNormedField 𝕜] {x : 𝕜} :
+theorem continuousAt_inv {𝕜 : Type*} [NontriviallyNormedField 𝕜] {x : 𝕜} :
     ContinuousAt Inv.inv x ↔ x ≠ 0 := by
   simpa [(zero_lt_one' ℤ).not_le] using @continuousAt_zpow _ _ (-1) x
 #align normed_field.continuous_at_inv NormedField.continuousAt_inv
@@ -184,7 +184,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
 #align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_pow
 
 /-- For any natural `k` and a real `r > 1` we have `n ^ k = o(r ^ n)` as `n → ∞`. -/
-theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k : ℕ) {r : ℝ}
+theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type*} [NormedRing R] (k : ℕ) {r : ℝ}
     (hr : 1 < r) : (fun n ↦ (n : R) ^ k : ℕ → R) =o[atTop] fun n ↦ r ^ n := by
   have : Tendsto (fun x : ℝ ↦ x ^ k) (𝓝[>] 1) (𝓝 1) :=
     ((continuous_id.pow k).tendsto' (1 : ℝ) 1 (one_pow _)).mono_left inf_le_left
@@ -203,13 +203,13 @@ theorem isLittleO_pow_const_const_pow_of_one_lt {R : Type _} [NormedRing R] (k :
 #align is_o_pow_const_const_pow_of_one_lt isLittleO_pow_const_const_pow_of_one_lt
 
 /-- For a real `r > 1` we have `n = o(r ^ n)` as `n → ∞`. -/
-theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ} (hr : 1 < r) :
+theorem isLittleO_coe_const_pow_of_one_lt {R : Type*} [NormedRing R] {r : ℝ} (hr : 1 < r) :
     ((↑) : ℕ → R) =o[atTop] fun n ↦ r ^ n := by
   simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
 #align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
 
 /-- If `‖r₁‖ < r₂`, then for any natural `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
-theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
+theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type*} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
     (fun n ↦ (n : R) ^ k * r₁ ^ n : ℕ → R) =o[atTop] fun n ↦ r₂ ^ n := by
   by_cases h0 : r₁ = 0
@@ -261,7 +261,7 @@ theorem tendsto_self_mul_const_pow_of_lt_one {r : ℝ} (hr : 0 ≤ r) (h'r : r <
 #align tendsto_self_mul_const_pow_of_lt_one tendsto_self_mul_const_pow_of_lt_one
 
 /-- In a normed ring, the powers of an element x with `‖x‖ < 1` tend to zero. -/
-theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type _} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
+theorem tendsto_pow_atTop_nhds_0_of_norm_lt_1 {R : Type*} [NormedRing R] {x : R} (h : ‖x‖ < 1) :
     Tendsto (fun n : ℕ ↦ x ^ n) atTop (𝓝 0) := by
   apply squeeze_zero_norm' (eventually_norm_pow_le x)
   exact tendsto_pow_atTop_nhds_0_of_lt_1 (norm_nonneg _) h
@@ -277,7 +277,7 @@ theorem tendsto_pow_atTop_nhds_0_of_abs_lt_1 {r : ℝ} (h : |r| < 1) :
 
 section Geometric
 
-variable {K : Type _} [NormedField K] {ξ : K}
+variable {K : Type*} [NormedField K] {ξ : K}
 
 theorem hasSum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : HasSum (fun n : ℕ ↦ ξ ^ n) (1 - ξ)⁻¹ := by
   have xi_ne_one : ξ ≠ 1 := by
@@ -326,20 +326,20 @@ end Geometric
 
 section MulGeometric
 
-theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] (k : ℕ) {r : R}
+theorem summable_norm_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R] (k : ℕ) {r : R}
     (hr : ‖r‖ < 1) : Summable fun n : ℕ ↦ ‖((n : R) ^ k * r ^ n : R)‖ := by
   rcases exists_between hr with ⟨r', hrr', h⟩
   exact summable_of_isBigO_nat (summable_geometric_of_lt_1 ((norm_nonneg _).trans hrr'.le) h)
     (isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt _ hrr').isBigO.norm_left
 #align summable_norm_pow_mul_geometric_of_norm_lt_1 summable_norm_pow_mul_geometric_of_norm_lt_1
 
-theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [CompleteSpace R]
+theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type*} [NormedRing R] [CompleteSpace R]
     (k : ℕ) {r : R} (hr : ‖r‖ < 1) : Summable (fun n ↦ (n : R) ^ k * r ^ n : ℕ → R) :=
   summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
-theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
+theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by
   have A : Summable (fun n ↦ (n : 𝕜) * r ^ n : ℕ → 𝕜) := by
     simpa only [pow_one] using summable_pow_mul_geometric_of_norm_lt_1 1 hr
@@ -361,7 +361,7 @@ theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜]
 #align has_sum_coe_mul_geometric_of_norm_lt_1 hasSum_coe_mul_geometric_of_norm_lt_1
 
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`. -/
-theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
+theorem tsum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type*} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : (∑' n : ℕ, n * r ^ n : 𝕜) = r / (1 - r) ^ 2 :=
   (hasSum_coe_mul_geometric_of_norm_lt_1 hr).tsum_eq
 #align tsum_coe_mul_geometric_of_norm_lt_1 tsum_coe_mul_geometric_of_norm_lt_1
@@ -448,7 +448,7 @@ end SummableLeGeometric
 
 section NormedRingGeometric
 
-variable {R : Type _} [NormedRing R] [CompleteSpace R]
+variable {R : Type*} [NormedRing R] [CompleteSpace R]
 
 open NormedSpace
 
@@ -499,7 +499,7 @@ end NormedRingGeometric
 /-! ### Summability tests based on comparison with geometric series -/
 
 
-theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGroup α]
+theorem summable_of_ratio_norm_eventually_le {α : Type*} [SeminormedAddCommGroup α]
     [CompleteSpace α] {f : ℕ → α} {r : ℝ} (hr₁ : r < 1)
     (h : ∀ᶠ n in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) : Summable f := by
   by_cases hr₀ : 0 ≤ r
@@ -521,7 +521,7 @@ theorem summable_of_ratio_norm_eventually_le {α : Type _} [SeminormedAddCommGro
     exact not_lt.mpr (norm_nonneg _) (lt_of_le_of_lt hn <| mul_neg_of_neg_of_pos hr₀ h)
 #align summable_of_ratio_norm_eventually_le summable_of_ratio_norm_eventually_le
 
-theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup α] [CompleteSpace α]
+theorem summable_of_ratio_test_tendsto_lt_one {α : Type*} [NormedAddCommGroup α] [CompleteSpace α]
     {f : ℕ → α} {l : ℝ} (hl₁ : l < 1) (hf : ∀ᶠ n in atTop, f n ≠ 0)
     (h : Tendsto (fun n ↦ ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) : Summable f := by
   rcases exists_between hl₁ with ⟨r, hr₀, hr₁⟩
@@ -530,7 +530,7 @@ theorem summable_of_ratio_test_tendsto_lt_one {α : Type _} [NormedAddCommGroup
   rwa [← div_le_iff (norm_pos_iff.mpr h₁)]
 #align summable_of_ratio_test_tendsto_lt_one summable_of_ratio_test_tendsto_lt_one
 
-theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCommGroup α] {f : ℕ → α}
+theorem not_summable_of_ratio_norm_eventually_ge {α : Type*} [SeminormedAddCommGroup α] {f : ℕ → α}
     {r : ℝ} (hr : 1 < r) (hf : ∃ᶠ n in atTop, ‖f n‖ ≠ 0)
     (h : ∀ᶠ n in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) : ¬Summable f := by
   rw [eventually_atTop] at h
@@ -552,7 +552,7 @@ theorem not_summable_of_ratio_norm_eventually_ge {α : Type _} [SeminormedAddCom
     ac_rfl
 #align not_summable_of_ratio_norm_eventually_ge not_summable_of_ratio_norm_eventually_ge
 
-theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type _} [SeminormedAddCommGroup α]
+theorem not_summable_of_ratio_test_tendsto_gt_one {α : Type*} [SeminormedAddCommGroup α]
     {f : ℕ → α} {l : ℝ} (hl : 1 < l) (h : Tendsto (fun n ↦ ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)) :
     ¬Summable f := by
   have key : ∀ᶠ n in atTop, ‖f n‖ ≠ 0 := by
@@ -570,7 +570,7 @@ section
 /-! ### Dirichlet and alternating series tests -/
 
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
 
 variable {b : ℝ} {f : ℕ → ℝ} {z : ℕ → E}
 

@@ -14,8 +14,7 @@ import Mathlib.Data.List.TFAE
 # A collection of specific limit computations
 
 This file contains important specific limit computations in (semi-)normed groups/rings/spaces, as
-as well as such computations in `ℝ` when the natural proof passes through a fact about normed
-spaces.
+well as such computations in `ℝ` when the natural proof passes through a fact about normed spaces.
 
 -/
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.specific_limits.normed
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.List.TFAE
 
+#align_import analysis.specific_limits.normed from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # A collection of specific limit computations
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -183,7 +183,7 @@ theorem TFAE_exists_lt_isLittleO_pow (f : ℕ → ℝ) (R : ℝ) :
     simpa only [Real.norm_eq_abs, one_mul, abs_pow, abs_of_nonneg this]
   -- porting note: used to work without explicitly having 6 → 7
   tfae_have 6 → 7
-  · exact fun h ↦  tfae_8_to_7 <| tfae_2_to_8 <| tfae_3_to_2 <| tfae_5_to_3 <| tfae_6_to_5 h
+  · exact fun h ↦ tfae_8_to_7 <| tfae_2_to_8 <| tfae_3_to_2 <| tfae_5_to_3 <| tfae_6_to_5 h
   tfae_finish
 #align tfae_exists_lt_is_o_pow TFAE_exists_lt_isLittleO_pow
 

@@ -238,7 +238,7 @@ theorem tendsto_pow_const_mul_const_pow_of_abs_lt_one (k : ℕ) {r : ℝ} (hr :
   by_cases h0 : r = 0
   · exact tendsto_const_nhds.congr'
       (mem_atTop_sets.2 ⟨1, fun n hn ↦ by simp [zero_lt_one.trans_le hn, h0]⟩)
-  have hr' : 1 < (|r|)⁻¹ := one_lt_inv (abs_pos.2 h0) hr
+  have hr' : 1 < |r|⁻¹ := one_lt_inv (abs_pos.2 h0) hr
   rw [tendsto_zero_iff_norm_tendsto_zero]
   simpa [div_eq_mul_inv] using tendsto_pow_const_div_const_pow_of_one_lt k hr'
 #align tendsto_pow_const_mul_const_pow_of_abs_lt_one tendsto_pow_const_mul_const_pow_of_abs_lt_one

• 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

@@ -298,7 +298,7 @@ theorem summable_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : Summable fun n : 
   ⟨_, hasSum_geometric_of_norm_lt_1 h⟩
 #align summable_geometric_of_norm_lt_1 summable_geometric_of_norm_lt_1
 
-theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : (∑' n : ℕ, ξ ^ n) = (1 - ξ)⁻¹ :=
+theorem tsum_geometric_of_norm_lt_1 (h : ‖ξ‖ < 1) : ∑' n : ℕ, ξ ^ n = (1 - ξ)⁻¹ :=
   (hasSum_geometric_of_norm_lt_1 h).tsum_eq
 #align tsum_geometric_of_norm_lt_1 tsum_geometric_of_norm_lt_1
 
@@ -310,7 +310,7 @@ theorem summable_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : Summable fun n
   summable_geometric_of_norm_lt_1 h
 #align summable_geometric_of_abs_lt_1 summable_geometric_of_abs_lt_1
 
-theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_of_abs_lt_1 {r : ℝ} (h : |r| < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   tsum_geometric_of_norm_lt_1 h
 #align tsum_geometric_of_abs_lt_1 tsum_geometric_of_abs_lt_1
 

Changes are of the form

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

@@ -71,7 +71,7 @@ theorem tendsto_zero_smul_of_tendsto_zero_of_bounded {ι 𝕜 𝔸 : Type _} [No
     [NormedAddCommGroup 𝔸] [NormedSpace 𝕜 𝔸] {l : Filter ι} {ε : ι → 𝕜} {f : ι → 𝔸}
     (hε : Tendsto ε l (𝓝 0)) (hf : Filter.IsBoundedUnder (· ≤ ·) l (norm ∘ f)) :
     Tendsto (ε • f) l (𝓝 0) := by
-  rw [← isLittleO_one_iff 𝕜] at hε⊢
+  rw [← isLittleO_one_iff 𝕜] at hε ⊢
   simpa using IsLittleO.smul_isBigO hε (hf.isBigO_const (one_ne_zero : (1 : 𝕜) ≠ 0))
 #align normed_field.tendsto_zero_smul_of_tendsto_zero_of_bounded NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded
 

These are all doc fixes

@@ -212,7 +212,7 @@ theorem isLittleO_coe_const_pow_of_one_lt {R : Type _} [NormedRing R] {r : ℝ}
   simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr
 #align is_o_coe_const_pow_of_one_lt isLittleO_coe_const_pow_of_one_lt
 
-/-- If `‖r₁‖ < r₂`, then for any naturak `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
+/-- If `‖r₁‖ < r₂`, then for any natural `k` we have `n ^ k r₁ ^ n = o (r₂ ^ n)` as `n → ∞`. -/
 theorem isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt {R : Type _} [NormedRing R] (k : ℕ)
     {r₁ : R} {r₂ : ℝ} (h : ‖r₁‖ < r₂) :
     (fun n ↦ (n : R) ^ k * r₁ ^ n : ℕ → R) =o[atTop] fun n ↦ r₂ ^ n := by

Run codespell Mathlib and keep some suggestions.

@@ -655,7 +655,7 @@ end
 for a version that also works in `ℂ`, and `exp_series_summable'` for a version that works in
 any normed algebra over `ℝ` or `ℂ`. -/
 theorem Real.summable_pow_div_factorial (x : ℝ) : Summable (fun n ↦ x ^ n / n ! : ℕ → ℝ) := by
-  -- We start with trivial extimates
+  -- We start with trivial estimates
   have A : (0 : ℝ) < ⌊‖x‖⌋₊ + 1 := zero_lt_one.trans_le (by simp)
   have B : ‖x‖ / (⌊‖x‖⌋₊ + 1) < 1 := (div_lt_one A).2 (Nat.lt_floor_add_one _)
   -- Then we apply the ratio test. The estimate works for `n ≥ ⌊‖x‖⌋₊`.

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -342,7 +342,6 @@ theorem summable_pow_mul_geometric_of_norm_lt_1 {R : Type _} [NormedRing R] [Com
   summable_of_summable_norm <| summable_norm_pow_mul_geometric_of_norm_lt_1 _ hr
 #align summable_pow_mul_geometric_of_norm_lt_1 summable_pow_mul_geometric_of_norm_lt_1
 
-set_option synthInstance.etaExperiment true in
 /-- If `‖r‖ < 1`, then `∑' n : ℕ, n * r ^ n = r / (1 - r) ^ 2`, `HasSum` version. -/
 theorem hasSum_coe_mul_geometric_of_norm_lt_1 {𝕜 : Type _} [NormedField 𝕜] [CompleteSpace 𝕜] {r : 𝕜}
     (hr : ‖r‖ < 1) : HasSum (fun n ↦ n * r ^ n : ℕ → 𝕜) (r / (1 - r) ^ 2) := by

Removes from Analysis/SpecificLimits/Normed.lean an import Mathlib.Tactic.LibrarySearch that was accidentally included in #3419.

@@ -12,7 +12,6 @@ import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Analysis.Asymptotics.Asymptotics
 import Mathlib.Analysis.SpecificLimits.Basic
 import Mathlib.Data.List.TFAE
-import Mathlib.Tactic.LibrarySearch
 
 /-!
 # A collection of specific limit computations

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>