analysis.specific_limits.basic ⟷ Mathlib.Analysis.SpecificLimits.Basic

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

@@ -33,7 +33,7 @@ variable {α : Type _} {β : Type _} {ι : Type _}
 
 #print tendsto_inverse_atTop_nhds_zero_nat /-
 theorem tendsto_inverse_atTop_nhds_zero_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
-  tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
+  tendsto_inv_atTop_zero.comp tendsto_natCast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_zero_nat
 -/
 

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

@@ -67,13 +67,13 @@ theorem tendsto_one_div_add_atTop_nhds_zero_nat :
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_zero_nat
 -/
 
-#print tendsto_coe_nat_div_add_atTop /-
+#print tendsto_natCast_div_add_atTop /-
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 
 TODO: introduce a typeclass saying that `1 / n` tends to 0 at top, making it possible to get this
 statement simultaneously on `ℚ`, `ℝ` and `ℂ`. -/
-theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
+theorem tendsto_natCast_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
     [CharZero 𝕜] [Algebra ℝ 𝕜] [ContinuousSMul ℝ 𝕜] [TopologicalDivisionRing 𝕜] (x : 𝕜) :
     Tendsto (fun n : ℕ => (n : 𝕜) / (n + x)) atTop (𝓝 1) :=
   by
@@ -93,7 +93,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
       rfl
     rw [this]
     exact ((continuous_algebraMap ℝ 𝕜).Tendsto _).comp tendsto_inverse_atTop_nhds_zero_nat
-#align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTop
+#align tendsto_coe_nat_div_add_at_top tendsto_natCast_div_add_atTop
 -/
 
 /-! ### Powers -/

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

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Masso
 import Algebra.GeomSum
 import Order.Filter.Archimedean
 import Order.Iterate
-import Topology.Instances.Ennreal
+import Topology.Instances.ENNReal
 import Topology.Algebra.Algebra
 
 #align_import analysis.specific_limits.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
@@ -128,7 +128,7 @@ theorem tendsto_pow_atTop_nhds_zero_of_lt_one {𝕜 : Type _} [LinearOrderedFiel
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   h₁.eq_or_lt.elim
     (fun this : 0 = r =>
-      (tendsto_add_atTop_iff_nat 1).mp <| by simp [pow_succ, ← this, tendsto_const_nhds])
+      (tendsto_add_atTop_iff_nat 1).mp <| by simp [pow_succ', ← this, tendsto_const_nhds])
     fun this : 0 < r =>
     have : Tendsto (fun n => (r⁻¹ ^ n)⁻¹) atTop (𝓝 0) :=
       tendsto_inv_atTop_zero.comp (tendsto_pow_atTop_atTop_of_one_lt <| one_lt_inv this h₂)
@@ -160,7 +160,7 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   by
   refine' (monotone_mul_left_of_nonneg hc).seq_pos_lt_seq_of_le_of_lt hn _ _ h
   · simp
-  · simp [pow_succ, mul_assoc, le_refl]
+  · simp [pow_succ', mul_assoc, le_refl]
 #align geom_lt geom_lt
 -/
 
@@ -168,7 +168,7 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
 theorem geom_le {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, c * u k ≤ u (k + 1)) :
     c ^ n * u 0 ≤ u n := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ _ h <;>
-    simp [pow_succ, mul_assoc, le_refl]
+    simp [pow_succ', mul_assoc, le_refl]
 #align geom_le geom_le
 -/
 
@@ -178,7 +178,7 @@ theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   by
   refine' (monotone_mul_left_of_nonneg hc).seq_pos_lt_seq_of_lt_of_le hn _ h _
   · simp
-  · simp [pow_succ, mul_assoc, le_refl]
+  · simp [pow_succ', mul_assoc, le_refl]
 #align lt_geom lt_geom
 -/
 
@@ -186,7 +186,7 @@ theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
 theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, u (k + 1) ≤ c * u k) :
     u n ≤ c ^ n * u 0 := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ h _ <;>
-    simp [pow_succ, mul_assoc, le_refl]
+    simp [pow_succ', mul_assoc, le_refl]
 #align le_geom le_geom
 -/
 

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

@@ -429,7 +429,7 @@ variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ →
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
-  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu 
+  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu
   refine' cauchySeq_of_edist_le_geometric 2⁻¹ C _ hC hu
   simp [ENNReal.one_lt_two]
 #align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_two
@@ -686,7 +686,7 @@ theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : 
       refine'
             mul_le_of_le_one_left (inv_nonneg.mpr <| by exact_mod_cast hn.le) (prod_le_one _ _) <;>
           intro x hx <;>
-        rw [Finset.mem_range] at hx 
+        rw [Finset.mem_range] at hx
       · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
       · refine' (div_le_one <| by exact_mod_cast hn).mpr _; norm_cast; linarith)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop
@@ -714,7 +714,7 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
   by
   have A : tendsto (fun x : R => a - x⁻¹) at_top (𝓝 (a - 0)) :=
     tendsto_const_nhds.sub tendsto_inv_atTop_zero
-  rw [sub_zero] at A 
+  rw [sub_zero] at A
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' A tendsto_const_nhds
   · refine' eventually_at_top.2 ⟨1, fun x hx => _⟩
     simp only [le_div_iff (zero_lt_one.trans_le hx), sub_mul,
@@ -739,7 +739,7 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
   by
   have A : tendsto (fun x : R => a + x⁻¹) at_top (𝓝 (a + 0)) :=
     tendsto_const_nhds.add tendsto_inv_atTop_zero
-  rw [add_zero] at A 
+  rw [add_zero] at A
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds A
   · refine' eventually_at_top.2 ⟨1, fun x hx => _⟩
     rw [le_div_iff (zero_lt_one.trans_le hx)]

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

@@ -31,37 +31,40 @@ open scoped Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
-#print tendsto_inverse_atTop_nhds_0_nat /-
-theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
+#print tendsto_inverse_atTop_nhds_zero_nat /-
+theorem tendsto_inverse_atTop_nhds_zero_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
-#align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
+#align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_zero_nat
 -/
 
-#print tendsto_const_div_atTop_nhds_0_nat /-
-theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
-  simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
-#align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
+#print tendsto_const_div_atTop_nhds_zero_nat /-
+theorem tendsto_const_div_atTop_nhds_zero_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) :=
+  by
+  simpa only [MulZeroClass.mul_zero] using
+    tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_zero_nat
+#align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_zero_nat
 -/
 
-#print NNReal.tendsto_inverse_atTop_nhds_0_nat /-
-theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
-  by rw [← NNReal.tendsto_coe]; exact tendsto_inverse_atTop_nhds_0_nat
-#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
+#print NNReal.tendsto_inverse_atTop_nhds_zero_nat /-
+theorem NNReal.tendsto_inverse_atTop_nhds_zero_nat :
+    Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by rw [← NNReal.tendsto_coe];
+  exact tendsto_inverse_atTop_nhds_zero_nat
+#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_zero_nat
 -/
 
-#print NNReal.tendsto_const_div_atTop_nhds_0_nat /-
-theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
+#print NNReal.tendsto_const_div_atTop_nhds_zero_nat /-
+theorem NNReal.tendsto_const_div_atTop_nhds_zero_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
-  simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
-#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
+  simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_zero_nat
+#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_zero_nat
 -/
 
-#print tendsto_one_div_add_atTop_nhds_0_nat /-
-theorem tendsto_one_div_add_atTop_nhds_0_nat :
+#print tendsto_one_div_add_atTop_nhds_zero_nat /-
+theorem tendsto_one_div_add_atTop_nhds_zero_nat :
     Tendsto (fun n : ℕ => 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ => 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
-  (tendsto_add_atTop_iff_nat 1).2 (tendsto_const_div_atTop_nhds_0_nat 1)
-#align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
+  (tendsto_add_atTop_iff_nat 1).2 (tendsto_const_div_atTop_nhds_zero_nat 1)
+#align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_zero_nat
 -/
 
 #print tendsto_coe_nat_div_add_atTop /-
@@ -89,7 +92,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
       rw [← map_natCast (algebraMap ℝ 𝕜) n, ← map_inv₀ (algebraMap ℝ 𝕜)]
       rfl
     rw [this]
-    exact ((continuous_algebraMap ℝ 𝕜).Tendsto _).comp tendsto_inverse_atTop_nhds_0_nat
+    exact ((continuous_algebraMap ℝ 𝕜).Tendsto _).comp tendsto_inverse_atTop_nhds_zero_nat
 #align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTop
 -/
 
@@ -119,8 +122,8 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 -/
 
-#print tendsto_pow_atTop_nhds_0_of_lt_1 /-
-theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+#print tendsto_pow_atTop_nhds_zero_of_lt_one /-
+theorem tendsto_pow_atTop_nhds_zero_of_lt_one {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   h₁.eq_or_lt.elim
@@ -130,25 +133,25 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
     have : Tendsto (fun n => (r⁻¹ ^ n)⁻¹) atTop (𝓝 0) :=
       tendsto_inv_atTop_zero.comp (tendsto_pow_atTop_atTop_of_one_lt <| one_lt_inv this h₂)
     this.congr fun n => by simp
-#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
+#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_zero_of_lt_one
 -/
 
-#print tendsto_pow_atTop_nhdsWithin_0_of_lt_1 /-
-theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
-    [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
+#print tendsto_pow_atTop_nhdsWithin_zero_of_lt_one /-
+theorem tendsto_pow_atTop_nhdsWithin_zero_of_lt_one {𝕜 : Type _} [LinearOrderedField 𝕜]
+    [Archimedean 𝕜] [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
   tendsto_inf.2
-    ⟨tendsto_pow_atTop_nhds_0_of_lt_1 h₁.le h₂,
+    ⟨tendsto_pow_atTop_nhds_zero_of_lt_one h₁.le h₂,
       tendsto_principal.2 <| eventually_of_forall fun n => pow_pos h₁ _⟩
-#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
+#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
 -/
 
-#print uniformity_basis_dist_pow_of_lt_1 /-
-theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
+#print uniformity_basis_dist_pow_of_lt_one /-
+theorem uniformity_basis_dist_pow_of_lt_one {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) : (𝓤 α).HasBasis (fun k : ℕ => True) fun k => {p : α × α | dist p.1 p.2 < r ^ k} :=
   Metric.mk_uniformity_basis (fun i _ => pow_pos h₀ _) fun ε ε0 =>
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun k hk => ⟨trivial, hk.le⟩
-#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
+#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_one
 -/
 
 #print geom_lt /-
@@ -197,23 +200,24 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
 -/
 
-#print NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 /-
-theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
+#print NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one /-
+theorem NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
-    simp only [NNReal.coe_pow, NNReal.coe_zero, tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
-#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+    simp only [NNReal.coe_pow, NNReal.coe_zero,
+      tendsto_pow_atTop_nhds_zero_of_lt_one r.coe_nonneg hr]
+#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 -/
 
-#print ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 /-
-theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
+#print ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one /-
+theorem ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   by
   rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
   rw [← ENNReal.coe_zero]
   norm_cast at *
-  apply NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 hr
-#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+  apply NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one hr
+#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 -/
 
 /-! ### Geometric series-/
@@ -221,33 +225,33 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
 
 section Geometric
 
-#print hasSum_geometric_of_lt_1 /-
-theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
+#print hasSum_geometric_of_lt_one /-
+theorem hasSum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
   have : Tendsto (fun n => (r ^ n - 1) * (r - 1)⁻¹) atTop (𝓝 ((0 - 1) * (r - 1)⁻¹)) :=
-    ((tendsto_pow_atTop_nhds_0_of_lt_1 h₁ h₂).sub tendsto_const_nhds).mul tendsto_const_nhds
+    ((tendsto_pow_atTop_nhds_zero_of_lt_one h₁ h₂).sub tendsto_const_nhds).mul tendsto_const_nhds
   (hasSum_iff_tendsto_nat_of_nonneg (pow_nonneg h₁) _).mpr <| by
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
-#align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
+#align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_one
 -/
 
-#print summable_geometric_of_lt_1 /-
-theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
+#print summable_geometric_of_lt_one /-
+theorem summable_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ => r ^ n :=
-  ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
-#align summable_geometric_of_lt_1 summable_geometric_of_lt_1
+  ⟨_, hasSum_geometric_of_lt_one h₁ h₂⟩
+#align summable_geometric_of_lt_1 summable_geometric_of_lt_one
 -/
 
-#print tsum_geometric_of_lt_1 /-
-theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
-  (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
-#align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
+#print tsum_geometric_of_lt_one /-
+theorem tsum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+  (hasSum_geometric_of_lt_one h₁ h₂).tsum_eq
+#align tsum_geometric_of_lt_1 tsum_geometric_of_lt_one
 -/
 
 #print hasSum_geometric_two /-
 theorem hasSum_geometric_two : HasSum (fun n : ℕ => ((1 : ℝ) / 2) ^ n) 2 := by
-  convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
+  convert hasSum_geometric_of_lt_one _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
 -/
 
@@ -303,7 +307,8 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) : ∑' i, ite (n ≤ i) ((2 : ℝ)
 #print hasSum_geometric_two' /-
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a :=
   by
-  convert HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one)
+  convert
+    HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_one (le_of_lt one_half_pos) one_half_lt_one)
   · funext n; simp; rfl
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
@@ -328,7 +333,7 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
   apply NNReal.hasSum_coe.1
   push_cast
   rw [NNReal.coe_sub (le_of_lt hr)]
-  exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
+  exact hasSum_geometric_of_lt_one r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
 -/
 
@@ -464,7 +469,7 @@ theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 -
   rcases sign_cases_of_C_mul_pow_nonneg fun n => dist_nonneg.trans (hu n) with (rfl | ⟨C₀, r₀⟩)
   · simp [hasSum_zero]
   · refine' HasSum.mul_left C _
-    simpa using hasSum_geometric_of_lt_1 r₀ hr
+    simpa using hasSum_geometric_of_lt_one r₀ hr
 #align aux_has_sum_of_le_geometric aux_hasSum_of_le_geometric
 -/
 
@@ -546,7 +551,7 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
   refine'
     Summable.of_nonneg_of_le (fun a => one_div_nonneg.mpr (pow_nonneg (zero_le_one.trans hm.le) _))
       (fun a => _)
-      (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
+      (summable_geometric_of_lt_one (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]
   refine' (one_div_le_one_div _ _).mpr (pow_le_pow_right hm.le (fi a)) <;>
@@ -667,7 +672,7 @@ theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
 #print tendsto_factorial_div_pow_self_atTop /-
 theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
-    (tendsto_const_div_atTop_nhds_0_nat 1)
+    (tendsto_const_div_atTop_nhds_zero_nat 1)
     (eventually_of_forall fun n =>
       div_nonneg (by exact_mod_cast n.factorial_pos.le)
         (pow_nonneg (by exact_mod_cast n.zero_le) _))

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

@@ -99,7 +99,8 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
 #print tendsto_add_one_pow_atTop_atTop_of_pos /-
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ => (r + 1) ^ n) atTop atTop :=
-  (tendsto_atTop_atTop_of_monotone' fun n m => pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
+  (tendsto_atTop_atTop_of_monotone' fun n m =>
+      pow_le_pow_right (le_add_of_nonneg_left (le_of_lt h))) <|
     not_bddAbove_iff.2 fun x => Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 -/
@@ -548,7 +549,7 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
       (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]
-  refine' (one_div_le_one_div _ _).mpr (pow_le_pow hm.le (fi a)) <;>
+  refine' (one_div_le_one_div _ _).mpr (pow_le_pow_right hm.le (fi a)) <;>
     exact pow_pos (zero_lt_one.trans hm) _
 #align summable_one_div_pow_of_le summable_one_div_pow_of_le
 -/

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

@@ -289,7 +289,7 @@ theorem tsum_geometric_inv_two : ∑' n : ℕ, (2 : ℝ)⁻¹ ^ n = 2 :=
 theorem tsum_geometric_inv_two_ge (n : ℕ) : ∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0 = 2 * 2⁻¹ ^ n :=
   by
   have A : Summable fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
-    apply summable_of_nonneg_of_le _ _ summable_geometric_two <;>
+    apply Summable.of_nonneg_of_le _ _ summable_geometric_two <;>
       · intro i; by_cases hi : n ≤ i <;> simp [hi]
   have B : ((Finset.range n).Sum fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0) = 0 :=
     Finset.sum_eq_zero fun i hi =>
@@ -543,7 +543,7 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
     Summable fun i => 1 / m ^ f i :=
   by
   refine'
-    summable_of_nonneg_of_le (fun a => one_div_nonneg.mpr (pow_nonneg (zero_le_one.trans hm.le) _))
+    Summable.of_nonneg_of_le (fun a => one_div_nonneg.mpr (pow_nonneg (zero_le_one.trans hm.le) _))
       (fun a => _)
       (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))

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

@@ -3,11 +3,11 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 -/
-import Mathbin.Algebra.GeomSum
-import Mathbin.Order.Filter.Archimedean
-import Mathbin.Order.Iterate
-import Mathbin.Topology.Instances.Ennreal
-import Mathbin.Topology.Algebra.Algebra
+import Algebra.GeomSum
+import Order.Filter.Archimedean
+import Order.Iterate
+import Topology.Instances.Ennreal
+import Topology.Algebra.Algebra
 
 #align_import analysis.specific_limits.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -337,10 +337,10 @@ theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n :
 #align nnreal.summable_geometric NNReal.summable_geometric
 -/
 
-#print tsum_geometric_nNReal /-
-theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+#print tsum_geometric_nnreal /-
+theorem tsum_geometric_nnreal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
-#align tsum_geometric_nnreal tsum_geometric_nNReal
+#align tsum_geometric_nnreal tsum_geometric_nnreal
 -/
 
 #print ENNReal.tsum_geometric /-

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.specific_limits.basic
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GeomSum
 import Mathbin.Order.Filter.Archimedean
@@ -14,6 +9,8 @@ import Mathbin.Order.Iterate
 import Mathbin.Topology.Instances.Ennreal
 import Mathbin.Topology.Algebra.Algebra
 
+#align_import analysis.specific_limits.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 # A collection of specific limit computations
 

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

@@ -34,29 +34,40 @@ open scoped Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
+#print tendsto_inverse_atTop_nhds_0_nat /-
 theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
+-/
 
+#print tendsto_const_div_atTop_nhds_0_nat /-
 theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
+-/
 
+#print NNReal.tendsto_inverse_atTop_nhds_0_nat /-
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
   by rw [← NNReal.tendsto_coe]; exact tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
+-/
 
+#print NNReal.tendsto_const_div_atTop_nhds_0_nat /-
 theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
+-/
 
+#print tendsto_one_div_add_atTop_nhds_0_nat /-
 theorem tendsto_one_div_add_atTop_nhds_0_nat :
     Tendsto (fun n : ℕ => 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ => 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
   (tendsto_add_atTop_iff_nat 1).2 (tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
+-/
 
+#print tendsto_coe_nat_div_add_atTop /-
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 
@@ -83,20 +94,25 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
     rw [this]
     exact ((continuous_algebraMap ℝ 𝕜).Tendsto _).comp tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTop
+-/
 
 /-! ### Powers -/
 
 
+#print tendsto_add_one_pow_atTop_atTop_of_pos /-
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ => (r + 1) ^ n) atTop atTop :=
   (tendsto_atTop_atTop_of_monotone' fun n m => pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
     not_bddAbove_iff.2 fun x => Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
+-/
 
+#print tendsto_pow_atTop_atTop_of_one_lt /-
 theorem tendsto_pow_atTop_atTop_of_one_lt [LinearOrderedRing α] [Archimedean α] {r : α}
     (h : 1 < r) : Tendsto (fun n : ℕ => r ^ n) atTop atTop :=
   sub_add_cancel r 1 ▸ tendsto_add_one_pow_atTop_atTop_of_pos (sub_pos.2 h)
 #align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_lt
+-/
 
 #print Nat.tendsto_pow_atTop_atTop_of_one_lt /-
 theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
@@ -105,6 +121,7 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 -/
 
+#print tendsto_pow_atTop_nhds_0_of_lt_1 /-
 theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
@@ -116,7 +133,9 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
       tendsto_inv_atTop_zero.comp (tendsto_pow_atTop_atTop_of_one_lt <| one_lt_inv this h₂)
     this.congr fun n => by simp
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
+-/
 
+#print tendsto_pow_atTop_nhdsWithin_0_of_lt_1 /-
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
@@ -124,13 +143,17 @@ theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedFie
     ⟨tendsto_pow_atTop_nhds_0_of_lt_1 h₁.le h₂,
       tendsto_principal.2 <| eventually_of_forall fun n => pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
+-/
 
+#print uniformity_basis_dist_pow_of_lt_1 /-
 theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) : (𝓤 α).HasBasis (fun k : ℕ => True) fun k => {p : α × α | dist p.1 p.2 < r ^ k} :=
   Metric.mk_uniformity_basis (fun i _ => pow_pos h₀ _) fun ε ε0 =>
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun k hk => ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
+-/
 
+#print geom_lt /-
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n :=
   by
@@ -138,13 +161,17 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp
   · simp [pow_succ, mul_assoc, le_refl]
 #align geom_lt geom_lt
+-/
 
+#print geom_le /-
 theorem geom_le {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, c * u k ≤ u (k + 1)) :
     c ^ n * u 0 ≤ u n := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ _ h <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align geom_le geom_le
+-/
 
+#print lt_geom /-
 theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, u (k + 1) < c * u k) : u n < c ^ n * u 0 :=
   by
@@ -152,13 +179,17 @@ theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp
   · simp [pow_succ, mul_assoc, le_refl]
 #align lt_geom lt_geom
+-/
 
+#print le_geom /-
 theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, u (k + 1) ≤ c * u k) :
     u n ≤ c ^ n * u 0 := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ h _ <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align le_geom le_geom
+-/
 
+#print tendsto_atTop_of_geom_le /-
 /-- If a sequence `v` of real numbers satisfies `k * v n ≤ v (n+1)` with `1 < k`,
 then it goes to +∞. -/
 theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (hc : 1 < c)
@@ -166,13 +197,17 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
   (tendsto_atTop_mono fun n => geom_le (zero_le_one.trans hc.le) n fun k hk => hu k) <|
     (tendsto_pow_atTop_atTop_of_one_lt hc).atTop_mul_const h₀
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
+-/
 
+#print NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 /-
 theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
     simp only [NNReal.coe_pow, NNReal.coe_zero, tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+-/
 
+#print ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 /-
 theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   by
@@ -181,12 +216,14 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
   norm_cast at *
   apply NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 hr
 #align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+-/
 
 /-! ### Geometric series-/
 
 
 section Geometric
 
+#print hasSum_geometric_of_lt_1 /-
 theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
@@ -195,44 +232,62 @@ theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
   (hasSum_iff_tendsto_nat_of_nonneg (pow_nonneg h₁) _).mpr <| by
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
 #align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
+-/
 
+#print summable_geometric_of_lt_1 /-
 theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ => r ^ n :=
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
+-/
 
+#print tsum_geometric_of_lt_1 /-
 theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
+-/
 
+#print hasSum_geometric_two /-
 theorem hasSum_geometric_two : HasSum (fun n : ℕ => ((1 : ℝ) / 2) ^ n) 2 := by
   convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
+-/
 
+#print summable_geometric_two /-
 theorem summable_geometric_two : Summable fun n : ℕ => ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
 #align summable_geometric_two summable_geometric_two
+-/
 
+#print summable_geometric_two_encode /-
 theorem summable_geometric_two_encode {ι : Type _} [Encodable ι] :
     Summable fun i : ι => (1 / 2 : ℝ) ^ Encodable.encode i :=
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
+-/
 
+#print tsum_geometric_two /-
 theorem tsum_geometric_two : ∑' n : ℕ, ((1 : ℝ) / 2) ^ n = 2 :=
   hasSum_geometric_two.tsum_eq
 #align tsum_geometric_two tsum_geometric_two
+-/
 
+#print sum_geometric_two_le /-
 theorem sum_geometric_two_le (n : ℕ) : ∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i ≤ 2 :=
   by
   have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by intro i; apply pow_nonneg; norm_num
   convert sum_le_tsum (range n) (fun i _ => this i) summable_geometric_two
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
+-/
 
+#print tsum_geometric_inv_two /-
 theorem tsum_geometric_inv_two : ∑' n : ℕ, (2 : ℝ)⁻¹ ^ n = 2 :=
   (inv_eq_one_div (2 : ℝ)).symm ▸ tsum_geometric_two
 #align tsum_geometric_inv_two tsum_geometric_inv_two
+-/
 
+#print tsum_geometric_inv_two_ge /-
 /-- The sum of `2⁻¹ ^ i` for `n ≤ i` equals `2 * 2⁻¹ ^ n`. -/
 theorem tsum_geometric_inv_two_ge (n : ℕ) : ∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0 = 2 * 2⁻¹ ^ n :=
   by
@@ -245,22 +300,30 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) : ∑' i, ite (n ≤ i) ((2 : ℝ)
   simp only [← sum_add_tsum_nat_add n A, B, if_true, zero_add, zero_le', le_add_iff_nonneg_left,
     pow_add, tsum_mul_right, tsum_geometric_inv_two]
 #align tsum_geometric_inv_two_ge tsum_geometric_inv_two_ge
+-/
 
+#print hasSum_geometric_two' /-
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a :=
   by
   convert HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one)
   · funext n; simp; rfl
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
+-/
 
+#print summable_geometric_two' /-
 theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^ n :=
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
+-/
 
+#print tsum_geometric_two' /-
 theorem tsum_geometric_two' (a : ℝ) : ∑' n : ℕ, a / 2 / 2 ^ n = a :=
   (hasSum_geometric_two' a).tsum_eq
 #align tsum_geometric_two' tsum_geometric_two'
+-/
 
+#print NNReal.hasSum_geometric /-
 /-- **Sum of a Geometric Series** -/
 theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   by
@@ -269,15 +332,21 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
   rw [NNReal.coe_sub (le_of_lt hr)]
   exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
+-/
 
+#print NNReal.summable_geometric /-
 theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ => r ^ n :=
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
+-/
 
+#print tsum_geometric_nNReal /-
 theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
 #align tsum_geometric_nnreal tsum_geometric_nNReal
+-/
 
+#print ENNReal.tsum_geometric /-
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
@@ -295,6 +364,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : ∑' n : ℕ, r ^ n = (1 - r)
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
       _ ≤ ∑ i in range n, r ^ i := sum_le_sum fun k _ => one_le_pow_of_one_le' hr k
 #align ennreal.tsum_geometric ENNReal.tsum_geometric
+-/
 
 end Geometric
 
@@ -313,8 +383,7 @@ section EdistLeGeometric
 variable [PseudoEMetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤) {f : ℕ → α}
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C * r ^ n)
 
-include hr hC hu
-
+#print cauchySeq_of_edist_le_geometric /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, `C ≠ ∞`, `r < 1`,
 then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
@@ -324,9 +393,9 @@ theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
   refine' ENNReal.mul_ne_top hC (ENNReal.inv_ne_top.2 _)
   exact (tsub_pos_iff_lt.2 hr).ne'
 #align cauchy_seq_of_edist_le_geometric cauchySeq_of_edist_le_geometric
+-/
 
-omit hr hC
-
+#print edist_le_of_edist_le_geometric_of_tendsto /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -335,13 +404,16 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
   convert edist_le_tsum_of_edist_le_of_tendsto _ hu ha _
   simp only [pow_add, ENNReal.tsum_mul_left, ENNReal.tsum_geometric, div_eq_mul_inv, mul_assoc]
 #align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendsto
+-/
 
+#print edist_le_of_edist_le_geometric_of_tendsto₀ /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
     edist (f 0) a ≤ C / (1 - r) := by
   simpa only [pow_zero, mul_one] using edist_le_of_edist_le_geometric_of_tendsto r C hu ha 0
 #align edist_le_of_edist_le_geometric_of_tendsto₀ edist_le_of_edist_le_geometric_of_tendsto₀
+-/
 
 end EdistLeGeometric
 
@@ -350,8 +422,7 @@ section EdistLeGeometricTwo
 variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ → α}
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C / 2 ^ n) {a : α} (ha : Tendsto f atTop (𝓝 a))
 
-include hC hu
-
+#print cauchySeq_of_edist_le_geometric_two /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
@@ -359,11 +430,9 @@ theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   refine' cauchySeq_of_edist_le_geometric 2⁻¹ C _ hC hu
   simp [ENNReal.one_lt_two]
 #align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_two
+-/
 
-omit hC
-
-include ha
-
+#print edist_le_of_edist_le_geometric_two_of_tendsto /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f n` to the limit of `f` is bounded above by `2 * C * 2^-n`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a ≤ 2 * C / 2 ^ n :=
@@ -373,13 +442,16 @@ theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a
   convert edist_le_of_edist_le_geometric_of_tendsto 2⁻¹ C hu ha n
   rw [ENNReal.one_sub_inv_two, inv_inv]
 #align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendsto
+-/
 
+#print edist_le_of_edist_le_geometric_two_of_tendsto₀ /-
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `2 * C`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto₀ : edist (f 0) a ≤ 2 * C := by
   simpa only [pow_zero, div_eq_mul_inv, inv_one, mul_one] using
     edist_le_of_edist_le_geometric_two_of_tendsto C hu ha 0
 #align edist_le_of_edist_le_geometric_two_of_tendsto₀ edist_le_of_edist_le_geometric_two_of_tendsto₀
+-/
 
 end EdistLeGeometricTwo
 
@@ -388,8 +460,7 @@ section LeGeometric
 variable [PseudoMetricSpace α] {r C : ℝ} (hr : r < 1) {f : ℕ → α}
   (hu : ∀ n, dist (f n) (f (n + 1)) ≤ C * r ^ n)
 
-include hr hu
-
+#print aux_hasSum_of_le_geometric /-
 theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 - r)) :=
   by
   rcases sign_cases_of_C_mul_pow_nonneg fun n => dist_nonneg.trans (hu n) with (rfl | ⟨C₀, r₀⟩)
@@ -397,15 +468,19 @@ theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 -
   · refine' HasSum.mul_left C _
     simpa using hasSum_geometric_of_lt_1 r₀ hr
 #align aux_has_sum_of_le_geometric aux_hasSum_of_le_geometric
+-/
 
 variable (r C)
 
+#print cauchySeq_of_le_geometric /-
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then `f` is a Cauchy sequence.
 Note that this lemma does not assume `0 ≤ C` or `0 ≤ r`. -/
 theorem cauchySeq_of_le_geometric : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩
 #align cauchy_seq_of_le_geometric cauchySeq_of_le_geometric
+-/
 
+#print dist_le_of_le_geometric_of_tendsto₀ /-
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -413,7 +488,9 @@ theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (
   (aux_hasSum_of_le_geometric hr hu).tsum_eq ▸
     dist_le_tsum_of_dist_le_of_tendsto₀ _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩ ha
 #align dist_le_of_le_geometric_of_tendsto₀ dist_le_of_le_geometric_of_tendsto₀
+-/
 
+#print dist_le_of_le_geometric_of_tendsto /-
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -425,25 +502,27 @@ theorem dist_le_of_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝
   rw [mul_comm]
   exact (this.mul_left _).tsum_eq.symm
 #align dist_le_of_le_geometric_of_tendsto dist_le_of_le_geometric_of_tendsto
-
-omit hr hu
+-/
 
 variable (hu₂ : ∀ n, dist (f n) (f (n + 1)) ≤ C / 2 / 2 ^ n)
 
+#print cauchySeq_of_le_geometric_two /-
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then `f` is a Cauchy sequence. -/
 theorem cauchySeq_of_le_geometric_two : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu₂ <| ⟨_, hasSum_geometric_two' C⟩
 #align cauchy_seq_of_le_geometric_two cauchySeq_of_le_geometric_two
+-/
 
+#print dist_le_of_le_geometric_two_of_tendsto₀ /-
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
     dist (f 0) a ≤ C :=
   tsum_geometric_two' C ▸ dist_le_tsum_of_dist_le_of_tendsto₀ _ hu₂ (summable_geometric_two' C) ha
 #align dist_le_of_le_geometric_two_of_tendsto₀ dist_le_of_le_geometric_two_of_tendsto₀
+-/
 
-include hu₂
-
+#print dist_le_of_le_geometric_two_of_tendsto /-
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C / 2^n`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -454,12 +533,14 @@ theorem dist_le_of_le_geometric_two_of_tendsto {a : α} (ha : Tendsto f atTop (
   symm
   exact ((hasSum_geometric_two' C).div_const _).tsum_eq
 #align dist_le_of_le_geometric_two_of_tendsto dist_le_of_le_geometric_two_of_tendsto
+-/
 
 end LeGeometric
 
 /-! ### Summability tests based on comparison with geometric series -/
 
 
+#print summable_one_div_pow_of_le /-
 /-- A series whose terms are bounded by the terms of a converging geometric series converges. -/
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
     Summable fun i => 1 / m ^ f i :=
@@ -473,10 +554,12 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
   refine' (one_div_le_one_div _ _).mpr (pow_le_pow hm.le (fi a)) <;>
     exact pow_pos (zero_lt_one.trans hm) _
 #align summable_one_div_pow_of_le summable_one_div_pow_of_le
+-/
 
 /-! ### Positive sequences with small sums on countable types -/
 
 
+#print posSumOfEncodable /-
 /-- For any positive `ε`, define on an encodable type a positive sequence with sum less than `ε` -/
 def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     { ε' : ι → ℝ // (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c ≤ ε } :=
@@ -490,7 +573,9 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
   · intro i _; exact le_of_lt (f0 _)
   · intro n; exact le_rfl
 #align pos_sum_of_encodable posSumOfEncodable
+-/
 
+#print Set.Countable.exists_pos_hasSum_le /-
 theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s => ε' i) c ∧ c ≤ ε :=
   by
@@ -500,7 +585,9 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   · split_ifs; exacts [hf0 _, zero_lt_one]
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
+-/
 
+#print Set.Countable.exists_pos_forall_sum_le /-
 theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → ∑ i in t, ε' i ≤ ε :=
   by
@@ -510,9 +597,11 @@ theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs :
   refine' (sum_le_hasSum _ _ hε'c).trans hcε
   exact fun _ _ => (hpos _).le
 #align set.countable.exists_pos_forall_sum_le Set.Countable.exists_pos_forall_sum_le
+-/
 
 namespace NNReal
 
+#print NNReal.exists_pos_sum_of_countable /-
 theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c < ε :=
   by
@@ -524,11 +613,13 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Counta
       ⟨c, hasSum_le (fun i => (hε' i).le) hasSum_zero hc⟩, NNReal.hasSum_coe.1 hc,
       aε.trans_le' <| NNReal.coe_le_coe.1 hcε⟩
 #align nnreal.exists_pos_sum_of_countable NNReal.exists_pos_sum_of_countable
+-/
 
 end NNReal
 
 namespace ENNReal
 
+#print ENNReal.exists_pos_sum_of_countable /-
 theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ ∑' i, (ε' i : ℝ≥0∞) < ε :=
   by
@@ -537,13 +628,17 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
   rcases NNReal.exists_pos_sum_of_countable (coe_pos.1 h0r).ne' ι with ⟨ε', hp, c, hc, hcr⟩
   exact ⟨ε', hp, (ENNReal.tsum_coe_eq hc).symm ▸ lt_trans (coe_lt_coe.2 hcr) hrε⟩
 #align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
+-/
 
+#print ENNReal.exists_pos_sum_of_countable' /-
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ ∑' i, ε' i < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
   ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
+-/
 
+#print ENNReal.exists_pos_tsum_mul_lt_of_countable /-
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
     (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ ∑' i, (w i * δ i : ℝ≥0∞) < ε :=
   by
@@ -556,6 +651,7 @@ theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {
   refine' mul_le_of_le_div' (mul_le_mul_left' (ENNReal.inv_le_inv.2 _) _)
   exact coe_le_coe.2 (le_max_right _ _)
 #align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countable
+-/
 
 end ENNReal
 
@@ -570,6 +666,7 @@ theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
 #align factorial_tendsto_at_top factorial_tendsto_atTop
 -/
 
+#print tendsto_factorial_div_pow_self_atTop /-
 theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
     (tendsto_const_div_atTop_nhds_0_nat 1)
@@ -590,6 +687,7 @@ theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : 
       · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
       · refine' (div_le_one <| by exact_mod_cast hn).mpr _; norm_cast; linarith)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop
+-/
 
 /-!
 ### Ceil and floor
@@ -607,6 +705,7 @@ theorem tendsto_nat_floor_atTop {α : Type _} [LinearOrderedSemiring α] [FloorS
 
 variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
+#print tendsto_nat_floor_mul_div_atTop /-
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -623,11 +722,15 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     rw [div_le_iff (zero_lt_one.trans_le hx)]
     simp [Nat.floor_le (mul_nonneg ha (zero_le_one.trans hx))]
 #align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTop
+-/
 
+#print tendsto_nat_floor_div_atTop /-
 theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_floor_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTop
+-/
 
+#print tendsto_nat_ceil_mul_div_atTop /-
 theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -642,10 +745,13 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     simp [div_le_iff (zero_lt_one.trans_le hx), inv_mul_cancel (zero_lt_one.trans_le hx).ne',
       (Nat.ceil_lt_add_one (mul_nonneg ha (zero_le_one.trans hx))).le, add_mul]
 #align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTop
+-/
 
+#print tendsto_nat_ceil_div_atTop /-
 theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop
+-/
 
 end
 

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

@@ -201,7 +201,7 @@ theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
 
-theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
 
@@ -218,23 +218,23 @@ theorem summable_geometric_two_encode {ι : Type _} [Encodable ι] :
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
 
-theorem tsum_geometric_two : (∑' n : ℕ, ((1 : ℝ) / 2) ^ n) = 2 :=
+theorem tsum_geometric_two : ∑' n : ℕ, ((1 : ℝ) / 2) ^ n = 2 :=
   hasSum_geometric_two.tsum_eq
 #align tsum_geometric_two tsum_geometric_two
 
-theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i) ≤ 2 :=
+theorem sum_geometric_two_le (n : ℕ) : ∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i ≤ 2 :=
   by
   have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by intro i; apply pow_nonneg; norm_num
   convert sum_le_tsum (range n) (fun i _ => this i) summable_geometric_two
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
 
-theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
+theorem tsum_geometric_inv_two : ∑' n : ℕ, (2 : ℝ)⁻¹ ^ n = 2 :=
   (inv_eq_one_div (2 : ℝ)).symm ▸ tsum_geometric_two
 #align tsum_geometric_inv_two tsum_geometric_inv_two
 
 /-- The sum of `2⁻¹ ^ i` for `n ≤ i` equals `2 * 2⁻¹ ^ n`. -/
-theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0) = 2 * 2⁻¹ ^ n :=
+theorem tsum_geometric_inv_two_ge (n : ℕ) : ∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0 = 2 * 2⁻¹ ^ n :=
   by
   have A : Summable fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
     apply summable_of_nonneg_of_le _ _ summable_geometric_two <;>
@@ -257,7 +257,7 @@ theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
 
-theorem tsum_geometric_two' (a : ℝ) : (∑' n : ℕ, a / 2 / 2 ^ n) = a :=
+theorem tsum_geometric_two' (a : ℝ) : ∑' n : ℕ, a / 2 / 2 ^ n = a :=
   (hasSum_geometric_two' a).tsum_eq
 #align tsum_geometric_two' tsum_geometric_two'
 
@@ -274,14 +274,14 @@ theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n :
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
-theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
 #align tsum_geometric_nnreal tsum_geometric_nNReal
 
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
-theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   by
   cases' lt_or_le r 1 with hr hr
   · rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
@@ -502,7 +502,7 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
 theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
-    (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → (∑ i in t, ε' i) ≤ ε :=
+    (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → ∑ i in t, ε' i ≤ ε :=
   by
   rcases hs.exists_pos_has_sum_le hε with ⟨ε', hpos, c, hε'c, hcε⟩
   refine' ⟨ε', hpos, fun t ht => _⟩
@@ -530,7 +530,7 @@ end NNReal
 namespace ENNReal
 
 theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
-    ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ (∑' i, (ε' i : ℝ≥0∞)) < ε :=
+    ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ ∑' i, (ε' i : ℝ≥0∞) < ε :=
   by
   rcases exists_between (pos_iff_ne_zero.2 hε) with ⟨r, h0r, hrε⟩
   rcases lt_iff_exists_coe.1 hrε with ⟨x, rfl, hx⟩
@@ -539,13 +539,13 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
 #align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
 
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
-    ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ (∑' i, ε' i) < ε :=
+    ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ ∑' i, ε' i < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
   ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
 
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
-    (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ (∑' i, (w i * δ i : ℝ≥0∞)) < ε :=
+    (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ ∑' i, (w i * δ i : ℝ≥0∞) < ε :=
   by
   lift w to ι → ℝ≥0 using hw
   rcases exists_pos_sum_of_countable hε ι with ⟨δ', Hpos, Hsum⟩

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

@@ -294,7 +294,6 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
     calc
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
       _ ≤ ∑ i in range n, r ^ i := sum_le_sum fun k _ => one_le_pow_of_one_le' hr k
-      
 #align ennreal.tsum_geometric ENNReal.tsum_geometric
 
 end Geometric

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

@@ -126,8 +126,7 @@ theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedFie
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
 
 theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
-    (h₁ : r < 1) :
-    (𝓤 α).HasBasis (fun k : ℕ => True) fun k => { p : α × α | dist p.1 p.2 < r ^ k } :=
+    (h₁ : r < 1) : (𝓤 α).HasBasis (fun k : ℕ => True) fun k => {p : α × α | dist p.1 p.2 < r ^ k} :=
   Metric.mk_uniformity_basis (fun i _ => pow_pos h₀ _) fun ε ε0 =>
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun k hk => ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
@@ -179,7 +178,7 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
   by
   rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
   rw [← ENNReal.coe_zero]
-  norm_cast  at *
+  norm_cast at *
   apply NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 hr
 #align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
@@ -286,7 +285,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
   by
   cases' lt_or_le r 1 with hr hr
   · rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
-    norm_cast  at *
+    norm_cast at *
     convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
     rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr]
   · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_iSup_nat, iSup_eq_top]

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

@@ -357,7 +357,7 @@ include hC hu
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
-  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu
+  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu 
   refine' cauchySeq_of_edist_le_geometric 2⁻¹ C _ hC hu
   simp [ENNReal.one_lt_two]
 #align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_two
@@ -499,7 +499,7 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   haveI := hs.to_encodable
   rcases posSumOfEncodable hε s with ⟨f, hf0, ⟨c, hfc, hcε⟩⟩
   refine' ⟨fun i => if h : i ∈ s then f ⟨i, h⟩ else 1, fun i => _, ⟨c, _, hcε⟩⟩
-  · split_ifs; exacts[hf0 _, zero_lt_one]
+  · split_ifs; exacts [hf0 _, zero_lt_one]
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
@@ -588,7 +588,7 @@ theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : 
       refine'
             mul_le_of_le_one_left (inv_nonneg.mpr <| by exact_mod_cast hn.le) (prod_le_one _ _) <;>
           intro x hx <;>
-        rw [Finset.mem_range] at hx
+        rw [Finset.mem_range] at hx 
       · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
       · refine' (div_le_one <| by exact_mod_cast hn).mpr _; norm_cast; linarith)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop
@@ -614,7 +614,7 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
   by
   have A : tendsto (fun x : R => a - x⁻¹) at_top (𝓝 (a - 0)) :=
     tendsto_const_nhds.sub tendsto_inv_atTop_zero
-  rw [sub_zero] at A
+  rw [sub_zero] at A 
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' A tendsto_const_nhds
   · refine' eventually_at_top.2 ⟨1, fun x hx => _⟩
     simp only [le_div_iff (zero_lt_one.trans_le hx), sub_mul,
@@ -635,7 +635,7 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
   by
   have A : tendsto (fun x : R => a + x⁻¹) at_top (𝓝 (a + 0)) :=
     tendsto_const_nhds.add tendsto_inv_atTop_zero
-  rw [add_zero] at A
+  rw [add_zero] at A 
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds A
   · refine' eventually_at_top.2 ⟨1, fun x hx => _⟩
     rw [le_div_iff (zero_lt_one.trans_le hx)]

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

@@ -30,7 +30,7 @@ noncomputable section
 
 open Classical Set Function Filter Finset Metric
 
-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

@@ -34,65 +34,29 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
-/- warning: tendsto_inverse_at_top_nhds_0_nat -> tendsto_inverse_atTop_nhds_0_nat is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) (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
-  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast 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_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_natₓ'. -/
 theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
 
-/- warning: tendsto_const_div_at_top_nhds_0_nat -> tendsto_const_div_atTop_nhds_0_nat is a dubious translation:
-lean 3 declaration is
-  forall (C : 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))) C ((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)) (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 (C : 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)) C (Nat.cast.{0} Real Real.natCast 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_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_natₓ'. -/
 theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
 
-/- warning: nnreal.tendsto_inverse_at_top_nhds_0_nat -> NNReal.tendsto_inverse_atTop_nhds_0_nat is a dubious translation:
-lean 3 declaration is
-  Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
-but is expected to have type
-  Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
-Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_natₓ'. -/
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
   by rw [← NNReal.tendsto_coe]; exact tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
 
-/- warning: nnreal.tendsto_const_div_at_top_nhds_0_nat -> NNReal.tendsto_const_div_atTop_nhds_0_nat is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_natₓ'. -/
 theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_natₓ'. -/
 theorem tendsto_one_div_add_atTop_nhds_0_nat :
     Tendsto (fun n : ℕ => 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ => 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
   (tendsto_add_atTop_iff_nat 1).2 (tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
-/- warning: tendsto_coe_nat_div_add_at_top -> tendsto_coe_nat_div_add_atTop is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTopₓ'. -/
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 
@@ -123,24 +87,12 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
 /-! ### Powers -/
 
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_posₓ'. -/
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ => (r + 1) ^ n) atTop atTop :=
   (tendsto_atTop_atTop_of_monotone' fun n m => pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
     not_bddAbove_iff.2 fun x => Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_ltₓ'. -/
 theorem tendsto_pow_atTop_atTop_of_one_lt [LinearOrderedRing α] [Archimedean α] {r : α}
     (h : 1 < r) : Tendsto (fun n : ℕ => r ^ n) atTop atTop :=
   sub_add_cancel r 1 ▸ tendsto_add_one_pow_atTop_atTop_of_pos (sub_pos.2 h)
@@ -153,12 +105,6 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 -/
 
-/- warning: tendsto_pow_at_top_nhds_0_of_lt_1 -> tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
-Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
@@ -171,12 +117,6 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
     this.congr fun n => by simp
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
 
-/- warning: tendsto_pow_at_top_nhds_within_0_of_lt_1 -> tendsto_pow_atTop_nhdsWithin_0_of_lt_1 is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
@@ -185,12 +125,6 @@ theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedFie
       tendsto_principal.2 <| eventually_of_forall fun n => pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
 
-/- warning: uniformity_basis_dist_pow_of_lt_1 -> uniformity_basis_dist_pow_of_lt_1 is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1ₓ'. -/
 theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
     (𝓤 α).HasBasis (fun k : ℕ => True) fun k => { p : α × α | dist p.1 p.2 < r ^ k } :=
@@ -198,12 +132,6 @@ theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun k hk => ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
 
-/- warning: geom_lt -> geom_lt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align geom_lt geom_ltₓ'. -/
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n :=
   by
@@ -212,24 +140,12 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp [pow_succ, mul_assoc, le_refl]
 #align geom_lt geom_lt
 
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-Case conversion may be inaccurate. Consider using '#align geom_le geom_leₓ'. -/
 theorem geom_le {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, c * u k ≤ u (k + 1)) :
     c ^ n * u 0 ≤ u n := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ _ h <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align geom_le geom_le
 
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-Case conversion may be inaccurate. Consider using '#align lt_geom lt_geomₓ'. -/
 theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, u (k + 1) < c * u k) : u n < c ^ n * u 0 :=
   by
@@ -238,24 +154,12 @@ theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp [pow_succ, mul_assoc, le_refl]
 #align lt_geom lt_geom
 
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 theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, u (k + 1) ≤ c * u k) :
     u n ≤ c ^ n * u 0 := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ h _ <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align le_geom le_geom
 
-/- warning: tendsto_at_top_of_geom_le -> tendsto_atTop_of_geom_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_leₓ'. -/
 /-- If a sequence `v` of real numbers satisfies `k * v n ≤ v (n+1)` with `1 < k`,
 then it goes to +∞. -/
 theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (hc : 1 < c)
@@ -264,24 +168,12 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
     (tendsto_pow_atTop_atTop_of_one_lt hc).atTop_mul_const h₀
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
 
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 theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
     simp only [NNReal.coe_pow, NNReal.coe_zero, tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
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 theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   by
@@ -296,12 +188,6 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
 
 section Geometric
 
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 theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
@@ -311,74 +197,32 @@ theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
 #align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
 
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 theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ => r ^ n :=
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
 
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 theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
 
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 theorem hasSum_geometric_two : HasSum (fun n : ℕ => ((1 : ℝ) / 2) ^ n) 2 := by
   convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
 
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 theorem summable_geometric_two : Summable fun n : ℕ => ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
 #align summable_geometric_two summable_geometric_two
 
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 theorem summable_geometric_two_encode {ι : Type _} [Encodable ι] :
     Summable fun i : ι => (1 / 2 : ℝ) ^ Encodable.encode i :=
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
 
-/- warning: tsum_geometric_two -> tsum_geometric_two is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tsum_geometric_two tsum_geometric_twoₓ'. -/
 theorem tsum_geometric_two : (∑' n : ℕ, ((1 : ℝ) / 2) ^ n) = 2 :=
   hasSum_geometric_two.tsum_eq
 #align tsum_geometric_two tsum_geometric_two
 
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 theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i) ≤ 2 :=
   by
   have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by intro i; apply pow_nonneg; norm_num
@@ -386,22 +230,10 @@ theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
 
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-Case conversion may be inaccurate. Consider using '#align tsum_geometric_inv_two tsum_geometric_inv_twoₓ'. -/
 theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
   (inv_eq_one_div (2 : ℝ)).symm ▸ tsum_geometric_two
 #align tsum_geometric_inv_two tsum_geometric_inv_two
 
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 /-- The sum of `2⁻¹ ^ i` for `n ≤ i` equals `2 * 2⁻¹ ^ n`. -/
 theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0) = 2 * 2⁻¹ ^ n :=
   by
@@ -415,12 +247,6 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)
     pow_add, tsum_mul_right, tsum_geometric_inv_two]
 #align tsum_geometric_inv_two_ge tsum_geometric_inv_two_ge
 
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-Case conversion may be inaccurate. Consider using '#align has_sum_geometric_two' hasSum_geometric_two'ₓ'. -/
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a :=
   by
   convert HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one)
@@ -428,32 +254,14 @@ theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n)
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
 
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-Case conversion may be inaccurate. Consider using '#align summable_geometric_two' summable_geometric_two'ₓ'. -/
 theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^ n :=
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
 
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 theorem tsum_geometric_two' (a : ℝ) : (∑' n : ℕ, a / 2 / 2 ^ n) = a :=
   (hasSum_geometric_two' a).tsum_eq
 #align tsum_geometric_two' tsum_geometric_two'
 
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-Case conversion may be inaccurate. Consider using '#align nnreal.has_sum_geometric NNReal.hasSum_geometricₓ'. -/
 /-- **Sum of a Geometric Series** -/
 theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   by
@@ -463,32 +271,14 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
   exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
 
-/- warning: nnreal.summable_geometric -> NNReal.summable_geometric is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nnreal.summable_geometric NNReal.summable_geometricₓ'. -/
 theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ => r ^ n :=
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
-/- warning: tsum_geometric_nnreal -> tsum_geometric_nNReal is a dubious translation:
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-  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
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-Case conversion may be inaccurate. Consider using '#align tsum_geometric_nnreal tsum_geometric_nNRealₓ'. -/
 theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
 #align tsum_geometric_nnreal tsum_geometric_nNReal
 
-/- warning: ennreal.tsum_geometric -> ENNReal.tsum_geometric is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.tsum_geometric ENNReal.tsum_geometricₓ'. -/
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
@@ -527,12 +317,6 @@ variable [PseudoEMetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤
 
 include hr hC hu
 
-/- warning: cauchy_seq_of_edist_le_geometric -> cauchySeq_of_edist_le_geometric is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric cauchySeq_of_edist_le_geometricₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, `C ≠ ∞`, `r < 1`,
 then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
@@ -545,12 +329,6 @@ theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
 
 omit hr hC
 
-/- warning: edist_le_of_edist_le_geometric_of_tendsto -> edist_le_of_edist_le_geometric_of_tendsto is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendstoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -560,12 +338,6 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
   simp only [pow_add, ENNReal.tsum_mul_left, ENNReal.tsum_geometric, div_eq_mul_inv, mul_assoc]
 #align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendsto
 
-/- warning: edist_le_of_edist_le_geometric_of_tendsto₀ -> edist_le_of_edist_le_geometric_of_tendsto₀ is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto₀ edist_le_of_edist_le_geometric_of_tendsto₀ₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -582,12 +354,6 @@ variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ →
 
 include hC hu
 
-/- warning: cauchy_seq_of_edist_le_geometric_two -> cauchySeq_of_edist_le_geometric_two is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_twoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
@@ -600,12 +366,6 @@ omit hC
 
 include ha
 
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-Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendstoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f n` to the limit of `f` is bounded above by `2 * C * 2^-n`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a ≤ 2 * C / 2 ^ n :=
@@ -616,12 +376,6 @@ theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a
   rw [ENNReal.one_sub_inv_two, inv_inv]
 #align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto₀ edist_le_of_edist_le_geometric_two_of_tendsto₀ₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `2 * C`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto₀ : edist (f 0) a ≤ 2 * C := by
@@ -638,12 +392,6 @@ variable [PseudoMetricSpace α] {r C : ℝ} (hr : r < 1) {f : ℕ → α}
 
 include hr hu
 
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-Case conversion may be inaccurate. Consider using '#align aux_has_sum_of_le_geometric aux_hasSum_of_le_geometricₓ'. -/
 theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 - r)) :=
   by
   rcases sign_cases_of_C_mul_pow_nonneg fun n => dist_nonneg.trans (hu n) with (rfl | ⟨C₀, r₀⟩)
@@ -654,24 +402,12 @@ theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 -
 
 variable (r C)
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then `f` is a Cauchy sequence.
 Note that this lemma does not assume `0 ≤ C` or `0 ≤ r`. -/
 theorem cauchySeq_of_le_geometric : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩
 #align cauchy_seq_of_le_geometric cauchySeq_of_le_geometric
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -680,12 +416,6 @@ theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (
     dist_le_tsum_of_dist_le_of_tendsto₀ _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩ ha
 #align dist_le_of_le_geometric_of_tendsto₀ dist_le_of_le_geometric_of_tendsto₀
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -702,23 +432,11 @@ omit hr hu
 
 variable (hu₂ : ∀ n, dist (f n) (f (n + 1)) ≤ C / 2 / 2 ^ n)
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then `f` is a Cauchy sequence. -/
 theorem cauchySeq_of_le_geometric_two : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu₂ <| ⟨_, hasSum_geometric_two' C⟩
 #align cauchy_seq_of_le_geometric_two cauchySeq_of_le_geometric_two
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -728,12 +446,6 @@ theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop
 
 include hu₂
 
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 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C / 2^n`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -750,12 +462,6 @@ end LeGeometric
 /-! ### Summability tests based on comparison with geometric series -/
 
 
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 /-- A series whose terms are bounded by the terms of a converging geometric series converges. -/
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
     Summable fun i => 1 / m ^ f i :=
@@ -773,12 +479,6 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
 /-! ### Positive sequences with small sums on countable types -/
 
 
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 /-- For any positive `ε`, define on an encodable type a positive sequence with sum less than `ε` -/
 def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     { ε' : ι → ℝ // (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c ≤ ε } :=
@@ -793,12 +493,6 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
   · intro n; exact le_rfl
 #align pos_sum_of_encodable posSumOfEncodable
 
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 theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s => ε' i) c ∧ c ≤ ε :=
   by
@@ -809,12 +503,6 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
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-  forall {ι : Type.{u1}} {s : Set.{u1} ι}, (Set.Countable.{u1} ι s) -> (forall {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ε' i)) (forall (t : Finset.{u1} ι), (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) s) -> (LE.le.{0} Real Real.hasLe (Finset.sum.{0, u1} Real ι Real.addCommMonoid t (fun (i : ι) => ε' i)) ε)))))
-but is expected to have type
-  forall {ι : Type.{u1}} {s : Set.{u1} ι}, (Set.Countable.{u1} ι s) -> (forall {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ε' i)) (forall (t : Finset.{u1} ι), (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) (Finset.toSet.{u1} ι t) s) -> (LE.le.{0} Real Real.instLEReal (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal t (fun (i : ι) => ε' i)) ε)))))
-Case conversion may be inaccurate. Consider using '#align set.countable.exists_pos_forall_sum_le Set.Countable.exists_pos_forall_sum_leₓ'. -/
 theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → (∑ i in t, ε' i) ≤ ε :=
   by
@@ -827,12 +515,6 @@ theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs :
 
 namespace NNReal
 
-/- warning: nnreal.exists_pos_sum_of_countable -> NNReal.exists_pos_sum_of_countable is a dubious translation:
-lean 3 declaration is
-  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ε' c) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c ε)))))
-but is expected to have type
-  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ε' c) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) c ε)))))
-Case conversion may be inaccurate. Consider using '#align nnreal.exists_pos_sum_of_countable NNReal.exists_pos_sum_of_countableₓ'. -/
 theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c < ε :=
   by
@@ -849,12 +531,6 @@ end NNReal
 
 namespace ENNReal
 
-/- warning: ennreal.exists_pos_sum_of_countable -> ENNReal.exists_pos_sum_of_countable is a dubious translation:
-lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (ε' i))) ε)))
-but is expected to have type
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ENNReal.some (ε' i))) ε)))
-Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countableₓ'. -/
 theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ (∑' i, (ε' i : ℝ≥0∞)) < ε :=
   by
@@ -864,24 +540,12 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
   exact ⟨ε', hp, (ENNReal.tsum_coe_eq hc).symm ▸ lt_trans (coe_lt_coe.2 hcr) hrε⟩
 #align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
 
-/- warning: ennreal.exists_pos_sum_of_countable' -> ENNReal.exists_pos_sum_of_countable' is a dubious translation:
-lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => ε' i)) ε)))
-but is expected to have type
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ε' i)) ε)))
-Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'ₓ'. -/
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ (∑' i, ε' i) < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
   ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
 
-/- warning: ennreal.exists_pos_tsum_mul_lt_of_countable -> ENNReal.exists_pos_tsum_mul_lt_of_countable is a dubious translation:
-lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (δ i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (δ i)))) ε))))
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-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (δ i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (w i) (ENNReal.some (δ i)))) ε))))
-Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countableₓ'. -/
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
     (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ (∑' i, (w i * δ i : ℝ≥0∞)) < ε :=
   by
@@ -908,12 +572,6 @@ theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
 #align factorial_tendsto_at_top factorial_tendsto_atTop
 -/
 
-/- warning: tendsto_factorial_div_pow_self_at_top -> tendsto_factorial_div_pow_self_atTop is a dubious translation:
-lean 3 declaration is
-  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))) ((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)) (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) 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
-  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)) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)) (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) 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_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTopₓ'. -/
 theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
     (tendsto_const_div_atTop_nhds_0_nat 1)
@@ -951,12 +609,6 @@ theorem tendsto_nat_floor_atTop {α : Type _} [LinearOrderedSemiring α] [FloorS
 
 variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
-/- warning: tendsto_nat_floor_mul_div_at_top -> tendsto_nat_floor_mul_div_atTop is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
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-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTopₓ'. -/
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -974,22 +626,10 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     simp [Nat.floor_le (mul_nonneg ha (zero_le_one.trans hx))]
 #align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTop
 
-/- warning: tendsto_nat_floor_div_at_top -> tendsto_nat_floor_div_atTop is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTopₓ'. -/
 theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_floor_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTop
 
-/- warning: tendsto_nat_ceil_mul_div_at_top -> tendsto_nat_ceil_mul_div_atTop is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -1005,12 +645,6 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
       (Nat.ceil_lt_add_one (mul_nonneg ha (zero_le_one.trans hx))).le, add_mul]
 #align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTop
 
-/- warning: tendsto_nat_ceil_div_at_top -> tendsto_nat_ceil_div_atTop is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))))))
-Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop

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

@@ -61,9 +61,7 @@ but is expected to have type
   Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
 Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_natₓ'. -/
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
-  by
-  rw [← NNReal.tendsto_coe]
-  exact tendsto_inverse_atTop_nhds_0_nat
+  by rw [← NNReal.tendsto_coe]; exact tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
 
 /- warning: nnreal.tendsto_const_div_at_top_nhds_0_nat -> NNReal.tendsto_const_div_atTop_nhds_0_nat is a dubious translation:
@@ -383,10 +381,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align sum_geometric_two_le sum_geometric_two_leₓ'. -/
 theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i) ≤ 2 :=
   by
-  have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by
-    intro i
-    apply pow_nonneg
-    norm_num
+  have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by intro i; apply pow_nonneg; norm_num
   convert sum_le_tsum (range n) (fun i _ => this i) summable_geometric_two
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
@@ -412,8 +407,7 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)
   by
   have A : Summable fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
     apply summable_of_nonneg_of_le _ _ summable_geometric_two <;>
-      · intro i
-        by_cases hi : n ≤ i <;> simp [hi]
+      · intro i; by_cases hi : n ≤ i <;> simp [hi]
   have B : ((Finset.range n).Sum fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0) = 0 :=
     Finset.sum_eq_zero fun i hi =>
       ite_eq_right_iff.2 fun h => (lt_irrefl _ ((Finset.mem_range.1 hi).trans_le h)).elim
@@ -430,9 +424,7 @@ Case conversion may be inaccurate. Consider using '#align has_sum_geometric_two'
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a :=
   by
   convert HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one)
-  · funext n
-    simp
-    rfl
+  · funext n; simp; rfl
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
 
@@ -797,10 +789,8 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
   refine' ⟨f ∘ Encodable.encode, fun i => f0 _, _⟩
   rcases hf.summable.comp_injective (@Encodable.encode_injective ι _) with ⟨c, hg⟩
   refine' ⟨c, hg, hasSum_le_inj _ (@Encodable.encode_injective ι _) _ _ hg hf⟩
-  · intro i _
-    exact le_of_lt (f0 _)
-  · intro n
-    exact le_rfl
+  · intro i _; exact le_of_lt (f0 _)
+  · intro n; exact le_rfl
 #align pos_sum_of_encodable posSumOfEncodable
 
 /- warning: set.countable.exists_pos_has_sum_le -> Set.Countable.exists_pos_hasSum_le is a dubious translation:
@@ -815,8 +805,7 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   haveI := hs.to_encodable
   rcases posSumOfEncodable hε s with ⟨f, hf0, ⟨c, hfc, hcε⟩⟩
   refine' ⟨fun i => if h : i ∈ s then f ⟨i, h⟩ else 1, fun i => _, ⟨c, _, hcε⟩⟩
-  · split_ifs
-    exacts[hf0 _, zero_lt_one]
+  · split_ifs; exacts[hf0 _, zero_lt_one]
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
@@ -943,9 +932,7 @@ theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : 
           intro x hx <;>
         rw [Finset.mem_range] at hx
       · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
-      · refine' (div_le_one <| by exact_mod_cast hn).mpr _
-        norm_cast
-        linarith)
+      · refine' (div_le_one <| by exact_mod_cast hn).mpr _; norm_cast; linarith)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop
 
 /-!

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

@@ -127,7 +127,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
 
 /- warning: tendsto_add_one_pow_at_top_at_top_of_pos -> tendsto_add_one_pow_atTop_atTop_of_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemiring.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))) r (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))))))) n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemiring.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))] {r : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))) r (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))))))) n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemiring.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))) r (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_posₓ'. -/
@@ -139,7 +139,7 @@ theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archi
 
 /- warning: tendsto_pow_at_top_at_top_of_one_lt -> tendsto_pow_atTop_atTop_of_one_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_ltₓ'. -/
@@ -157,7 +157,7 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
 
 /- warning: tendsto_pow_at_top_nhds_0_of_lt_1 -> tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
@@ -175,7 +175,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
 
 /- warning: tendsto_pow_at_top_nhds_within_0_of_lt_1 -> tendsto_pow_atTop_nhdsWithin_0_of_lt_1 is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1ₓ'. -/
@@ -268,7 +268,7 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
 
 /- warning: nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 -> NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
 but is expected to have type
   forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))))
 Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
@@ -280,7 +280,7 @@ theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
 
 /- warning: ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 -> ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
 lean 3 declaration is
-  forall {r : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Filter.Tendsto.{0, 0} Nat ENNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))))
+  forall {r : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Filter.Tendsto.{0, 0} Nat ENNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))))
 but is expected to have type
   forall {r : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) r (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (Filter.Tendsto.{0, 0} Nat ENNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))))
 Case conversion may be inaccurate. Consider using '#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
@@ -458,7 +458,7 @@ theorem tsum_geometric_two' (a : ℝ) : (∑' n : ℕ, a / 2 / 2 ^ n) = a :=
 
 /- warning: nnreal.has_sum_geometric -> NNReal.hasSum_geometric is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (HasSum.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (HasSum.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
 but is expected to have type
   forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (HasSum.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) r)))
 Case conversion may be inaccurate. Consider using '#align nnreal.has_sum_geometric NNReal.hasSum_geometricₓ'. -/
@@ -473,7 +473,7 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
 
 /- warning: nnreal.summable_geometric -> NNReal.summable_geometric is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n))
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n))
 but is expected to have type
   forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n))
 Case conversion may be inaccurate. Consider using '#align nnreal.summable_geometric NNReal.summable_geometricₓ'. -/
@@ -483,7 +483,7 @@ theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n :
 
 /- warning: tsum_geometric_nnreal -> tsum_geometric_nNReal is a dubious translation:
 lean 3 declaration is
-  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
 but is expected to have type
   forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n)) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) r)))
 Case conversion may be inaccurate. Consider using '#align tsum_geometric_nnreal tsum_geometric_nNRealₓ'. -/
@@ -537,7 +537,7 @@ include hr hC hu
 
 /- warning: cauchy_seq_of_edist_le_geometric -> cauchySeq_of_edist_le_geometric is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) r (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f))
 Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric cauchySeq_of_edist_le_geometricₓ'. -/
@@ -555,7 +555,7 @@ omit hr hC
 
 /- warning: edist_le_of_edist_le_geometric_of_tendsto -> edist_le_of_edist_le_geometric_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendstoₓ'. -/
@@ -570,7 +570,7 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
 
 /- warning: edist_le_of_edist_le_geometric_of_tendsto₀ -> edist_le_of_edist_le_geometric_of_tendsto₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto₀ edist_le_of_edist_le_geometric_of_tendsto₀ₓ'. -/
@@ -592,7 +592,7 @@ include hC hu
 
 /- warning: cauchy_seq_of_edist_le_geometric_two -> cauchySeq_of_edist_le_geometric_two is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal), (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal), (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal), (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f))
 Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_twoₓ'. -/
@@ -610,7 +610,7 @@ include ha
 
 /- warning: edist_le_of_edist_le_geometric_two_of_tendsto -> edist_le_of_edist_le_geometric_two_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) C) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) C) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) C) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendstoₓ'. -/
@@ -626,7 +626,7 @@ theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a
 
 /- warning: edist_le_of_edist_le_geometric_two_of_tendsto₀ -> edist_le_of_edist_le_geometric_two_of_tendsto₀ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) C)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) C)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) C)))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto₀ edist_le_of_edist_le_geometric_two_of_tendsto₀ₓ'. -/
@@ -840,7 +840,7 @@ namespace NNReal
 
 /- warning: nnreal.exists_pos_sum_of_countable -> NNReal.exists_pos_sum_of_countable is a dubious translation:
 lean 3 declaration is
-  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ε' c) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c ε)))))
+  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ε' c) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c ε)))))
 but is expected to have type
   forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ε' c) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) c ε)))))
 Case conversion may be inaccurate. Consider using '#align nnreal.exists_pos_sum_of_countable NNReal.exists_pos_sum_of_countableₓ'. -/
@@ -862,7 +862,7 @@ namespace ENNReal
 
 /- warning: ennreal.exists_pos_sum_of_countable -> ENNReal.exists_pos_sum_of_countable is a dubious translation:
 lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (ε' i))) ε)))
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (ε' i))) ε)))
 but is expected to have type
   forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ENNReal.some (ε' i))) ε)))
 Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countableₓ'. -/
@@ -877,7 +877,7 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
 
 /- warning: ennreal.exists_pos_sum_of_countable' -> ENNReal.exists_pos_sum_of_countable' is a dubious translation:
 lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => ε' i)) ε)))
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => ε' i)) ε)))
 but is expected to have type
   forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ε' i)) ε)))
 Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'ₓ'. -/
@@ -889,7 +889,7 @@ theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Co
 
 /- warning: ennreal.exists_pos_tsum_mul_lt_of_countable -> ENNReal.exists_pos_tsum_mul_lt_of_countable is a dubious translation:
 lean 3 declaration is
-  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (δ i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (δ i)))) ε))))
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (δ i)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (δ i)))) ε))))
 but is expected to have type
   forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (δ i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (w i) (ENNReal.some (δ i)))) ε))))
 Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countableₓ'. -/
@@ -966,7 +966,7 @@ variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology
 
 /- warning: tendsto_nat_floor_mul_div_at_top -> tendsto_nat_floor_mul_div_atTop is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTopₓ'. -/
@@ -999,7 +999,7 @@ theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) at
 
 /- warning: tendsto_nat_ceil_mul_div_at_top -> tendsto_nat_ceil_mul_div_atTop is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTopₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -495,7 +495,7 @@ theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n)
 lean 3 declaration is
   forall (r : ENNReal), Eq.{1} ENNReal (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (Inv.inv.{0} ENNReal ENNReal.hasInv (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))
 but is expected to have type
-  forall (r : ENNReal), Eq.{1} ENNReal (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))
+  forall (r : ENNReal), Eq.{1} ENNReal (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))
 Case conversion may be inaccurate. Consider using '#align ennreal.tsum_geometric ENNReal.tsum_geometricₓ'. -/
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
@@ -557,7 +557,7 @@ omit hr hC
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendstoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
@@ -572,7 +572,7 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSub) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
 Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto₀ edist_le_of_edist_le_geometric_of_tendsto₀ₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/

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

@@ -507,7 +507,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
     norm_cast  at *
     convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
     rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr]
-  · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_supᵢ_nat, supᵢ_eq_top]
+  · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_iSup_nat, iSup_eq_top]
     refine' fun a ha =>
       (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
     calc

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

@@ -93,7 +93,7 @@ theorem tendsto_one_div_add_atTop_nhds_0_nat :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : DivisionRing.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : CharZero.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))] [_inst_4 : Algebra.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))] [_inst_5 : ContinuousSMul.{0, u1} Real 𝕜 (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)) _inst_4))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_2] [_inst_6 : TopologicalDivisionRing.{u1} 𝕜 _inst_1 _inst_2] (x : 𝕜), Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) n) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) n) x)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_2 (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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : DivisionRing.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : CharZero.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))] [_inst_4 : Algebra.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))] [_inst_5 : ContinuousSMul.{0, u1} Real 𝕜 (Algebra.toSMul.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1)) _inst_4) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_2] [_inst_6 : TopologicalDivisionRing.{u1} 𝕜 _inst_1 _inst_2] (x : 𝕜), Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivisionRing.toDiv.{u1} 𝕜 _inst_1)) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))) n) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))) n) x)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : DivisionRing.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : CharZero.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))] [_inst_4 : Algebra.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))] [_inst_5 : ContinuousSMul.{0, u1} Real 𝕜 (Algebra.toSMul.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1)) _inst_4) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_2] [_inst_6 : TopologicalDivisionRing.{u1} 𝕜 _inst_1 _inst_2] (x : 𝕜), Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivisionRing.toDiv.{u1} 𝕜 _inst_1)) (Nat.cast.{u1} 𝕜 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))) n) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))) n) x)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTopₓ'. -/
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
@@ -141,7 +141,7 @@ theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archi
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_ltₓ'. -/
 theorem tendsto_pow_atTop_atTop_of_one_lt [LinearOrderedRing α] [Archimedean α] {r : α}
     (h : 1 < r) : Tendsto (fun n : ℕ => r ^ n) atTop atTop :=
@@ -159,7 +159,7 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
@@ -177,7 +177,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
@@ -968,7 +968,7 @@ variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTopₓ'. -/
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) :=
@@ -991,7 +991,7 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTopₓ'. -/
 theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_floor_mul_div_atTop (zero_le_one' R)
@@ -1001,7 +1001,7 @@ theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) at
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) :=
@@ -1022,7 +1022,7 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2)))))))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module analysis.specific_limits.basic
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Topology.Algebra.Algebra
 /-!
 # 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, by design, is independent of `normed_space` in the import hierarchy.  It contains
 important specific limit computations in metric spaces, in ordered rings/fields, and in specific
 instances of these such as `ℝ`, `ℝ≥0` and `ℝ≥0∞`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -31,31 +31,67 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
+/- warning: tendsto_inverse_at_top_nhds_0_nat -> tendsto_inverse_atTop_nhds_0_nat is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Inv.inv.{0} Real Real.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) (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
+  Filter.Tendsto.{0, 0} Nat Real (fun (n : Nat) => Inv.inv.{0} Real Real.instInvReal (Nat.cast.{0} Real Real.natCast 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_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_natₓ'. -/
 theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
 
+/- warning: tendsto_const_div_at_top_nhds_0_nat -> tendsto_const_div_atTop_nhds_0_nat is a dubious translation:
+lean 3 declaration is
+  forall (C : 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))) C ((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)) (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 (C : 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)) C (Nat.cast.{0} Real Real.natCast 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_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_natₓ'. -/
 theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
 
+/- warning: nnreal.tendsto_inverse_at_top_nhds_0_nat -> NNReal.tendsto_inverse_atTop_nhds_0_nat is a dubious translation:
+lean 3 declaration is
+  Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+but is expected to have type
+  Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
+Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_natₓ'. -/
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
   by
   rw [← NNReal.tendsto_coe]
   exact tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
 
+/- warning: nnreal.tendsto_const_div_at_top_nhds_0_nat -> NNReal.tendsto_const_div_atTop_nhds_0_nat is a dubious translation:
+lean 3 declaration is
+  forall (C : NNReal), Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal NNReal.hasDiv) C ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat NNReal (HasLiftT.mk.{1, 1} Nat NNReal (CoeTCₓ.coe.{1, 1} Nat NNReal (Nat.castCoe.{0} NNReal (AddMonoidWithOne.toNatCast.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))))
+but is expected to have type
+  forall (C : NNReal), Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} NNReal NNReal NNReal (instHDiv.{0} NNReal (CanonicallyLinearOrderedSemifield.toDiv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal)) C (Nat.cast.{0} NNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} NNReal instNNRealCanonicallyOrderedCommSemiring) n)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)))
+Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_natₓ'. -/
 theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
   simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
 
+/- warning: tendsto_one_div_add_at_top_nhds_0_nat -> tendsto_one_div_add_atTop_nhds_0_nat is a dubious translation:
+lean 3 declaration is
+  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))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (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
+  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)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Nat.cast.{0} Real Real.natCast n) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (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_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_natₓ'. -/
 theorem tendsto_one_div_add_atTop_nhds_0_nat :
     Tendsto (fun n : ℕ => 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ => 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
   (tendsto_add_atTop_iff_nat 1).2 (tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
+/- warning: tendsto_coe_nat_div_add_at_top -> tendsto_coe_nat_div_add_atTop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : DivisionRing.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : CharZero.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))] [_inst_4 : Algebra.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))] [_inst_5 : ContinuousSMul.{0, u1} Real 𝕜 (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)) _inst_4))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_2] [_inst_6 : TopologicalDivisionRing.{u1} 𝕜 _inst_1 _inst_2] (x : 𝕜), Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) n) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))) n) x)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_2 (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 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : DivisionRing.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : CharZero.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1)))] [_inst_4 : Algebra.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1))] [_inst_5 : ContinuousSMul.{0, u1} Real 𝕜 (Algebra.toSMul.{0, u1} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u1} 𝕜 (DivisionRing.toDivisionSemiring.{u1} 𝕜 _inst_1)) _inst_4) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_2] [_inst_6 : TopologicalDivisionRing.{u1} 𝕜 _inst_1 _inst_2] (x : 𝕜), Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivisionRing.toDiv.{u1} 𝕜 _inst_1)) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))) n) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))))) (Nat.cast.{u1} 𝕜 (NonAssocRing.toNatCast.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))) n) x)) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_2 (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTopₓ'. -/
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 
@@ -86,22 +122,42 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
 /-! ### Powers -/
 
 
+/- warning: tendsto_add_one_pow_at_top_at_top_of_pos -> tendsto_add_one_pow_atTop_atTop_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemiring.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))) r (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))))))) n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemiring.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1))))))) r (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))) n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_posₓ'. -/
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ => (r + 1) ^ n) atTop atTop :=
   (tendsto_atTop_atTop_of_monotone' fun n m => pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
     not_bddAbove_iff.2 fun x => Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 
+/- warning: tendsto_pow_at_top_at_top_of_one_lt -> tendsto_pow_atTop_atTop_of_one_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (Ring.toMonoid.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedRing.{u1} α] [_inst_2 : Archimedean.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))] {r : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))) r) -> (Filter.Tendsto.{0, u1} Nat α (fun (n : Nat) => HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toLinearOrderedSemiring.{u1} α _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_ltₓ'. -/
 theorem tendsto_pow_atTop_atTop_of_one_lt [LinearOrderedRing α] [Archimedean α] {r : α}
     (h : 1 < r) : Tendsto (fun n : ℕ => r ^ n) atTop atTop :=
   sub_add_cancel r 1 ▸ tendsto_add_one_pow_atTop_atTop_of_pos (sub_pos.2 h)
 #align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_lt
 
+#print Nat.tendsto_pow_atTop_atTop_of_one_lt /-
 theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
     Tendsto (fun n : ℕ => m ^ n) atTop atTop :=
   tsub_add_cancel_of_le (le_of_lt h) ▸ tendsto_add_one_pow_atTop_atTop_of_pos (tsub_pos_of_lt h)
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
+-/
 
+/- warning: tendsto_pow_at_top_nhds_0_of_lt_1 -> tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
@@ -114,6 +170,12 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
     this.congr fun n => by simp
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
 
+/- warning: tendsto_pow_at_top_nhds_within_0_of_lt_1 -> tendsto_pow_atTop_nhdsWithin_0_of_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (fun (n : Nat) => HPow.hPow.{u1, 0, u1} 𝕜 Nat 𝕜 (instHPow.{u1, 0} 𝕜 Nat (Monoid.Pow.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} 𝕜 _inst_3 (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : Archimedean.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))] [_inst_3 : TopologicalSpace.{u1} 𝕜] [_inst_4 : OrderTopology.{u1} 𝕜 _inst_3 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))] {r : 𝕜}, (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) r) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) r (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{0, u1} Nat 𝕜 (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 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} 𝕜 _inst_3 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (Set.Ioi.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{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 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1ₓ'. -/
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
@@ -122,6 +184,12 @@ theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedFie
       tendsto_principal.2 <| eventually_of_forall fun n => pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
 
+/- warning: uniformity_basis_dist_pow_of_lt_1 -> uniformity_basis_dist_pow_of_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {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)))) -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (k : Nat) => True) (fun (k : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r k))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {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))) -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (k : Nat) => True) (fun (k : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r k))))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1ₓ'. -/
 theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
     (𝓤 α).HasBasis (fun k : ℕ => True) fun k => { p : α × α | dist p.1 p.2 < r ^ k } :=
@@ -129,6 +197,12 @@ theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun k hk => ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
 
+/- warning: geom_lt -> geom_lt is a dubious translation:
+lean 3 declaration is
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) c) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall (k : Nat), (LT.lt.{0} Nat Nat.hasLt k n) -> (LT.lt.{0} Real Real.hasLt (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) c (u k)) (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) -> (LT.lt.{0} Real Real.hasLt (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (u n)))
+but is expected to have type
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) c) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (k : Nat), (LT.lt.{0} Nat instLTNat k n) -> (LT.lt.{0} Real Real.instLTReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) c (u k)) (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (LT.lt.{0} Real Real.instLTReal (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (u n)))
+Case conversion may be inaccurate. Consider using '#align geom_lt geom_ltₓ'. -/
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n :=
   by
@@ -137,12 +211,24 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp [pow_succ, mul_assoc, le_refl]
 #align geom_lt geom_lt
 
+/- warning: geom_le -> geom_le is a dubious translation:
+lean 3 declaration is
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) c) -> (forall (n : Nat), (forall (k : Nat), (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) c (u k)) (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) -> (LE.le.{0} Real Real.hasLe (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (u n)))
+but is expected to have type
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) c) -> (forall (n : Nat), (forall (k : Nat), (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) c (u k)) (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (LE.le.{0} Real Real.instLEReal (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (u n)))
+Case conversion may be inaccurate. Consider using '#align geom_le geom_leₓ'. -/
 theorem geom_le {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, c * u k ≤ u (k + 1)) :
     c ^ n * u 0 ≤ u n := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ _ h <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align geom_le geom_le
 
+/- warning: lt_geom -> lt_geom is a dubious translation:
+lean 3 declaration is
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) c) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall (k : Nat), (LT.lt.{0} Nat Nat.hasLt k n) -> (LT.lt.{0} Real Real.hasLt (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) c (u k)))) -> (LT.lt.{0} Real Real.hasLt (u n) (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))))
+but is expected to have type
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) c) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (k : Nat), (LT.lt.{0} Nat instLTNat k n) -> (LT.lt.{0} Real Real.instLTReal (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) c (u k)))) -> (LT.lt.{0} Real Real.instLTReal (u n) (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align lt_geom lt_geomₓ'. -/
 theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, u (k + 1) < c * u k) : u n < c ^ n * u 0 :=
   by
@@ -151,12 +237,24 @@ theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
   · simp [pow_succ, mul_assoc, le_refl]
 #align lt_geom lt_geom
 
+/- warning: le_geom -> le_geom is a dubious translation:
+lean 3 declaration is
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) c) -> (forall (n : Nat), (forall (k : Nat), (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} Real Real.hasLe (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) c (u k)))) -> (LE.le.{0} Real Real.hasLe (u n) (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))))
+but is expected to have type
+  forall {u : Nat -> Real} {c : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) c) -> (forall (n : Nat), (forall (k : Nat), (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} Real Real.instLEReal (u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) c (u k)))) -> (LE.le.{0} Real Real.instLEReal (u n) (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)) c n) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align le_geom le_geomₓ'. -/
 theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, u (k + 1) ≤ c * u k) :
     u n ≤ c ^ n * u 0 := by
   refine' (monotone_mul_left_of_nonneg hc).seq_le_seq n _ h _ <;>
     simp [pow_succ, mul_assoc, le_refl]
 #align le_geom le_geom
 
+/- warning: tendsto_at_top_of_geom_le -> tendsto_atTop_of_geom_le is a dubious translation:
+lean 3 declaration is
+  forall {v : Nat -> Real} {c : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (v (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) c) -> (forall (n : Nat), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) c (v n)) (v (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.Tendsto.{0, 0} Nat Real v (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (Filter.atTop.{0} Real Real.preorder))
+but is expected to have type
+  forall {v : Nat -> Real} {c : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (v (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) c) -> (forall (n : Nat), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) c (v n)) (v (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) -> (Filter.Tendsto.{0, 0} Nat Real v (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (Filter.atTop.{0} Real Real.instPreorderReal))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_leₓ'. -/
 /-- If a sequence `v` of real numbers satisfies `k * v n ≤ v (n+1)` with `1 < k`,
 then it goes to +∞. -/
 theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (hc : 1 < c)
@@ -165,12 +263,24 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
     (tendsto_pow_atTop_atTop_of_one_lt hc).atTop_mul_const h₀
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
 
+/- warning: nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 -> NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} NNReal NNReal.topologicalSpace (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
+but is expected to have type
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Filter.Tendsto.{0, 0} Nat NNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} NNReal NNReal.instTopologicalSpaceNNReal (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))))
+Case conversion may be inaccurate. Consider using '#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
 theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
     simp only [NNReal.coe_pow, NNReal.coe_zero, tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
+/- warning: ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 -> ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 is a dubious translation:
+lean 3 declaration is
+  forall {r : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Filter.Tendsto.{0, 0} Nat ENNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} ENNReal ENNReal.topologicalSpace (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))))
+but is expected to have type
+  forall {r : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) r (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (Filter.Tendsto.{0, 0} Nat ENNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))))
+Case conversion may be inaccurate. Consider using '#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1ₓ'. -/
 theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   by
@@ -185,6 +295,12 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
 
 section Geometric
 
+/- warning: has_sum_geometric_of_lt_1 -> hasSum_geometric_of_lt_1 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)))) -> (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}, (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))) -> (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_lt_1 hasSum_geometric_of_lt_1ₓ'. -/
 theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
@@ -194,32 +310,74 @@ theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
 #align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
 
+/- warning: summable_geometric_of_lt_1 -> summable_geometric_of_lt_1 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)))) -> (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}, (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))) -> (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_lt_1 summable_geometric_of_lt_1ₓ'. -/
 theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ => r ^ n :=
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
 
+/- warning: tsum_geometric_of_lt_1 -> tsum_geometric_of_lt_1 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)))) -> (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}, (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))) -> (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_lt_1 tsum_geometric_of_lt_1ₓ'. -/
 theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
 
+/- warning: has_sum_geometric_two -> hasSum_geometric_two is a dubious translation:
+lean 3 declaration is
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) n) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align has_sum_geometric_two hasSum_geometric_twoₓ'. -/
 theorem hasSum_geometric_two : HasSum (fun n : ℕ => ((1 : ℝ) / 2) ^ n) 2 := by
   convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
 
+/- warning: summable_geometric_two -> summable_geometric_two is a dubious translation:
+lean 3 declaration is
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) n)
+but is expected to have type
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)
+Case conversion may be inaccurate. Consider using '#align summable_geometric_two summable_geometric_twoₓ'. -/
 theorem summable_geometric_two : Summable fun n : ℕ => ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
 #align summable_geometric_two summable_geometric_two
 
+/- warning: summable_geometric_two_encode -> summable_geometric_two_encode is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Encodable.{u1} ι], Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (Encodable.encode.{u1} ι _inst_1 i))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Encodable.{u1} ι], Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Encodable.encode.{u1} ι _inst_1 i))
+Case conversion may be inaccurate. Consider using '#align summable_geometric_two_encode summable_geometric_two_encodeₓ'. -/
 theorem summable_geometric_two_encode {ι : Type _} [Encodable ι] :
     Summable fun i : ι => (1 / 2 : ℝ) ^ Encodable.encode i :=
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
 
+/- warning: tsum_geometric_two -> tsum_geometric_two is a dubious translation:
+lean 3 declaration is
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) n)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_two tsum_geometric_twoₓ'. -/
 theorem tsum_geometric_two : (∑' n : ℕ, ((1 : ℝ) / 2) ^ n) = 2 :=
   hasSum_geometric_two.tsum_eq
 #align tsum_geometric_two tsum_geometric_two
 
+/- warning: sum_geometric_two_le -> sum_geometric_two_le is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), LE.le.{0} Real Real.hasLe (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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) i)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall (n : Nat), LE.le.{0} Real Real.instLEReal (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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) i)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align sum_geometric_two_le sum_geometric_two_leₓ'. -/
 theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)) ^ i) ≤ 2 :=
   by
   have : ∀ i, 0 ≤ (1 / (2 : ℝ)) ^ i := by
@@ -230,10 +388,22 @@ theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
 
+/- warning: tsum_geometric_inv_two -> tsum_geometric_inv_two is a dubious translation:
+lean 3 declaration is
+  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)) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) n)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  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)) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_inv_two tsum_geometric_inv_twoₓ'. -/
 theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
   (inv_eq_one_div (2 : ℝ)).symm ▸ tsum_geometric_two
 #align tsum_geometric_inv_two tsum_geometric_inv_two
 
+/- warning: tsum_geometric_inv_two_ge -> tsum_geometric_inv_two_ge is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (tsum.{0, 0} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (i : Nat) => ite.{1} Real (LE.le.{0} Nat Nat.hasLe n i) (Nat.decidableLe n i) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) i) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) n))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Real (tsum.{0, 0} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (i : Nat) => ite.{1} Real (LE.le.{0} Nat instLENat n i) (Nat.decLe n i) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) i) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_inv_two_ge tsum_geometric_inv_two_geₓ'. -/
 /-- The sum of `2⁻¹ ^ i` for `n ≤ i` equals `2 * 2⁻¹ ^ n`. -/
 theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0) = 2 * 2⁻¹ ^ n :=
   by
@@ -248,6 +418,12 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) : (∑' i, ite (n ≤ i) ((2 : ℝ)
     pow_add, tsum_mul_right, tsum_geometric_inv_two]
 #align tsum_geometric_inv_two_ge tsum_geometric_inv_two_ge
 
+/- warning: has_sum_geometric_two' -> hasSum_geometric_two' is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), HasSum.{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))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) a (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) n)) a
+but is expected to have type
+  forall (a : Real), HasSum.{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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) a (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n)) a
+Case conversion may be inaccurate. Consider using '#align has_sum_geometric_two' hasSum_geometric_two'ₓ'. -/
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a :=
   by
   convert HasSum.mul_left (a / 2) (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one)
@@ -257,14 +433,32 @@ theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n)
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
 
+/- warning: summable_geometric_two' -> summable_geometric_two' is a dubious translation:
+lean 3 declaration is
+  forall (a : 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))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) a (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) n))
+but is expected to have type
+  forall (a : 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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) a (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))
+Case conversion may be inaccurate. Consider using '#align summable_geometric_two' summable_geometric_two'ₓ'. -/
 theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^ n :=
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
 
+/- warning: tsum_geometric_two' -> tsum_geometric_two' is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} Real (tsum.{0, 0} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) a (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) n))) a
+but is expected to have type
+  forall (a : Real), Eq.{1} Real (tsum.{0, 0} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Nat (fun (n : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) a (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) a
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_two' tsum_geometric_two'ₓ'. -/
 theorem tsum_geometric_two' (a : ℝ) : (∑' n : ℕ, a / 2 / 2 ^ n) = a :=
   (hasSum_geometric_two' a).tsum_eq
 #align tsum_geometric_two' tsum_geometric_two'
 
+/- warning: nnreal.has_sum_geometric -> NNReal.hasSum_geometric is a dubious translation:
+lean 3 declaration is
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (HasSum.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
+but is expected to have type
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (HasSum.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) r)))
+Case conversion may be inaccurate. Consider using '#align nnreal.has_sum_geometric NNReal.hasSum_geometricₓ'. -/
 /-- **Sum of a Geometric Series** -/
 theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
   by
@@ -274,14 +468,32 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
   exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
 
+/- warning: nnreal.summable_geometric -> NNReal.summable_geometric is a dubious translation:
+lean 3 declaration is
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n))
+but is expected to have type
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Summable.{0, 0} NNReal Nat (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n))
+Case conversion may be inaccurate. Consider using '#align nnreal.summable_geometric NNReal.summable_geometricₓ'. -/
 theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ => r ^ n :=
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
+/- warning: tsum_geometric_nnreal -> tsum_geometric_nNReal is a dubious translation:
+lean 3 declaration is
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) r (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) r n)) (Inv.inv.{0} NNReal (DivInvMonoid.toHasInv.{0} NNReal (GroupWithZero.toDivInvMonoid.{0} NNReal (DivisionSemiring.toGroupWithZero.{0} NNReal (Semifield.toDivisionSemiring.{0} NNReal (LinearOrderedSemifield.toSemifield.{0} NNReal (CanonicallyLinearOrderedSemifield.toLinearOrderedSemifield.{0} NNReal NNReal.canonicallyLinearOrderedSemifield)))))) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.hasSub) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) r)))
+but is expected to have type
+  forall {r : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) r (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne))) -> (Eq.{1} NNReal (tsum.{0, 0} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) r n)) (Inv.inv.{0} NNReal (CanonicallyLinearOrderedSemifield.toInv.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (HSub.hSub.{0, 0, 0} NNReal NNReal NNReal (instHSub.{0} NNReal NNReal.instSubNNReal) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) r)))
+Case conversion may be inaccurate. Consider using '#align tsum_geometric_nnreal tsum_geometric_nNRealₓ'. -/
 theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
 #align tsum_geometric_nnreal tsum_geometric_nNReal
 
+/- warning: ennreal.tsum_geometric -> ENNReal.tsum_geometric is a dubious translation:
+lean 3 declaration is
+  forall (r : ENNReal), Eq.{1} ENNReal (tsum.{0, 0} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (Inv.inv.{0} ENNReal ENNReal.hasInv (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))
+but is expected to have type
+  forall (r : ENNReal), Eq.{1} ENNReal (tsum.{0, 0} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal Nat (fun (n : Nat) => HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))
+Case conversion may be inaccurate. Consider using '#align ennreal.tsum_geometric ENNReal.tsum_geometricₓ'. -/
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
@@ -320,6 +532,12 @@ variable [PseudoEMetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤
 
 include hr hC hu
 
+/- warning: cauchy_seq_of_edist_le_geometric -> cauchySeq_of_edist_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) r (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) -> (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) r (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) -> (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric cauchySeq_of_edist_le_geometricₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, `C ≠ ∞`, `r < 1`,
 then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
@@ -332,6 +550,12 @@ theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
 
 omit hr hC
 
+/- warning: edist_le_of_edist_le_geometric_of_tendsto -> edist_le_of_edist_le_geometric_of_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n)) (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
+Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendstoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -341,6 +565,12 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
   simp only [pow_add, ENNReal.tsum_mul_left, ENNReal.tsum_geometric, div_eq_mul_inv, mul_assoc]
 #align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendsto
 
+/- warning: edist_le_of_edist_le_geometric_of_tendsto₀ -> edist_le_of_edist_le_geometric_of_tendsto₀ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.hasSub) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) r))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (r : ENNReal) (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (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} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) r n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HSub.hSub.{0, 0, 0} ENNReal ENNReal ENNReal (instHSub.{0} ENNReal ENNReal.instSubENNReal) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) r))))
+Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_of_tendsto₀ edist_le_of_edist_le_geometric_of_tendsto₀ₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem edist_le_of_edist_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -357,6 +587,12 @@ variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ →
 
 include hC hu
 
+/- warning: cauchy_seq_of_edist_le_geometric_two -> cauchySeq_of_edist_le_geometric_two is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal), (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal), (Ne.{1} ENNReal C (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_twoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
@@ -369,6 +605,12 @@ omit hC
 
 include ha
 
+/- warning: edist_le_of_edist_le_geometric_two_of_tendsto -> edist_le_of_edist_le_geometric_two_of_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) (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)))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toHasDiv.{0} ENNReal ENNReal.divInvMonoid)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) C) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) n))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (C : ENNReal) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) C (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (forall {a : α}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (forall (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f n) a) (HDiv.hDiv.{0, 0, 0} ENNReal ENNReal ENNReal (instHDiv.{0} ENNReal (DivInvMonoid.toDiv.{0} ENNReal ENNReal.instDivInvMonoidENNReal)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) C) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))))
+Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendstoₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f n` to the limit of `f` is bounded above by `2 * C * 2^-n`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a ≤ 2 * C / 2 ^ n :=
@@ -379,6 +621,12 @@ theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a
   rw [ENNReal.one_sub_inv_two, inv_inv]
 #align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendsto
 
+/- warning: edist_le_of_edist_le_geometric_two_of_tendsto₀ -> edist_le_of_edist_le_geometric_two_of_tendsto₀ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align edist_le_of_edist_le_geometric_two_of_tendsto₀ edist_le_of_edist_le_geometric_two_of_tendsto₀ₓ'. -/
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `2 * C`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto₀ : edist (f 0) a ≤ 2 * C := by
@@ -395,6 +643,12 @@ variable [PseudoMetricSpace α] {r C : ℝ} (hr : r < 1) {f : ℕ → α}
 
 include hr hu
 
+/- warning: aux_has_sum_of_le_geometric -> aux_hasSum_of_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {r : Real} {C : 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 {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (f n) (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) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n))) -> (HasSum.{0, 0} Real Nat Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) C (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 : PseudoMetricSpace.{u1} α] {r : Real} {C : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (f n) (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) C (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n))) -> (HasSum.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (n : Nat) => 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)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) C (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 aux_has_sum_of_le_geometric aux_hasSum_of_le_geometricₓ'. -/
 theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 - r)) :=
   by
   rcases sign_cases_of_C_mul_pow_nonneg fun n => dist_nonneg.trans (hu n) with (rfl | ⟨C₀, r₀⟩)
@@ -405,12 +659,24 @@ theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 -
 
 variable (r C)
 
+/- warning: cauchy_seq_of_le_geometric -> cauchySeq_of_le_geometric is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] (r : Real) (C : 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 {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (f n) (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) 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 _inst_1) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] (r : Real) (C : Real), (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (f n) (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) 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 _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_le_geometric cauchySeq_of_le_geometricₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then `f` is a Cauchy sequence.
 Note that this lemma does not assume `0 ≤ C` or `0 ≤ r`. -/
 theorem cauchySeq_of_le_geometric : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩
 #align cauchy_seq_of_le_geometric cauchySeq_of_le_geometric
 
+/- warning: dist_le_of_le_geometric_of_tendsto₀ -> dist_le_of_le_geometric_of_tendsto₀ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] (r : Real) (C : 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 {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (f n) (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) 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}, (Filter.Tendsto.{0, u1} Nat α f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) a) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) C (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)))))
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+Case conversion may be inaccurate. Consider using '#align dist_le_of_le_geometric_of_tendsto₀ dist_le_of_le_geometric_of_tendsto₀ₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f n` to the limit of `f` is bounded above by `C * r^n / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -419,6 +685,12 @@ theorem dist_le_of_le_geometric_of_tendsto₀ {a : α} (ha : Tendsto f atTop (
     dist_le_tsum_of_dist_le_of_tendsto₀ _ hu ⟨_, aux_hasSum_of_le_geometric hr hu⟩ ha
 #align dist_le_of_le_geometric_of_tendsto₀ dist_le_of_le_geometric_of_tendsto₀
 
+/- warning: dist_le_of_le_geometric_of_tendsto -> dist_le_of_le_geometric_of_tendsto is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dist_le_of_le_geometric_of_tendsto dist_le_of_le_geometric_of_tendstoₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C / (1 - r)`. -/
 theorem dist_le_of_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -435,11 +707,23 @@ omit hr hu
 
 variable (hu₂ : ∀ n, dist (f n) (f (n + 1)) ≤ C / 2 / 2 ^ n)
 
+/- warning: cauchy_seq_of_le_geometric_two -> cauchySeq_of_le_geometric_two is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] (C : Real) {f : Nat -> α}, (forall (n : Nat), LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) (f n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) C (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) n))) -> (CauchySeq.{u1, 0} α Nat (PseudoMetricSpace.toUniformSpace.{u1} α _inst_1) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) f)
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_le_geometric_two cauchySeq_of_le_geometric_twoₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then `f` is a Cauchy sequence. -/
 theorem cauchySeq_of_le_geometric_two : CauchySeq f :=
   cauchySeq_of_dist_le_of_summable _ hu₂ <| ⟨_, hasSum_geometric_two' C⟩
 #align cauchy_seq_of_le_geometric_two cauchySeq_of_le_geometric_two
 
+/- warning: dist_le_of_le_geometric_two_of_tendsto₀ -> dist_le_of_le_geometric_two_of_tendsto₀ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align dist_le_of_le_geometric_two_of_tendsto₀ dist_le_of_le_geometric_two_of_tendsto₀ₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f 0` to the limit of `f` is bounded above by `C`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop (𝓝 a)) :
@@ -449,6 +733,12 @@ theorem dist_le_of_le_geometric_two_of_tendsto₀ {a : α} (ha : Tendsto f atTop
 
 include hu₂
 
+/- warning: dist_le_of_le_geometric_two_of_tendsto -> dist_le_of_le_geometric_two_of_tendsto is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align dist_le_of_le_geometric_two_of_tendsto dist_le_of_le_geometric_two_of_tendstoₓ'. -/
 /-- If `dist (f n) (f (n+1))` is bounded by `(C / 2) / 2^n`, then the distance from
 `f n` to the limit of `f` is bounded above by `C / 2^n`. -/
 theorem dist_le_of_le_geometric_two_of_tendsto {a : α} (ha : Tendsto f atTop (𝓝 a)) (n : ℕ) :
@@ -465,6 +755,12 @@ end LeGeometric
 /-! ### Summability tests based on comparison with geometric series -/
 
 
+/- warning: summable_one_div_pow_of_le -> summable_one_div_pow_of_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {m : Real} {f : Nat -> Nat}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) m) -> (forall (i : Nat), LE.le.{0} Nat instLENat i (f i)) -> (Summable.{0, 0} Real Nat Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : Nat) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) m (f i))))
+Case conversion may be inaccurate. Consider using '#align summable_one_div_pow_of_le summable_one_div_pow_of_leₓ'. -/
 /-- A series whose terms are bounded by the terms of a converging geometric series converges. -/
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
     Summable fun i => 1 / m ^ f i :=
@@ -482,6 +778,12 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
 /-! ### Positive sequences with small sums on countable types -/
 
 
+/- warning: pos_sum_of_encodable -> posSumOfEncodable is a dubious translation:
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+  forall {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (forall (ι : Type.{u1}) [_inst_1 : Encodable.{u1} ι], Subtype.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ε' i)) (Exists.{1} Real (fun (c : Real) => And (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ε' c) (LE.le.{0} Real Real.hasLe c ε)))))
+but is expected to have type
+  forall {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (forall (ι : Type.{u1}) [_inst_1 : Encodable.{u1} ι], Subtype.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ε' i)) (Exists.{1} Real (fun (c : Real) => And (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ε' c) (LE.le.{0} Real Real.instLEReal c ε)))))
+Case conversion may be inaccurate. Consider using '#align pos_sum_of_encodable posSumOfEncodableₓ'. -/
 /-- For any positive `ε`, define on an encodable type a positive sequence with sum less than `ε` -/
 def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     { ε' : ι → ℝ // (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c ≤ ε } :=
@@ -498,6 +800,12 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     exact le_rfl
 #align pos_sum_of_encodable posSumOfEncodable
 
+/- warning: set.countable.exists_pos_has_sum_le -> Set.Countable.exists_pos_hasSum_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_leₓ'. -/
 theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s => ε' i) c ∧ c ≤ ε :=
   by
@@ -509,6 +817,12 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
+/- warning: set.countable.exists_pos_forall_sum_le -> Set.Countable.exists_pos_forall_sum_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {s : Set.{u1} ι}, (Set.Countable.{u1} ι s) -> (forall {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ε' i)) (forall (t : Finset.{u1} ι), (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.hasSubset.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} ι) (Set.{u1} ι) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} ι) (Set.{u1} ι) (Finset.Set.hasCoeT.{u1} ι))) t) s) -> (LE.le.{0} Real Real.hasLe (Finset.sum.{0, u1} Real ι Real.addCommMonoid t (fun (i : ι) => ε' i)) ε)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {s : Set.{u1} ι}, (Set.Countable.{u1} ι s) -> (forall {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} (ι -> Real) (fun (ε' : ι -> Real) => And (forall (i : ι), LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ε' i)) (forall (t : Finset.{u1} ι), (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) (Finset.toSet.{u1} ι t) s) -> (LE.le.{0} Real Real.instLEReal (Finset.sum.{0, u1} Real ι Real.instAddCommMonoidReal t (fun (i : ι) => ε' i)) ε)))))
+Case conversion may be inaccurate. Consider using '#align set.countable.exists_pos_forall_sum_le Set.Countable.exists_pos_forall_sum_leₓ'. -/
 theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → (∑ i in t, ε' i) ≤ ε :=
   by
@@ -521,6 +835,12 @@ theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs :
 
 namespace NNReal
 
+/- warning: nnreal.exists_pos_sum_of_countable -> NNReal.exists_pos_sum_of_countable is a dubious translation:
+lean 3 declaration is
+  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ε' c) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) c ε)))))
+but is expected to have type
+  forall {ε : NNReal}, (Ne.{1} NNReal ε (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (Exists.{1} NNReal (fun (c : NNReal) => And (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ε' c) (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) c ε)))))
+Case conversion may be inaccurate. Consider using '#align nnreal.exists_pos_sum_of_countable NNReal.exists_pos_sum_of_countableₓ'. -/
 theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c < ε :=
   by
@@ -537,6 +857,12 @@ end NNReal
 
 namespace ENNReal
 
+/- warning: ennreal.exists_pos_sum_of_countable -> ENNReal.exists_pos_sum_of_countable is a dubious translation:
+lean 3 declaration is
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (ε' i))) ε)))
+but is expected to have type
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> NNReal) (fun (ε' : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ENNReal.some (ε' i))) ε)))
+Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countableₓ'. -/
 theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ (∑' i, (ε' i : ℝ≥0∞)) < ε :=
   by
@@ -546,12 +872,24 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
   exact ⟨ε', hp, (ENNReal.tsum_coe_eq hc).symm ▸ lt_trans (coe_lt_coe.2 hcr) hrε⟩
 #align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
 
+/- warning: ennreal.exists_pos_sum_of_countable' -> ENNReal.exists_pos_sum_of_countable' is a dubious translation:
+lean 3 declaration is
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => ε' i)) ε)))
+but is expected to have type
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (ι : Type.{u1}) [_inst_1 : Countable.{succ u1} ι], Exists.{succ u1} (ι -> ENNReal) (fun (ε' : ι -> ENNReal) => And (forall (i : ι), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (ε' i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => ε' i)) ε)))
+Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'ₓ'. -/
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ (∑' i, ε' i) < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
   ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
 
+/- warning: ennreal.exists_pos_tsum_mul_lt_of_countable -> ENNReal.exists_pos_tsum_mul_lt_of_countable is a dubious translation:
+lean 3 declaration is
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (δ i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (w i) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (δ i)))) ε))))
+but is expected to have type
+  forall {ε : ENNReal}, (Ne.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall {ι : Type.{u1}} [_inst_1 : Countable.{succ u1} ι] (w : ι -> ENNReal), (forall (i : ι), Ne.{1} ENNReal (w i) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Exists.{succ u1} (ι -> NNReal) (fun (δ : ι -> NNReal) => And (forall (i : ι), LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) (δ i)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (w i) (ENNReal.some (δ i)))) ε))))
+Case conversion may be inaccurate. Consider using '#align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countableₓ'. -/
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
     (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ (∑' i, (w i * δ i : ℝ≥0∞)) < ε :=
   by
@@ -572,10 +910,18 @@ end ENNReal
 -/
 
 
+#print factorial_tendsto_atTop /-
 theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
   tendsto_atTop_atTop_of_monotone Nat.monotone_factorial fun n => ⟨n, n.self_le_factorial⟩
 #align factorial_tendsto_at_top factorial_tendsto_atTop
+-/
 
+/- warning: tendsto_factorial_div_pow_self_at_top -> tendsto_factorial_div_pow_self_atTop is a dubious translation:
+lean 3 declaration is
+  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))) ((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)) (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) 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
+  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)) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)) (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) 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_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTopₓ'. -/
 theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
     (tendsto_const_div_atTop_nhds_0_nat 1)
@@ -606,13 +952,21 @@ theorem tendsto_factorial_div_pow_self_atTop : Tendsto (fun n => n ! / n ^ n : 
 
 section
 
+#print tendsto_nat_floor_atTop /-
 theorem tendsto_nat_floor_atTop {α : Type _} [LinearOrderedSemiring α] [FloorSemiring α] :
     Tendsto (fun x : α => ⌊x⌋₊) atTop atTop :=
   Nat.floor_mono.tendsto_atTop_atTop fun x => ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
 #align tendsto_nat_floor_at_top tendsto_nat_floor_atTop
+-/
 
 variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
+/- warning: tendsto_nat_floor_mul_div_at_top -> tendsto_nat_floor_mul_div_atTop is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTopₓ'. -/
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -630,10 +984,22 @@ theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     simp [Nat.floor_le (mul_nonneg ha (zero_le_one.trans hx))]
 #align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTop
 
+/- warning: tendsto_nat_floor_div_at_top -> tendsto_nat_floor_div_atTop is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.floor.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.floor.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTopₓ'. -/
 theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_floor_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTop
 
+/- warning: tendsto_nat_ceil_mul_div_at_top -> tendsto_nat_ceil_mul_div_atTop is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{u1} R _inst_1 a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))] {a : R}, (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (LinearOrderedSemifield.toSemifield.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))))) a) -> (Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))) a x))) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) :=
   by
@@ -649,6 +1015,12 @@ theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
       (Nat.ceil_lt_add_one (mul_nonneg ha (zero_le_one.trans hx))).le, add_mul]
 #align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTop
 
+/- warning: tendsto_nat_ceil_div_at_top -> tendsto_nat_ceil_div_atTop is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_2))))) ((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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))) (Nat.ceil.{u1} R (StrictOrderedSemiring.toOrderedSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))) (nhds.{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 (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : LinearOrderedField.{u1} R] [_inst_3 : OrderTopology.{u1} R _inst_1 (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))] [_inst_4 : FloorRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2))], Filter.Tendsto.{u1, u1} R R (fun (x : R) => HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (LinearOrderedField.toDiv.{u1} R _inst_2)) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (Nat.ceil.{u1} R (OrderedCommSemiring.toOrderedSemiring.{u1} R (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} R (LinearOrderedField.toLinearOrderedSemifield.{u1} R _inst_2))))) (FloorRing.toFloorSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)) _inst_4) x)) x) (Filter.atTop.{u1} R (PartialOrder.toPreorder.{u1} R (StrictOrderedRing.toPartialOrder.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))) (nhds.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_2)))))))))
+Case conversion may be inaccurate. Consider using '#align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTopₓ'. -/
 theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop

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

@@ -36,7 +36,7 @@ theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
 
 theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
-  simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
+  simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
 
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) :=
@@ -69,7 +69,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
   · exact fun n : ℕ => 1 / (1 + x / n)
   · field_simp [nat.cast_ne_zero.mpr hn]
   · have : 𝓝 (1 : 𝕜) = 𝓝 (1 / (1 + x * ↑(0 : ℝ))) := by
-      rw [algebraMap.coe_zero, mul_zero, add_zero, div_one]
+      rw [algebraMap.coe_zero, MulZeroClass.mul_zero, add_zero, div_one]
     rw [this]
     refine' tendsto_const_nhds.div (tendsto_const_nhds.add _) (by simp)
     simp_rw [div_eq_mul_inv]

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

@@ -315,7 +315,7 @@ decaying terms.
 
 section EdistLeGeometric
 
-variable [PseudoEmetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤) {f : ℕ → α}
+variable [PseudoEMetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤) {f : ℕ → α}
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C * r ^ n)
 
 include hr hC hu
@@ -352,7 +352,7 @@ end EdistLeGeometric
 
 section EdistLeGeometricTwo
 
-variable [PseudoEmetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ → α}
+variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ → α}
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C / 2 ^ n) {a : α} (ha : Tendsto f atTop (𝓝 a))
 
 include hC hu

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module analysis.specific_limits.basic
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -561,7 +561,7 @@ theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {
   refine' ⟨fun i => δ' i / max 1 (w i), fun i => div_pos (Hpos _) (this i), _⟩
   refine' lt_of_le_of_lt (ENNReal.tsum_le_tsum fun i => _) Hsum
   rw [coe_div (this i).ne']
-  refine' mul_le_of_le_div' (ENNReal.mul_le_mul le_rfl <| ENNReal.inv_le_inv.2 _)
+  refine' mul_le_of_le_div' (mul_le_mul_left' (ENNReal.inv_le_inv.2 _) _)
   exact coe_le_coe.2 (le_max_right _ _)
 #align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countable
 

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

@@ -27,7 +27,7 @@ noncomputable section
 
 open Classical Set Function Filter Finset Metric
 
-open Classical Topology Nat BigOperators uniformity NNReal Ennreal
+open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type _} {β : Type _} {ι : Type _}
 
@@ -171,14 +171,14 @@ theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
     simp only [NNReal.coe_pow, NNReal.coe_zero, tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
-theorem Ennreal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
+theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   by
-  rcases Ennreal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
-  rw [← Ennreal.coe_zero]
+  rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
+  rw [← ENNReal.coe_zero]
   norm_cast  at *
   apply NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 hr
-#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 Ennreal.tendsto_pow_atTop_nhds_0_of_lt_1
+#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
 /-! ### Geometric series-/
 
@@ -285,21 +285,21 @@ theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n)
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
-theorem Ennreal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
   by
   cases' lt_or_le r 1 with hr hr
-  · rcases Ennreal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
+  · rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
     norm_cast  at *
-    convert Ennreal.tsum_coe_eq (NNReal.hasSum_geometric hr)
-    rw [Ennreal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr]
-  · rw [tsub_eq_zero_iff_le.mpr hr, Ennreal.inv_zero, Ennreal.tsum_eq_supᵢ_nat, supᵢ_eq_top]
+    convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
+    rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr]
+  · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_supᵢ_nat, supᵢ_eq_top]
     refine' fun a ha =>
-      (Ennreal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
+      (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
     calc
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
       _ ≤ ∑ i in range n, r ^ i := sum_le_sum fun k _ => one_le_pow_of_one_le' hr k
       
-#align ennreal.tsum_geometric Ennreal.tsum_geometric
+#align ennreal.tsum_geometric ENNReal.tsum_geometric
 
 end Geometric
 
@@ -325,8 +325,8 @@ then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric : CauchySeq f :=
   by
   refine' cauchySeq_of_edist_le_of_tsum_ne_top _ hu _
-  rw [Ennreal.tsum_mul_left, Ennreal.tsum_geometric]
-  refine' Ennreal.mul_ne_top hC (Ennreal.inv_ne_top.2 _)
+  rw [ENNReal.tsum_mul_left, ENNReal.tsum_geometric]
+  refine' ENNReal.mul_ne_top hC (ENNReal.inv_ne_top.2 _)
   exact (tsub_pos_iff_lt.2 hr).ne'
 #align cauchy_seq_of_edist_le_geometric cauchySeq_of_edist_le_geometric
 
@@ -338,7 +338,7 @@ theorem edist_le_of_edist_le_geometric_of_tendsto {a : α} (ha : Tendsto f atTop
     edist (f n) a ≤ C * r ^ n / (1 - r) :=
   by
   convert edist_le_tsum_of_edist_le_of_tendsto _ hu ha _
-  simp only [pow_add, Ennreal.tsum_mul_left, Ennreal.tsum_geometric, div_eq_mul_inv, mul_assoc]
+  simp only [pow_add, ENNReal.tsum_mul_left, ENNReal.tsum_geometric, div_eq_mul_inv, mul_assoc]
 #align edist_le_of_edist_le_geometric_of_tendsto edist_le_of_edist_le_geometric_of_tendsto
 
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, then the distance from
@@ -360,9 +360,9 @@ include hC hu
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f :=
   by
-  simp only [div_eq_mul_inv, Ennreal.inv_pow] at hu
+  simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu
   refine' cauchySeq_of_edist_le_geometric 2⁻¹ C _ hC hu
-  simp [Ennreal.one_lt_two]
+  simp [ENNReal.one_lt_two]
 #align cauchy_seq_of_edist_le_geometric_two cauchySeq_of_edist_le_geometric_two
 
 omit hC
@@ -373,10 +373,10 @@ include ha
 `f n` to the limit of `f` is bounded above by `2 * C * 2^-n`. -/
 theorem edist_le_of_edist_le_geometric_two_of_tendsto (n : ℕ) : edist (f n) a ≤ 2 * C / 2 ^ n :=
   by
-  simp only [div_eq_mul_inv, Ennreal.inv_pow] at *
+  simp only [div_eq_mul_inv, ENNReal.inv_pow] at *
   rw [mul_assoc, mul_comm]
   convert edist_le_of_edist_le_geometric_of_tendsto 2⁻¹ C hu ha n
-  rw [Ennreal.one_sub_inv_two, inv_inv]
+  rw [ENNReal.one_sub_inv_two, inv_inv]
 #align edist_le_of_edist_le_geometric_two_of_tendsto edist_le_of_edist_le_geometric_two_of_tendsto
 
 /-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then the distance from
@@ -535,7 +535,7 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Counta
 
 end NNReal
 
-namespace Ennreal
+namespace ENNReal
 
 theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0, (∀ i, 0 < ε' i) ∧ (∑' i, (ε' i : ℝ≥0∞)) < ε :=
@@ -543,14 +543,14 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
   rcases exists_between (pos_iff_ne_zero.2 hε) with ⟨r, h0r, hrε⟩
   rcases lt_iff_exists_coe.1 hrε with ⟨x, rfl, hx⟩
   rcases NNReal.exists_pos_sum_of_countable (coe_pos.1 h0r).ne' ι with ⟨ε', hp, c, hc, hcr⟩
-  exact ⟨ε', hp, (Ennreal.tsum_coe_eq hc).symm ▸ lt_trans (coe_lt_coe.2 hcr) hrε⟩
-#align ennreal.exists_pos_sum_of_countable Ennreal.exists_pos_sum_of_countable
+  exact ⟨ε', hp, (ENNReal.tsum_coe_eq hc).symm ▸ lt_trans (coe_lt_coe.2 hcr) hrε⟩
+#align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
 
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ (∑' i, ε' i) < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
-  ⟨fun i => δ i, fun i => Ennreal.coe_pos.2 (δpos i), hδ⟩
-#align ennreal.exists_pos_sum_of_countable' Ennreal.exists_pos_sum_of_countable'
+  ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
+#align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
 
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
     (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ (∑' i, (w i * δ i : ℝ≥0∞)) < ε :=
@@ -559,13 +559,13 @@ theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {
   rcases exists_pos_sum_of_countable hε ι with ⟨δ', Hpos, Hsum⟩
   have : ∀ i, 0 < max 1 (w i) := fun i => zero_lt_one.trans_le (le_max_left _ _)
   refine' ⟨fun i => δ' i / max 1 (w i), fun i => div_pos (Hpos _) (this i), _⟩
-  refine' lt_of_le_of_lt (Ennreal.tsum_le_tsum fun i => _) Hsum
+  refine' lt_of_le_of_lt (ENNReal.tsum_le_tsum fun i => _) Hsum
   rw [coe_div (this i).ne']
-  refine' mul_le_of_le_div' (Ennreal.mul_le_mul le_rfl <| Ennreal.inv_le_inv.2 _)
+  refine' mul_le_of_le_div' (ENNReal.mul_le_mul le_rfl <| ENNReal.inv_le_inv.2 _)
   exact coe_le_coe.2 (le_max_right _ _)
-#align ennreal.exists_pos_tsum_mul_lt_of_countable Ennreal.exists_pos_tsum_mul_lt_of_countable
+#align ennreal.exists_pos_tsum_mul_lt_of_countable ENNReal.exists_pos_tsum_mul_lt_of_countable
 
-end Ennreal
+end ENNReal
 
 /-!
 ### Factorial

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module analysis.specific_limits.basic
-! leanprover-community/mathlib commit 372edc36e5d2caafdd135769e0136b5a59186834
+! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -558,7 +558,7 @@ theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {
   lift w to ι → ℝ≥0 using hw
   rcases exists_pos_sum_of_countable hε ι with ⟨δ', Hpos, Hsum⟩
   have : ∀ i, 0 < max 1 (w i) := fun i => zero_lt_one.trans_le (le_max_left _ _)
-  refine' ⟨fun i => δ' i / max 1 (w i), fun i => NNReal.div_pos (Hpos _) (this i), _⟩
+  refine' ⟨fun i => δ' i / max 1 (w i), fun i => div_pos (Hpos _) (this i), _⟩
   refine' lt_of_le_of_lt (Ennreal.tsum_le_tsum fun i => _) Hsum
   rw [coe_div (this i).ne']
   refine' mul_le_of_le_div' (Ennreal.mul_le_mul le_rfl <| Ennreal.inv_le_inv.2 _)

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

We move some lemmas out of Topology/Instances/ENNReal into Topology/Algebra/InfiniteSum/Real. Also use this to address a porting TODO.

This was originally part of #12446

Co-authored-by: Chris Birkbeck <c.birkbeck@uea.ac.uk>

@@ -6,8 +6,8 @@ Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Masso
 import Mathlib.Algebra.GeomSum
 import Mathlib.Order.Filter.Archimedean
 import Mathlib.Order.Iterate
-import Mathlib.Topology.Instances.ENNReal
 import Mathlib.Topology.Algebra.Algebra
+import Mathlib.Topology.Algebra.InfiniteSum.Real
 
 #align_import analysis.specific_limits.basic from "leanprover-community/mathlib"@"57ac39bd365c2f80589a700f9fbb664d3a1a30c2"
 

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -155,10 +155,11 @@ alias tendsto_pow_atTop_nhds_0_of_lt_1 := tendsto_pow_atTop_nhds_zero_of_lt_one
       simp only [hr.symm, one_pow] at h
       exact zero_ne_one <| tendsto_nhds_unique h tendsto_const_nhds
     · apply @not_tendsto_nhds_of_tendsto_atTop 𝕜 ℕ _ _ _ _ atTop _ (fun n ↦ |r| ^ n) _ 0 _
-      refine (pow_right_strictMono <| lt_of_le_of_ne (le_of_not_lt hr_le)
-        hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
-      obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
-      exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
+      · refine (pow_right_strictMono <| lt_of_le_of_ne (le_of_not_lt hr_le)
+          hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
+        obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
+        exact ⟨n, le_of_lt hn⟩
+      · simpa only [← abs_pow]
   · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_zero_of_lt_one (abs_nonneg r)) h
 @[deprecated] alias tendsto_pow_atTop_nhds_0_iff := tendsto_pow_atTop_nhds_zero_iff -- 2024-01-31
 

@@ -33,39 +33,43 @@ variable {α : Type*} {β : Type*} {ι : Type*}
 theorem tendsto_inverse_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_natCast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_zero_nat
-@[deprecated] alias tendsto_inverse_atTop_nhds_0_nat := tendsto_inverse_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias tendsto_inverse_atTop_nhds_0_nat := tendsto_inverse_atTop_nhds_zero_nat
 
 theorem tendsto_const_div_atTop_nhds_zero_nat (C : ℝ) :
     Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
   simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_zero_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_zero_nat
-@[deprecated]  alias tendsto_const_div_atTop_nhds_0_nat := tendsto_const_div_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias tendsto_const_div_atTop_nhds_0_nat := tendsto_const_div_atTop_nhds_zero_nat
 
 theorem tendsto_one_div_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ 1/(n : ℝ)) atTop (𝓝 0) :=
   tendsto_const_div_atTop_nhds_zero_nat 1
-@[deprecated] alias tendsto_one_div_atTop_nhds_0_nat := tendsto_one_div_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias tendsto_one_div_atTop_nhds_0_nat := tendsto_one_div_atTop_nhds_zero_nat
 
 theorem NNReal.tendsto_inverse_atTop_nhds_zero_nat :
     Tendsto (fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by
   rw [← NNReal.tendsto_coe]
   exact _root_.tendsto_inverse_atTop_nhds_zero_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_zero_nat
-@[deprecated] alias NNReal.tendsto_inverse_atTop_nhds_0_nat :=
-  NNReal.tendsto_inverse_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias NNReal.tendsto_inverse_atTop_nhds_0_nat := NNReal.tendsto_inverse_atTop_nhds_zero_nat
 
 theorem NNReal.tendsto_const_div_atTop_nhds_zero_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
   simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_zero_nat
 #align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_zero_nat
-@[deprecated] alias NNReal.tendsto_const_div_atTop_nhds_0_nat :=
-  NNReal.tendsto_const_div_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias NNReal.tendsto_const_div_atTop_nhds_0_nat := NNReal.tendsto_const_div_atTop_nhds_zero_nat
 
 theorem tendsto_one_div_add_atTop_nhds_zero_nat :
     Tendsto (fun n : ℕ ↦ 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ ↦ 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
   (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_zero_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_zero_nat
-@[deprecated] alias tendsto_one_div_add_atTop_nhds_0_nat := tendsto_one_div_add_atTop_nhds_zero_nat
+@[deprecated] -- 2024-01-31
+alias tendsto_one_div_add_atTop_nhds_0_nat := tendsto_one_div_add_atTop_nhds_zero_nat
 
 theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜]
     [Algebra ℝ≥0 𝕜] [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
@@ -73,14 +77,16 @@ theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Se
   convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp
     tendsto_inverse_atTop_nhds_zero_nat
   rw [map_zero]
-@[deprecated] alias NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
+@[deprecated] -- 2024-01-31
+alias NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
   NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat
 
 theorem tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
     Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
   NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat 𝕜
-@[deprecated] alias tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
+@[deprecated] -- 2024-01-31
+alias tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
   _root_.tendsto_algebraMap_inverse_atTop_nhds_zero_nat
 
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
@@ -136,7 +142,8 @@ theorem tendsto_pow_atTop_nhds_zero_of_lt_one {𝕜 : Type*} [LinearOrderedField
       have := one_lt_inv hr h₂ |> tendsto_pow_atTop_atTop_of_one_lt
       (tendsto_inv_atTop_zero.comp this).congr fun n ↦ by simp)
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_zero_of_lt_one
-@[deprecated] alias tendsto_pow_atTop_nhds_0_of_lt_1 := tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] -- 2024-01-31
+alias tendsto_pow_atTop_nhds_0_of_lt_1 := tendsto_pow_atTop_nhds_zero_of_lt_one
 
 @[simp] theorem tendsto_pow_atTop_nhds_zero_iff {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} :
@@ -153,7 +160,7 @@ theorem tendsto_pow_atTop_nhds_zero_of_lt_one {𝕜 : Type*} [LinearOrderedField
       obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
       exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
   · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_zero_of_lt_one (abs_nonneg r)) h
-@[deprecated] alias tendsto_pow_atTop_nhds_0_iff := tendsto_pow_atTop_nhds_zero_iff
+@[deprecated] alias tendsto_pow_atTop_nhds_0_iff := tendsto_pow_atTop_nhds_zero_iff -- 2024-01-31
 
 theorem tendsto_pow_atTop_nhdsWithin_zero_of_lt_one {𝕜 : Type*} [LinearOrderedField 𝕜]
     [Archimedean 𝕜] [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
@@ -162,8 +169,8 @@ theorem tendsto_pow_atTop_nhdsWithin_zero_of_lt_one {𝕜 : Type*} [LinearOrdere
     ⟨tendsto_pow_atTop_nhds_zero_of_lt_one h₁.le h₂,
       tendsto_principal.2 <| eventually_of_forall fun _ ↦ pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
-@[deprecated] alias tendsto_pow_atTop_nhdsWithin_0_of_lt_1 :=
-  tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
+@[deprecated] -- 2024-01-31
+alias tendsto_pow_atTop_nhdsWithin_0_of_lt_1 := tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
 
 theorem uniformity_basis_dist_pow_of_lt_one {α : Type*} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
@@ -171,7 +178,8 @@ theorem uniformity_basis_dist_pow_of_lt_one {α : Type*} [PseudoMetricSpace α]
   Metric.mk_uniformity_basis (fun _ _ ↦ pow_pos h₀ _) fun _ ε0 ↦
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun _ hk ↦ ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_one
-@[deprecated] alias uniformity_basis_dist_pow_of_lt_1 := uniformity_basis_dist_pow_of_lt_one
+@[deprecated] -- 2024-01-31
+alias uniformity_basis_dist_pow_of_lt_1 := uniformity_basis_dist_pow_of_lt_one
 
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n := by
@@ -213,8 +221,8 @@ theorem NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0} (hr : r < 1)
     simp only [NNReal.coe_pow, NNReal.coe_zero,
       _root_.tendsto_pow_atTop_nhds_zero_of_lt_one r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
-@[deprecated] alias NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
-  NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] -- 2024-01-31
+alias NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 := NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
 @[simp]
 protected theorem NNReal.tendsto_pow_atTop_nhds_zero_iff {r : ℝ≥0} :
@@ -229,8 +237,8 @@ theorem ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0∞} (hr : r <
   norm_cast at *
   apply NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one hr
 #align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
-@[deprecated] alias ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
-  ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] -- 2024-01-31
+alias ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 := ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
 @[simp]
 protected theorem ENNReal.tendsto_pow_atTop_nhds_zero_iff {r : ℝ≥0∞} :
@@ -256,18 +264,18 @@ theorem hasSum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
   (hasSum_iff_tendsto_nat_of_nonneg (pow_nonneg h₁) _).mpr <| by
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
 #align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_one
-@[deprecated] alias hasSum_geometric_of_lt_1 := hasSum_geometric_of_lt_one
+@[deprecated] alias hasSum_geometric_of_lt_1 := hasSum_geometric_of_lt_one -- 2024-01-31
 
 theorem summable_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ ↦ r ^ n :=
   ⟨_, hasSum_geometric_of_lt_one h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_one
-@[deprecated] alias summable_geometric_of_lt_1 := summable_geometric_of_lt_one
+@[deprecated] alias summable_geometric_of_lt_1 := summable_geometric_of_lt_one -- 2024-01-31
 
 theorem tsum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_one h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_one
-@[deprecated] alias tsum_geometric_of_lt_1 := tsum_geometric_of_lt_one
+@[deprecated] alias tsum_geometric_of_lt_1 := tsum_geometric_of_lt_one -- 2024-01-31
 
 theorem hasSum_geometric_two : HasSum (fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n) 2 := by
   convert hasSum_geometric_of_lt_one _ _ <;> norm_num

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

@@ -31,7 +31,7 @@ open Topology Nat BigOperators uniformity NNReal ENNReal
 variable {α : Type*} {β : Type*} {ι : Type*}
 
 theorem tendsto_inverse_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
-  tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
+  tendsto_inv_atTop_zero.comp tendsto_natCast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_zero_nat
 @[deprecated] alias tendsto_inverse_atTop_nhds_0_nat := tendsto_inverse_atTop_nhds_zero_nat
 
@@ -651,7 +651,7 @@ lemma tendsto_nat_ceil_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSemir
 lemma tendsto_nat_floor_mul_atTop {α : Type _} [LinearOrderedSemifield α] [FloorSemiring α]
     [Archimedean α] (a : α) (ha : 0 < a) : Tendsto (fun (x:ℕ) => ⌊a * x⌋₊) atTop atTop :=
   Tendsto.comp tendsto_nat_floor_atTop
-    <| Tendsto.const_mul_atTop ha tendsto_nat_cast_atTop_atTop
+    <| Tendsto.const_mul_atTop ha tendsto_natCast_atTop_atTop
 
 variable {R : Type*} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 

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

@@ -88,7 +88,7 @@ algebra over `ℝ`, e.g., `ℂ`).
 
 TODO: introduce a typeclass saying that `1 / n` tends to 0 at top, making it possible to get this
 statement simultaneously on `ℚ`, `ℝ` and `ℂ`. -/
-theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
+theorem tendsto_natCast_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
     [CharZero 𝕜] [Algebra ℝ 𝕜] [ContinuousSMul ℝ 𝕜] [TopologicalDivisionRing 𝕜] (x : 𝕜) :
     Tendsto (fun n : ℕ ↦ (n : 𝕜) / (n + x)) atTop (𝓝 1) := by
   refine' Tendsto.congr' ((eventually_ne_atTop 0).mp (eventually_of_forall fun n hn ↦ _)) _
@@ -105,7 +105,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
     refine' Iff.mpr tendsto_atTop' _
     intros
     simp_all only [comp_apply, map_inv₀, map_natCast]
-#align tendsto_coe_nat_div_add_at_top tendsto_coe_nat_div_add_atTop
+#align tendsto_coe_nat_div_add_at_top tendsto_natCast_div_add_atTop
 
 /-! ### Powers -/
 

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -380,7 +380,7 @@ variable [PseudoEMetricSpace α] (r C : ℝ≥0∞) (hr : r < 1) (hC : C ≠ ⊤
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C * r ^ n)
 
 /-- If `edist (f n) (f (n+1))` is bounded by `C * r^n`, `C ≠ ∞`, `r < 1`,
-then `f` is a Cauchy sequence.-/
+then `f` is a Cauchy sequence. -/
 theorem cauchySeq_of_edist_le_geometric : CauchySeq f := by
   refine' cauchySeq_of_edist_le_of_tsum_ne_top _ hu _
   rw [ENNReal.tsum_mul_left, ENNReal.tsum_geometric]
@@ -410,7 +410,7 @@ section EdistLeGeometricTwo
 variable [PseudoEMetricSpace α] (C : ℝ≥0∞) (hC : C ≠ ⊤) {f : ℕ → α}
   (hu : ∀ n, edist (f n) (f (n + 1)) ≤ C / 2 ^ n) {a : α} (ha : Tendsto f atTop (𝓝 a))
 
-/-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence.-/
+/-- If `edist (f n) (f (n+1))` is bounded by `C * 2^-n`, then `f` is a Cauchy sequence. -/
 theorem cauchySeq_of_edist_le_geometric_two : CauchySeq f := by
   simp only [div_eq_mul_inv, ENNReal.inv_pow] at hu
   refine' cauchySeq_of_edist_le_geometric 2⁻¹ C _ hC hu

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.

@@ -177,26 +177,26 @@ theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n := by
   apply (monotone_mul_left_of_nonneg hc).seq_pos_lt_seq_of_le_of_lt hn _ _ h
   · simp
-  · simp [_root_.pow_succ, mul_assoc, le_refl]
+  · simp [_root_.pow_succ', mul_assoc, le_refl]
 #align geom_lt geom_lt
 
 theorem geom_le {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, c * u k ≤ u (k + 1)) :
     c ^ n * u 0 ≤ u n := by
   apply (monotone_mul_left_of_nonneg hc).seq_le_seq n _ _ h <;>
-    simp [_root_.pow_succ, mul_assoc, le_refl]
+    simp [_root_.pow_succ', mul_assoc, le_refl]
 #align geom_le geom_le
 
 theorem lt_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, u (k + 1) < c * u k) : u n < c ^ n * u 0 := by
   apply (monotone_mul_left_of_nonneg hc).seq_pos_lt_seq_of_lt_of_le hn _ h _
   · simp
-  · simp [_root_.pow_succ, mul_assoc, le_refl]
+  · simp [_root_.pow_succ', mul_assoc, le_refl]
 #align lt_geom lt_geom
 
 theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k < n, u (k + 1) ≤ c * u k) :
     u n ≤ c ^ n * u 0 := by
   apply (monotone_mul_left_of_nonneg hc).seq_le_seq n _ h _ <;>
-    simp [_root_.pow_succ, mul_assoc, le_refl]
+    simp [_root_.pow_succ', mul_assoc, le_refl]
 #align le_geom le_geom
 
 /-- If a sequence `v` of real numbers satisfies `k * v n ≤ v (n+1)` with `1 < k`,

Make use of Nat-specific lemmas from Std rather than the general ones provided by mathlib.

The ultimate goal here is to carve out Data, Algebra and Order sublibraries.

@@ -604,7 +604,7 @@ end ENNReal
 
 
 theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
-  tendsto_atTop_atTop_of_monotone Nat.monotone_factorial fun n ↦ ⟨n, n.self_le_factorial⟩
+  tendsto_atTop_atTop_of_monotone (fun _ _ ↦ Nat.factorial_le) fun n ↦ ⟨n, n.self_le_factorial⟩
 #align factorial_tendsto_at_top factorial_tendsto_atTop
 
 theorem tendsto_factorial_div_pow_self_atTop :

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -693,7 +693,7 @@ theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x ↦ (⌈x⌉₊ : R) / x) at
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop
 
-lemma Nat.tendsto_div_const_atTop {n : ℕ} (hn : n ≠ 0) : Tendsto (λ x ↦ x / n) atTop atTop := by
+lemma Nat.tendsto_div_const_atTop {n : ℕ} (hn : n ≠ 0) : Tendsto (· / n) atTop atTop := by
   rw [Tendsto, map_div_atTop_eq_nat n hn.bot_lt]
 
 end

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.

@@ -22,9 +22,11 @@ instances of these such as `ℝ`, `ℝ≥0` and `ℝ≥0∞`.
 
 noncomputable section
 
-open Classical Set Function Filter Finset Metric
+open scoped Classical
+open Set Function Filter Finset Metric
 
-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*}
 

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

@@ -626,7 +626,7 @@ theorem tendsto_factorial_div_pow_self_atTop :
       · positivity
       · refine' (div_le_one <| mod_cast hn).mpr _
         norm_cast
-        linarith)
+        omega)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop
 
 /-!

Add the two iff versions (for NNReals and ENNReals) of the statement that $x^n$ tends to $0$ if and only if $x<1$.

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

@@ -214,6 +214,12 @@ theorem NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0} (hr : r < 1)
 @[deprecated] alias NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
   NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
+@[simp]
+protected theorem NNReal.tendsto_pow_atTop_nhds_zero_iff {r : ℝ≥0} :
+    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) ↔ r < 1 :=
+  ⟨fun h => by simpa [coe_pow, coe_zero, abs_eq, coe_lt_one, val_eq_coe] using
+    tendsto_pow_atTop_nhds_zero_iff.mp <| tendsto_coe.mpr h, tendsto_pow_atTop_nhds_zero_of_lt_one⟩
+
 theorem ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) := by
   rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
@@ -224,6 +230,17 @@ theorem ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0∞} (hr : r <
 @[deprecated] alias ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
   ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
+@[simp]
+protected theorem ENNReal.tendsto_pow_atTop_nhds_zero_iff {r : ℝ≥0∞} :
+    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) ↔ r < 1 := by
+  refine ⟨fun h ↦ ?_, tendsto_pow_atTop_nhds_zero_of_lt_one⟩
+  lift r to NNReal
+  · refine fun hr ↦ top_ne_zero (tendsto_nhds_unique (EventuallyEq.tendsto ?_) (hr ▸ h))
+    exact eventually_atTop.mpr ⟨1, fun _ hn ↦ pow_eq_top_iff.mpr ⟨rfl, Nat.pos_iff_ne_zero.mp hn⟩⟩
+  rw [← coe_zero] at h
+  norm_cast at h ⊢
+  exact NNReal.tendsto_pow_atTop_nhds_zero_iff.mp h
+
 /-! ### Geometric series-/
 
 

@@ -624,6 +624,11 @@ theorem tendsto_nat_floor_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSe
   Nat.floor_mono.tendsto_atTop_atTop fun x ↦ ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
 #align tendsto_nat_floor_at_top tendsto_nat_floor_atTop
 
+lemma tendsto_nat_ceil_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSemiring α] :
+    Tendsto (fun x : α ↦ ⌈x⌉₊) atTop atTop := by
+  refine Nat.ceil_mono.tendsto_atTop_atTop (fun x ↦ ⟨x, ?_⟩)
+  simp only [Nat.ceil_natCast, le_refl]
+
 lemma tendsto_nat_floor_mul_atTop {α : Type _} [LinearOrderedSemifield α] [FloorSemiring α]
     [Archimedean α] (a : α) (ha : 0 < a) : Tendsto (fun (x:ℕ) => ⌊a * x⌋₊) atTop atTop :=
   Tendsto.comp tendsto_nat_floor_atTop

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

@@ -67,7 +67,7 @@ theorem tendsto_one_div_add_atTop_nhds_zero_nat :
 
 theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜]
     [Algebra ℝ≥0 𝕜] [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
-    Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
+    Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by
   convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp
     tendsto_inverse_atTop_nhds_zero_nat
   rw [map_zero]
@@ -76,7 +76,7 @@ theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Se
 
 theorem tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
-    Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (nhds 0) :=
+    Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
   NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat 𝕜
 @[deprecated] alias tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
   _root_.tendsto_algebraMap_inverse_atTop_nhds_zero_nat

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.

@@ -28,44 +28,58 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type*} {β : Type*} {ι : Type*}
 
-theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
+theorem tendsto_inverse_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
-#align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
+#align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_zero_nat
+@[deprecated] alias tendsto_inverse_atTop_nhds_0_nat := tendsto_inverse_atTop_nhds_zero_nat
 
-theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
-  simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
-#align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
+theorem tendsto_const_div_atTop_nhds_zero_nat (C : ℝ) :
+    Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
+  simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_zero_nat
+#align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_zero_nat
+@[deprecated]  alias tendsto_const_div_atTop_nhds_0_nat := tendsto_const_div_atTop_nhds_zero_nat
 
-theorem tendsto_one_div_atTop_nhds_0_nat : Tendsto (fun n : ℕ ↦ 1/(n : ℝ)) atTop (𝓝 0) :=
-  tendsto_const_div_atTop_nhds_0_nat 1
+theorem tendsto_one_div_atTop_nhds_zero_nat : Tendsto (fun n : ℕ ↦ 1/(n : ℝ)) atTop (𝓝 0) :=
+  tendsto_const_div_atTop_nhds_zero_nat 1
+@[deprecated] alias tendsto_one_div_atTop_nhds_0_nat := tendsto_one_div_atTop_nhds_zero_nat
 
-theorem NNReal.tendsto_inverse_atTop_nhds_0_nat :
+theorem NNReal.tendsto_inverse_atTop_nhds_zero_nat :
     Tendsto (fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by
   rw [← NNReal.tendsto_coe]
-  exact _root_.tendsto_inverse_atTop_nhds_0_nat
-#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
+  exact _root_.tendsto_inverse_atTop_nhds_zero_nat
+#align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_zero_nat
+@[deprecated] alias NNReal.tendsto_inverse_atTop_nhds_0_nat :=
+  NNReal.tendsto_inverse_atTop_nhds_zero_nat
 
-theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
+theorem NNReal.tendsto_const_div_atTop_nhds_zero_nat (C : ℝ≥0) :
     Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
-  simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
-#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
+  simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_zero_nat
+#align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_zero_nat
+@[deprecated] alias NNReal.tendsto_const_div_atTop_nhds_0_nat :=
+  NNReal.tendsto_const_div_atTop_nhds_zero_nat
 
-theorem tendsto_one_div_add_atTop_nhds_0_nat :
+theorem tendsto_one_div_add_atTop_nhds_zero_nat :
     Tendsto (fun n : ℕ ↦ 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
   suffices Tendsto (fun n : ℕ ↦ 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
-  (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_0_nat 1)
-#align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
+  (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_zero_nat 1)
+#align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_zero_nat
+@[deprecated] alias tendsto_one_div_add_atTop_nhds_0_nat := tendsto_one_div_add_atTop_nhds_zero_nat
 
-theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ≥0 𝕜]
-    [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
+theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜]
+    [Algebra ℝ≥0 𝕜] [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
     Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
-  convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp tendsto_inverse_atTop_nhds_0_nat
+  convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp
+    tendsto_inverse_atTop_nhds_zero_nat
   rw [map_zero]
+@[deprecated] alias NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
+  NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat
 
-theorem tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
+theorem tendsto_algebraMap_inverse_atTop_nhds_zero_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
     Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (nhds 0) :=
-  NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat 𝕜
+  NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat 𝕜
+@[deprecated] alias tendsto_algebraMap_inverse_atTop_nhds_0_nat :=
+  _root_.tendsto_algebraMap_inverse_atTop_nhds_zero_nat
 
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
@@ -84,7 +98,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
     refine' tendsto_const_nhds.div (tendsto_const_nhds.add _) (by simp)
     simp_rw [div_eq_mul_inv]
     refine' tendsto_const_nhds.mul _
-    have := ((continuous_algebraMap ℝ 𝕜).tendsto _).comp tendsto_inverse_atTop_nhds_0_nat
+    have := ((continuous_algebraMap ℝ 𝕜).tendsto _).comp tendsto_inverse_atTop_nhds_zero_nat
     rw [map_zero, Filter.tendsto_atTop'] at this
     refine' Iff.mpr tendsto_atTop' _
     intros
@@ -110,7 +124,7 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
   tsub_add_cancel_of_le (le_of_lt h) ▸ tendsto_add_one_pow_atTop_atTop_of_pos (tsub_pos_of_lt h)
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 
-theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+theorem tendsto_pow_atTop_nhds_zero_of_lt_one {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
   h₁.eq_or_lt.elim
@@ -119,9 +133,10 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜
     (fun hr ↦
       have := one_lt_inv hr h₂ |> tendsto_pow_atTop_atTop_of_one_lt
       (tendsto_inv_atTop_zero.comp this).congr fun n ↦ by simp)
-#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
+#align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] alias tendsto_pow_atTop_nhds_0_of_lt_1 := tendsto_pow_atTop_nhds_zero_of_lt_one
 
-@[simp] theorem tendsto_pow_atTop_nhds_0_iff {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+@[simp] theorem tendsto_pow_atTop_nhds_zero_iff {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) ↔ |r| < 1 := by
   rw [tendsto_zero_iff_abs_tendsto_zero]
@@ -135,22 +150,26 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜
         hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
       obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
       exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
-  · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_0_of_lt_1 (abs_nonneg r)) h
+  · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_zero_of_lt_one (abs_nonneg r)) h
+@[deprecated] alias tendsto_pow_atTop_nhds_0_iff := tendsto_pow_atTop_nhds_zero_iff
 
-theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
-    [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
+theorem tendsto_pow_atTop_nhdsWithin_zero_of_lt_one {𝕜 : Type*} [LinearOrderedField 𝕜]
+    [Archimedean 𝕜] [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝[>] 0) :=
   tendsto_inf.2
-    ⟨tendsto_pow_atTop_nhds_0_of_lt_1 h₁.le h₂,
+    ⟨tendsto_pow_atTop_nhds_zero_of_lt_one h₁.le h₂,
       tendsto_principal.2 <| eventually_of_forall fun _ ↦ pow_pos h₁ _⟩
-#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
+#align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
+@[deprecated] alias tendsto_pow_atTop_nhdsWithin_0_of_lt_1 :=
+  tendsto_pow_atTop_nhdsWithin_zero_of_lt_one
 
-theorem uniformity_basis_dist_pow_of_lt_1 {α : Type*} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
+theorem uniformity_basis_dist_pow_of_lt_one {α : Type*} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
     (uniformity α).HasBasis (fun _ : ℕ ↦ True) fun k ↦ { p : α × α | dist p.1 p.2 < r ^ k } :=
   Metric.mk_uniformity_basis (fun _ _ ↦ pow_pos h₀ _) fun _ ε0 ↦
     (exists_pow_lt_of_lt_one ε0 h₁).imp fun _ hk ↦ ⟨trivial, hk.le⟩
-#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
+#align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_one
+@[deprecated] alias uniformity_basis_dist_pow_of_lt_1 := uniformity_basis_dist_pow_of_lt_one
 
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
     (h : ∀ k < n, c * u k < u (k + 1)) : c ^ n * u 0 < u n := by
@@ -186,46 +205,53 @@ theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (h
     (tendsto_pow_atTop_atTop_of_one_lt hc).atTop_mul_const h₀
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
 
-theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
+theorem NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0} (hr : r < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
     simp only [NNReal.coe_pow, NNReal.coe_zero,
-      _root_.tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
-#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+      _root_.tendsto_pow_atTop_nhds_zero_of_lt_one r.coe_nonneg hr]
+#align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] alias NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
+  NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
-theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
+theorem ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one {r : ℝ≥0∞} (hr : r < 1) :
     Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) := by
   rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
   rw [← ENNReal.coe_zero]
   norm_cast at *
-  apply NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 hr
-#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1
+  apply NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one hr
+#align ennreal.tendsto_pow_at_top_nhds_0_of_lt_1 ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
+@[deprecated] alias ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 :=
+  ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one
 
 /-! ### Geometric series-/
 
 
 section Geometric
 
-theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
+theorem hasSum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
   have : Tendsto (fun n ↦ (r ^ n - 1) * (r - 1)⁻¹) atTop (𝓝 ((0 - 1) * (r - 1)⁻¹)) :=
-    ((tendsto_pow_atTop_nhds_0_of_lt_1 h₁ h₂).sub tendsto_const_nhds).mul tendsto_const_nhds
+    ((tendsto_pow_atTop_nhds_zero_of_lt_one h₁ h₂).sub tendsto_const_nhds).mul tendsto_const_nhds
   (hasSum_iff_tendsto_nat_of_nonneg (pow_nonneg h₁) _).mpr <| by
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
-#align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
+#align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_one
+@[deprecated] alias hasSum_geometric_of_lt_1 := hasSum_geometric_of_lt_one
 
-theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
+theorem summable_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Summable fun n : ℕ ↦ r ^ n :=
-  ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
-#align summable_geometric_of_lt_1 summable_geometric_of_lt_1
+  ⟨_, hasSum_geometric_of_lt_one h₁ h₂⟩
+#align summable_geometric_of_lt_1 summable_geometric_of_lt_one
+@[deprecated] alias summable_geometric_of_lt_1 := summable_geometric_of_lt_one
 
-theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
-  (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
-#align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
+theorem tsum_geometric_of_lt_one {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+  (hasSum_geometric_of_lt_one h₁ h₂).tsum_eq
+#align tsum_geometric_of_lt_1 tsum_geometric_of_lt_one
+@[deprecated] alias tsum_geometric_of_lt_1 := tsum_geometric_of_lt_one
 
 theorem hasSum_geometric_two : HasSum (fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n) 2 := by
-  convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
+  convert hasSum_geometric_of_lt_one _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
 
 theorem summable_geometric_two : Summable fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n :=
@@ -269,7 +295,7 @@ theorem tsum_geometric_inv_two_ge (n : ℕ) :
 
 theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ ↦ a / 2 / 2 ^ n) a := by
   convert HasSum.mul_left (a / 2)
-      (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one) using 1
+      (hasSum_geometric_of_lt_one (le_of_lt one_half_pos) one_half_lt_one) using 1
   · funext n
     simp only [one_div, inv_pow]
     rfl
@@ -289,7 +315,7 @@ theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ
   apply NNReal.hasSum_coe.1
   push_cast
   rw [NNReal.coe_sub (le_of_lt hr)]
-  exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
+  exact hasSum_geometric_of_lt_one r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
 
 theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ ↦ r ^ n :=
@@ -399,7 +425,7 @@ theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ ↦ C * r ^ n) (C / (1
   rcases sign_cases_of_C_mul_pow_nonneg fun n ↦ dist_nonneg.trans (hu n) with (rfl | ⟨_, r₀⟩)
   · simp [hasSum_zero]
   · refine' HasSum.mul_left C _
-    simpa using hasSum_geometric_of_lt_1 r₀ hr
+    simpa using hasSum_geometric_of_lt_one r₀ hr
 #align aux_has_sum_of_le_geometric aux_hasSum_of_le_geometric
 
 variable (r C)
@@ -462,7 +488,7 @@ end LeGeometric
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
     Summable fun i ↦ 1 / m ^ f i := by
   refine .of_nonneg_of_le (fun a ↦ by positivity) (fun a ↦ ?_)
-      (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
+      (summable_geometric_of_lt_one (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]
   refine' (one_div_le_one_div _ _).mpr (pow_le_pow_right hm.le (fi a)) <;>
@@ -565,7 +591,7 @@ theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
 theorem tendsto_factorial_div_pow_self_atTop :
     Tendsto (fun n ↦ n ! / (n : ℝ) ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
-    (tendsto_const_div_atTop_nhds_0_nat 1)
+    (tendsto_const_div_atTop_nhds_zero_nat 1)
     (eventually_of_forall fun n ↦
       div_nonneg (mod_cast n.factorial_pos.le)
         (pow_nonneg (mod_cast n.zero_le) _))

Algebra.GroupPower.Lemmas used to be a big bag of lemmas that made it there on the criterion that they needed "more imports". This was completely untrue, as all lemmas could be moved to earlier files in PRs:

• #9440
• #9442
• #9443
• #9455
• #9456
• #9457
• #9459
• #9461
• #9463
• #9466
• #9501
• #9502
• #9503
• #9505
• #9551
• #9553
• #9720
• #9739
• #9740
• #9805
• #9806
• and this one

There are several reasons for this:

• Necessary lemmas have been moved to earlier files since lemmas were dumped in Algebra.GroupPower.Lemmas
• In the Lean 3 → Lean 4 transition, Std acquired basic Int and Nat lemmas which let us shortcircuit the part of the algebraic order hierarchy on which the corresponding general lemmas rest
• Some proofs were overpowered
• Some earlier files were tangled and I have untangled them

This PR finishes the job by moving the last few lemmas out of Algebra.GroupPower.Lemmas, which is therefore deleted.

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 -/
 import Mathlib.Algebra.GeomSum
-import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Order.Filter.Archimedean
 import Mathlib.Order.Iterate
 import Mathlib.Topology.Instances.ENNReal

These lemmas can be proved earlier.

Part of #9411

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
 -/
 import Mathlib.Algebra.GeomSum
+import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Order.Filter.Archimedean
 import Mathlib.Order.Iterate
 import Mathlib.Topology.Instances.ENNReal

@@ -580,7 +580,7 @@ theorem tendsto_factorial_div_pow_self_atTop :
             mul_le_of_le_one_left (inv_nonneg.mpr <| mod_cast hn.le) (prod_le_one _ _) <;>
           intro x hx <;>
         rw [Finset.mem_range] at hx
-      · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
+      · positivity
       · refine' (div_le_one <| mod_cast hn).mpr _
         norm_cast
         linarith)

See Zulip thread for the discussion.

@@ -96,7 +96,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
 
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ ↦ (r + 1) ^ n) atTop atTop :=
-  tendsto_atTop_atTop_of_monotone' (fun _ _ ↦ pow_le_pow_right $ le_add_of_nonneg_left h.le) <|
+  tendsto_atTop_atTop_of_monotone' (fun _ _ ↦ pow_le_pow_right <| le_add_of_nonneg_left h.le) <|
     not_bddAbove_iff.2 fun _ ↦ Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 
@@ -131,7 +131,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜
       simp only [hr.symm, one_pow] at h
       exact zero_ne_one <| tendsto_nhds_unique h tendsto_const_nhds
     · apply @not_tendsto_nhds_of_tendsto_atTop 𝕜 ℕ _ _ _ _ atTop _ (fun n ↦ |r| ^ n) _ 0 _
-      refine (pow_right_strictMono $ lt_of_le_of_ne (le_of_not_lt hr_le)
+      refine (pow_right_strictMono <| lt_of_le_of_ne (le_of_not_lt hr_le)
         hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
       obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
       exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]

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.

@@ -96,7 +96,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
 
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
     (h : 0 < r) : Tendsto (fun n : ℕ ↦ (r + 1) ^ n) atTop atTop :=
-  (tendsto_atTop_atTop_of_monotone' fun _ _ ↦ pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
+  tendsto_atTop_atTop_of_monotone' (fun _ _ ↦ pow_le_pow_right $ le_add_of_nonneg_left h.le) <|
     not_bddAbove_iff.2 fun _ ↦ Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 
@@ -131,7 +131,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜
       simp only [hr.symm, one_pow] at h
       exact zero_ne_one <| tendsto_nhds_unique h tendsto_const_nhds
     · apply @not_tendsto_nhds_of_tendsto_atTop 𝕜 ℕ _ _ _ _ atTop _ (fun n ↦ |r| ^ n) _ 0 _
-      refine (pow_strictMono_right $ lt_of_le_of_ne (le_of_not_lt hr_le)
+      refine (pow_right_strictMono $ lt_of_le_of_ne (le_of_not_lt hr_le)
         hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
       obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
       exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
@@ -465,7 +465,7 @@ theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi
       (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]
-  refine' (one_div_le_one_div _ _).mpr (pow_le_pow hm.le (fi a)) <;>
+  refine' (one_div_le_one_div _ _).mpr (pow_le_pow_right hm.le (fi a)) <;>
     exact pow_pos (zero_lt_one.trans hm) _
 #align summable_one_div_pow_of_le summable_one_div_pow_of_le
 

Adding Tendsto (fun n : ℕ ↦ 1/(n : ℝ)) atTop (𝓝 0). We already have an equivalent statement but it is very hard to find and I've seen several students struggling to find it.

I also took the opportunity to fix mapsto arrows in this file, but tendsto_one_div_atTop_nhds_0_nat is the only new content.

@@ -28,40 +28,43 @@ open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
 variable {α : Type*} {β : Type*} {ι : Type*}
 
-theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
+theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
 
-theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
+theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
   simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
 
+theorem tendsto_one_div_atTop_nhds_0_nat : Tendsto (fun n : ℕ ↦ 1/(n : ℝ)) atTop (𝓝 0) :=
+  tendsto_const_div_atTop_nhds_0_nat 1
+
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat :
-    Tendsto (fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by
+    Tendsto (fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (𝓝 0) := by
   rw [← NNReal.tendsto_coe]
   exact _root_.tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_inverse_at_top_nhds_0_nat NNReal.tendsto_inverse_atTop_nhds_0_nat
 
 theorem NNReal.tendsto_const_div_atTop_nhds_0_nat (C : ℝ≥0) :
-    Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
+    Tendsto (fun n : ℕ ↦ C / n) atTop (𝓝 0) := by
   simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat
 #align nnreal.tendsto_const_div_at_top_nhds_0_nat NNReal.tendsto_const_div_atTop_nhds_0_nat
 
 theorem tendsto_one_div_add_atTop_nhds_0_nat :
-    Tendsto (fun n : ℕ => 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
-  suffices Tendsto (fun n : ℕ => 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
+    Tendsto (fun n : ℕ ↦ 1 / ((n : ℝ) + 1)) atTop (𝓝 0) :=
+  suffices Tendsto (fun n : ℕ ↦ 1 / (↑(n + 1) : ℝ)) atTop (𝓝 0) by simpa
   (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
 theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ≥0 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
-    Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
+    Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ ↦ (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
   convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp tendsto_inverse_atTop_nhds_0_nat
   rw [map_zero]
 
 theorem tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
-    Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ => (n : ℝ)⁻¹) atTop (nhds 0) :=
+    Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ ↦ (n : ℝ)⁻¹) atTop (nhds 0) :=
   NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat 𝕜
 
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
@@ -71,9 +74,9 @@ TODO: introduce a typeclass saying that `1 / n` tends to 0 at top, making it pos
 statement simultaneously on `ℚ`, `ℝ` and `ℂ`. -/
 theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
     [CharZero 𝕜] [Algebra ℝ 𝕜] [ContinuousSMul ℝ 𝕜] [TopologicalDivisionRing 𝕜] (x : 𝕜) :
-    Tendsto (fun n : ℕ => (n : 𝕜) / (n + x)) atTop (𝓝 1) := by
-  refine' Tendsto.congr' ((eventually_ne_atTop 0).mp (eventually_of_forall fun n hn => _)) _
-  · exact fun n : ℕ => 1 / (1 + x / n)
+    Tendsto (fun n : ℕ ↦ (n : 𝕜) / (n + x)) atTop (𝓝 1) := by
+  refine' Tendsto.congr' ((eventually_ne_atTop 0).mp (eventually_of_forall fun n hn ↦ _)) _
+  · exact fun n : ℕ ↦ 1 / (1 + x / n)
   · field_simp [Nat.cast_ne_zero.mpr hn]
   · have : 𝓝 (1 : 𝕜) = 𝓝 (1 / (1 + x * (0 : 𝕜))) := by
       rw [mul_zero, add_zero, div_one]
@@ -92,35 +95,35 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
 
 
 theorem tendsto_add_one_pow_atTop_atTop_of_pos [LinearOrderedSemiring α] [Archimedean α] {r : α}
-    (h : 0 < r) : Tendsto (fun n : ℕ => (r + 1) ^ n) atTop atTop :=
-  (tendsto_atTop_atTop_of_monotone' fun _ _ => pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
-    not_bddAbove_iff.2 fun _ => Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
+    (h : 0 < r) : Tendsto (fun n : ℕ ↦ (r + 1) ^ n) atTop atTop :=
+  (tendsto_atTop_atTop_of_monotone' fun _ _ ↦ pow_le_pow (le_add_of_nonneg_left (le_of_lt h))) <|
+    not_bddAbove_iff.2 fun _ ↦ Set.exists_range_iff.2 <| add_one_pow_unbounded_of_pos _ h
 #align tendsto_add_one_pow_at_top_at_top_of_pos tendsto_add_one_pow_atTop_atTop_of_pos
 
 theorem tendsto_pow_atTop_atTop_of_one_lt [LinearOrderedRing α] [Archimedean α] {r : α}
-    (h : 1 < r) : Tendsto (fun n : ℕ => r ^ n) atTop atTop :=
+    (h : 1 < r) : Tendsto (fun n : ℕ ↦ r ^ n) atTop atTop :=
   sub_add_cancel r 1 ▸ tendsto_add_one_pow_atTop_atTop_of_pos (sub_pos.2 h)
 #align tendsto_pow_at_top_at_top_of_one_lt tendsto_pow_atTop_atTop_of_one_lt
 
 theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
-    Tendsto (fun n : ℕ => m ^ n) atTop atTop :=
+    Tendsto (fun n : ℕ ↦ m ^ n) atTop atTop :=
   tsub_add_cancel_of_le (le_of_lt h) ▸ tendsto_add_one_pow_atTop_atTop_of_pos (tsub_pos_of_lt h)
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 
 theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
-    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
+    Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
   h₁.eq_or_lt.elim
-    (fun hr => (tendsto_add_atTop_iff_nat 1).mp <| by
+    (fun hr ↦ (tendsto_add_atTop_iff_nat 1).mp <| by
       simp [_root_.pow_succ, ← hr, tendsto_const_nhds])
-    (fun hr =>
+    (fun hr ↦
       have := one_lt_inv hr h₂ |> tendsto_pow_atTop_atTop_of_one_lt
-      (tendsto_inv_atTop_zero.comp this).congr fun n => by simp)
+      (tendsto_inv_atTop_zero.comp this).congr fun n ↦ by simp)
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
 
 @[simp] theorem tendsto_pow_atTop_nhds_0_iff {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} :
-    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) ↔ |r| < 1 := by
+    Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) ↔ |r| < 1 := by
   rw [tendsto_zero_iff_abs_tendsto_zero]
   refine ⟨fun h ↦ by_contra (fun hr_le ↦ ?_), fun h ↦ ?_⟩
   · by_cases hr : 1 = |r|
@@ -136,17 +139,17 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜
 
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
-    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
+    Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝[>] 0) :=
   tendsto_inf.2
     ⟨tendsto_pow_atTop_nhds_0_of_lt_1 h₁.le h₂,
-      tendsto_principal.2 <| eventually_of_forall fun _ => pow_pos h₁ _⟩
+      tendsto_principal.2 <| eventually_of_forall fun _ ↦ pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
 
 theorem uniformity_basis_dist_pow_of_lt_1 {α : Type*} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
-    (uniformity α).HasBasis (fun _ : ℕ => True) fun k => { p : α × α | dist p.1 p.2 < r ^ k } :=
-  Metric.mk_uniformity_basis (fun _ _ => pow_pos h₀ _) fun _ ε0 =>
-    (exists_pow_lt_of_lt_one ε0 h₁).imp fun _ hk => ⟨trivial, hk.le⟩
+    (uniformity α).HasBasis (fun _ : ℕ ↦ True) fun k ↦ { p : α × α | dist p.1 p.2 < r ^ k } :=
+  Metric.mk_uniformity_basis (fun _ _ ↦ pow_pos h₀ _) fun _ ε0 ↦
+    (exists_pow_lt_of_lt_one ε0 h₁).imp fun _ hk ↦ ⟨trivial, hk.le⟩
 #align uniformity_basis_dist_pow_of_lt_1 uniformity_basis_dist_pow_of_lt_1
 
 theorem geom_lt {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) {n : ℕ} (hn : 0 < n)
@@ -179,19 +182,19 @@ theorem le_geom {u : ℕ → ℝ} {c : ℝ} (hc : 0 ≤ c) (n : ℕ) (h : ∀ k
 then it goes to +∞. -/
 theorem tendsto_atTop_of_geom_le {v : ℕ → ℝ} {c : ℝ} (h₀ : 0 < v 0) (hc : 1 < c)
     (hu : ∀ n, c * v n ≤ v (n + 1)) : Tendsto v atTop atTop :=
-  (tendsto_atTop_mono fun n => geom_le (zero_le_one.trans hc.le) n fun k _ => hu k) <|
+  (tendsto_atTop_mono fun n ↦ geom_le (zero_le_one.trans hc.le) n fun k _ ↦ hu k) <|
     (tendsto_pow_atTop_atTop_of_one_lt hc).atTop_mul_const h₀
 #align tendsto_at_top_of_geom_le tendsto_atTop_of_geom_le
 
 theorem NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0} (hr : r < 1) :
-    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
+    Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) :=
   NNReal.tendsto_coe.1 <| by
     simp only [NNReal.coe_pow, NNReal.coe_zero,
       _root_.tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]
 #align nnreal.tendsto_pow_at_top_nhds_0_of_lt_1 NNReal.tendsto_pow_atTop_nhds_0_of_lt_1
 
 theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
-    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) := by
+    Tendsto (fun n : ℕ ↦ r ^ n) atTop (𝓝 0) := by
   rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
   rw [← ENNReal.coe_zero]
   norm_cast at *
@@ -204,16 +207,16 @@ theorem ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 {r : ℝ≥0∞} (hr : r < 1) :
 section Geometric
 
 theorem hasSum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
-    HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ :=
+    HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ :=
   have : r ≠ 1 := ne_of_lt h₂
-  have : Tendsto (fun n => (r ^ n - 1) * (r - 1)⁻¹) atTop (𝓝 ((0 - 1) * (r - 1)⁻¹)) :=
+  have : Tendsto (fun n ↦ (r ^ n - 1) * (r - 1)⁻¹) atTop (𝓝 ((0 - 1) * (r - 1)⁻¹)) :=
     ((tendsto_pow_atTop_nhds_0_of_lt_1 h₁ h₂).sub tendsto_const_nhds).mul tendsto_const_nhds
   (hasSum_iff_tendsto_nat_of_nonneg (pow_nonneg h₁) _).mpr <| by
     simp_all [neg_inv, geom_sum_eq, div_eq_mul_inv]
 #align has_sum_geometric_of_lt_1 hasSum_geometric_of_lt_1
 
 theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
-    Summable fun n : ℕ => r ^ n :=
+    Summable fun n : ℕ ↦ r ^ n :=
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
 
@@ -221,16 +224,16 @@ theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑'
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
 
-theorem hasSum_geometric_two : HasSum (fun n : ℕ => ((1 : ℝ) / 2) ^ n) 2 := by
+theorem hasSum_geometric_two : HasSum (fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n) 2 := by
   convert hasSum_geometric_of_lt_1 _ _ <;> norm_num
 #align has_sum_geometric_two hasSum_geometric_two
 
-theorem summable_geometric_two : Summable fun n : ℕ => ((1 : ℝ) / 2) ^ n :=
+theorem summable_geometric_two : Summable fun n : ℕ ↦ ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
 #align summable_geometric_two summable_geometric_two
 
 theorem summable_geometric_two_encode {ι : Type*} [Encodable ι] :
-    Summable fun i : ι => (1 / 2 : ℝ) ^ Encodable.encode i :=
+    Summable fun i : ι ↦ (1 / 2 : ℝ) ^ Encodable.encode i :=
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
 
@@ -243,7 +246,7 @@ theorem sum_geometric_two_le (n : ℕ) : (∑ i : ℕ in range n, (1 / (2 : ℝ)
     intro i
     apply pow_nonneg
     norm_num
-  convert sum_le_tsum (range n) (fun i _ => this i) summable_geometric_two
+  convert sum_le_tsum (range n) (fun i _ ↦ this i) summable_geometric_two
   exact tsum_geometric_two.symm
 #align sum_geometric_two_le sum_geometric_two_le
 
@@ -254,17 +257,17 @@ theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
 /-- The sum of `2⁻¹ ^ i` for `n ≤ i` equals `2 * 2⁻¹ ^ n`. -/
 theorem tsum_geometric_inv_two_ge (n : ℕ) :
     (∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0) = 2 * 2⁻¹ ^ n := by
-  have A : Summable fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
+  have A : Summable fun i : ℕ ↦ ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
     simpa only [← piecewise_eq_indicator, one_div]
       using summable_geometric_two.indicator {i | n ≤ i}
-  have B : ((Finset.range n).sum fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0) = 0 :=
-    Finset.sum_eq_zero fun i hi =>
-      ite_eq_right_iff.2 fun h => (lt_irrefl _ ((Finset.mem_range.1 hi).trans_le h)).elim
+  have B : ((Finset.range n).sum fun i : ℕ ↦ ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0) = 0 :=
+    Finset.sum_eq_zero fun i hi ↦
+      ite_eq_right_iff.2 fun h ↦ (lt_irrefl _ ((Finset.mem_range.1 hi).trans_le h)).elim
   simp only [← _root_.sum_add_tsum_nat_add n A, B, if_true, zero_add, zero_le',
     le_add_iff_nonneg_left, pow_add, _root_.tsum_mul_right, tsum_geometric_inv_two]
 #align tsum_geometric_inv_two_ge tsum_geometric_inv_two_ge
 
-theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n) a := by
+theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ ↦ a / 2 / 2 ^ n) a := by
   convert HasSum.mul_left (a / 2)
       (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one) using 1
   · funext n
@@ -273,7 +276,7 @@ theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n)
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'
 
-theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^ n :=
+theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ ↦ a / 2 / 2 ^ n :=
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
 
@@ -282,14 +285,14 @@ theorem tsum_geometric_two' (a : ℝ) : ∑' n : ℕ, a / 2 / 2 ^ n = a :=
 #align tsum_geometric_two' tsum_geometric_two'
 
 /-- **Sum of a Geometric Series** -/
-theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ => r ^ n) (1 - r)⁻¹ := by
+theorem NNReal.hasSum_geometric {r : ℝ≥0} (hr : r < 1) : HasSum (fun n : ℕ ↦ r ^ n) (1 - r)⁻¹ := by
   apply NNReal.hasSum_coe.1
   push_cast
   rw [NNReal.coe_sub (le_of_lt hr)]
   exact hasSum_geometric_of_lt_1 r.coe_nonneg hr
 #align nnreal.has_sum_geometric NNReal.hasSum_geometric
 
-theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ => r ^ n :=
+theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n : ℕ ↦ r ^ n :=
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
@@ -307,8 +310,8 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : ∑' n : ℕ, r ^ n = (1 - r)
     convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
     rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr, coe_sub, coe_one]
   · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_iSup_nat, iSup_eq_top]
-    refine' fun a ha =>
-      (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
+    refine' fun a ha ↦
+      (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn ↦ lt_of_lt_of_le hn _
     calc
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
       _ ≤ ∑ i in range n, r ^ i := by gcongr; apply one_le_pow_of_one_le' hr
@@ -392,8 +395,8 @@ section LeGeometric
 variable [PseudoMetricSpace α] {r C : ℝ} (hr : r < 1) {f : ℕ → α}
   (hu : ∀ n, dist (f n) (f (n + 1)) ≤ C * r ^ n)
 
-theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ => C * r ^ n) (C / (1 - r)) := by
-  rcases sign_cases_of_C_mul_pow_nonneg fun n => dist_nonneg.trans (hu n) with (rfl | ⟨_, r₀⟩)
+theorem aux_hasSum_of_le_geometric : HasSum (fun n : ℕ ↦ C * r ^ n) (C / (1 - r)) := by
+  rcases sign_cases_of_C_mul_pow_nonneg fun n ↦ dist_nonneg.trans (hu n) with (rfl | ⟨_, r₀⟩)
   · simp [hasSum_zero]
   · refine' HasSum.mul_left C _
     simpa using hasSum_geometric_of_lt_1 r₀ hr
@@ -457,8 +460,8 @@ end LeGeometric
 
 /-- A series whose terms are bounded by the terms of a converging geometric series converges. -/
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
-    Summable fun i => 1 / m ^ f i := by
-  refine .of_nonneg_of_le (fun a => by positivity) (fun a => ?_)
+    Summable fun i ↦ 1 / m ^ f i := by
+  refine .of_nonneg_of_le (fun a ↦ by positivity) (fun a ↦ ?_)
       (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]
@@ -474,8 +477,8 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     { ε' : ι → ℝ // (∀ i, 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c ≤ ε } := by
   let f n := ε / 2 / 2 ^ n
   have hf : HasSum f ε := hasSum_geometric_two' _
-  have f0 : ∀ n, 0 < f n := fun n => div_pos (half_pos hε) (pow_pos zero_lt_two _)
-  refine' ⟨f ∘ Encodable.encode, fun i => f0 _, _⟩
+  have f0 : ∀ n, 0 < f n := fun n ↦ div_pos (half_pos hε) (pow_pos zero_lt_two _)
+  refine' ⟨f ∘ Encodable.encode, fun i ↦ f0 _, _⟩
   rcases hf.summable.comp_injective (@Encodable.encode_injective ι _) with ⟨c, hg⟩
   refine' ⟨c, hg, hasSum_le_inj _ (@Encodable.encode_injective ι _) _ _ hg hf⟩
   · intro i _
@@ -485,10 +488,10 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
 #align pos_sum_of_encodable posSumOfEncodable
 
 theorem Set.Countable.exists_pos_hasSum_le {ι : Type*} {s : Set ι} (hs : s.Countable) {ε : ℝ}
-    (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s => ε' i) c ∧ c ≤ ε := by
+    (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s ↦ ε' i) c ∧ c ≤ ε := by
   haveI := hs.toEncodable
   rcases posSumOfEncodable hε s with ⟨f, hf0, ⟨c, hfc, hcε⟩⟩
-  refine' ⟨fun i => if h : i ∈ s then f ⟨i, h⟩ else 1, fun i => _, ⟨c, _, hcε⟩⟩
+  refine' ⟨fun i ↦ if h : i ∈ s then f ⟨i, h⟩ else 1, fun i ↦ _, ⟨c, _, hcε⟩⟩
   · conv_rhs => simp
     split_ifs
     exacts [hf0 _, zero_lt_one]
@@ -499,10 +502,10 @@ theorem Set.Countable.exists_pos_forall_sum_le {ι : Type*} {s : Set ι} (hs : s
     (hε : 0 < ε) : ∃ ε' : ι → ℝ,
     (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → ∑ i in t, ε' i ≤ ε := by
   rcases hs.exists_pos_hasSum_le hε with ⟨ε', hpos, c, hε'c, hcε⟩
-  refine' ⟨ε', hpos, fun t ht => _⟩
+  refine' ⟨ε', hpos, fun t ht ↦ _⟩
   rw [← sum_subtype_of_mem _ ht]
   refine' (sum_le_hasSum _ _ hε'c).trans hcε
-  exact fun _ _ => (hpos _).le
+  exact fun _ _ ↦ (hpos _).le
 #align set.countable.exists_pos_forall_sum_le Set.Countable.exists_pos_forall_sum_le
 
 namespace NNReal
@@ -513,8 +516,8 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0} (hε : ε ≠ 0) (ι) [Counta
   obtain ⟨a, a0, aε⟩ := exists_between (pos_iff_ne_zero.2 hε)
   obtain ⟨ε', hε', c, hc, hcε⟩ := posSumOfEncodable a0 ι
   exact
-    ⟨fun i => ⟨ε' i, (hε' i).le⟩, fun i => NNReal.coe_lt_coe.1 <| hε' i,
-      ⟨c, hasSum_le (fun i => (hε' i).le) hasSum_zero hc⟩, NNReal.hasSum_coe.1 hc,
+    ⟨fun i ↦ ⟨ε' i, (hε' i).le⟩, fun i ↦ NNReal.coe_lt_coe.1 <| hε' i,
+      ⟨c, hasSum_le (fun i ↦ (hε' i).le) hasSum_zero hc⟩, NNReal.hasSum_coe.1 hc,
       aε.trans_le' <| NNReal.coe_le_coe.1 hcε⟩
 #align nnreal.exists_pos_sum_of_countable NNReal.exists_pos_sum_of_countable
 
@@ -533,16 +536,16 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
     ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ ∑' i, ε' i < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
-  ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
+  ⟨fun i ↦ δ i, fun i ↦ ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'
 
 theorem exists_pos_tsum_mul_lt_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) {ι} [Countable ι] (w : ι → ℝ≥0∞)
     (hw : ∀ i, w i ≠ ∞) : ∃ δ : ι → ℝ≥0, (∀ i, 0 < δ i) ∧ (∑' i, (w i * δ i : ℝ≥0∞)) < ε := by
   lift w to ι → ℝ≥0 using hw
   rcases exists_pos_sum_of_countable hε ι with ⟨δ', Hpos, Hsum⟩
-  have : ∀ i, 0 < max 1 (w i) := fun i => zero_lt_one.trans_le (le_max_left _ _)
-  refine' ⟨fun i => δ' i / max 1 (w i), fun i => div_pos (Hpos _) (this i), _⟩
-  refine' lt_of_le_of_lt (ENNReal.tsum_le_tsum fun i => _) Hsum
+  have : ∀ i, 0 < max 1 (w i) := fun i ↦ zero_lt_one.trans_le (le_max_left _ _)
+  refine' ⟨fun i ↦ δ' i / max 1 (w i), fun i ↦ div_pos (Hpos _) (this i), _⟩
+  refine' lt_of_le_of_lt (ENNReal.tsum_le_tsum fun i ↦ _) Hsum
   rw [coe_div (this i).ne']
   refine' mul_le_of_le_div' (mul_le_mul_left' (ENNReal.inv_le_inv.2 _) _)
   exact coe_le_coe.2 (le_max_right _ _)
@@ -556,18 +559,18 @@ end ENNReal
 
 
 theorem factorial_tendsto_atTop : Tendsto Nat.factorial atTop atTop :=
-  tendsto_atTop_atTop_of_monotone Nat.monotone_factorial fun n => ⟨n, n.self_le_factorial⟩
+  tendsto_atTop_atTop_of_monotone Nat.monotone_factorial fun n ↦ ⟨n, n.self_le_factorial⟩
 #align factorial_tendsto_at_top factorial_tendsto_atTop
 
 theorem tendsto_factorial_div_pow_self_atTop :
-    Tendsto (fun n => n ! / (n : ℝ) ^ n : ℕ → ℝ) atTop (𝓝 0) :=
+    Tendsto (fun n ↦ n ! / (n : ℝ) ^ n : ℕ → ℝ) atTop (𝓝 0) :=
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
     (tendsto_const_div_atTop_nhds_0_nat 1)
-    (eventually_of_forall fun n =>
+    (eventually_of_forall fun n ↦
       div_nonneg (mod_cast n.factorial_pos.le)
         (pow_nonneg (mod_cast n.zero_le) _))
     (by
-      refine' (eventually_gt_atTop 0).mono fun n hn => _
+      refine' (eventually_gt_atTop 0).mono fun n hn ↦ _
       rcases Nat.exists_eq_succ_of_ne_zero hn.ne.symm with ⟨k, rfl⟩
       rw [← prod_range_add_one_eq_factorial, pow_eq_prod_const, div_eq_mul_inv, ← inv_eq_one_div,
         prod_natCast, Nat.cast_succ, ← prod_inv_distrib, ← prod_mul_distrib,
@@ -591,8 +594,8 @@ theorem tendsto_factorial_div_pow_self_atTop :
 section
 
 theorem tendsto_nat_floor_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSemiring α] :
-    Tendsto (fun x : α => ⌊x⌋₊) atTop atTop :=
-  Nat.floor_mono.tendsto_atTop_atTop fun x => ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
+    Tendsto (fun x : α ↦ ⌊x⌋₊) atTop atTop :=
+  Nat.floor_mono.tendsto_atTop_atTop fun x ↦ ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
 #align tendsto_nat_floor_at_top tendsto_nat_floor_atTop
 
 lemma tendsto_nat_floor_mul_atTop {α : Type _} [LinearOrderedSemifield α] [FloorSemiring α]
@@ -603,40 +606,40 @@ lemma tendsto_nat_floor_mul_atTop {α : Type _} [LinearOrderedSemifield α] [Flo
 variable {R : Type*} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
-    Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) := by
-  have A : Tendsto (fun x : R => a - x⁻¹) atTop (𝓝 (a - 0)) :=
+    Tendsto (fun x ↦ (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) := by
+  have A : Tendsto (fun x : R ↦ a - x⁻¹) atTop (𝓝 (a - 0)) :=
     tendsto_const_nhds.sub tendsto_inv_atTop_zero
   rw [sub_zero] at A
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' A tendsto_const_nhds
-  · refine' eventually_atTop.2 ⟨1, fun x hx => _⟩
+  · refine' eventually_atTop.2 ⟨1, fun x hx ↦ _⟩
     simp only [le_div_iff (zero_lt_one.trans_le hx), _root_.sub_mul,
       inv_mul_cancel (zero_lt_one.trans_le hx).ne']
     have := Nat.lt_floor_add_one (a * x)
     linarith
-  · refine' eventually_atTop.2 ⟨1, fun x hx => _⟩
+  · refine' eventually_atTop.2 ⟨1, fun x hx ↦ _⟩
     rw [div_le_iff (zero_lt_one.trans_le hx)]
     simp [Nat.floor_le (mul_nonneg ha (zero_le_one.trans hx))]
 #align tendsto_nat_floor_mul_div_at_top tendsto_nat_floor_mul_div_atTop
 
-theorem tendsto_nat_floor_div_atTop : Tendsto (fun x => (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
+theorem tendsto_nat_floor_div_atTop : Tendsto (fun x ↦ (⌊x⌋₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_floor_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_floor_div_at_top tendsto_nat_floor_div_atTop
 
 theorem tendsto_nat_ceil_mul_div_atTop {a : R} (ha : 0 ≤ a) :
-    Tendsto (fun x => (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) := by
-  have A : Tendsto (fun x : R => a + x⁻¹) atTop (𝓝 (a + 0)) :=
+    Tendsto (fun x ↦ (⌈a * x⌉₊ : R) / x) atTop (𝓝 a) := by
+  have A : Tendsto (fun x : R ↦ a + x⁻¹) atTop (𝓝 (a + 0)) :=
     tendsto_const_nhds.add tendsto_inv_atTop_zero
   rw [add_zero] at A
   apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds A
-  · refine' eventually_atTop.2 ⟨1, fun x hx => _⟩
+  · refine' eventually_atTop.2 ⟨1, fun x hx ↦ _⟩
     rw [le_div_iff (zero_lt_one.trans_le hx)]
     exact Nat.le_ceil _
-  · refine' eventually_atTop.2 ⟨1, fun x hx => _⟩
+  · refine' eventually_atTop.2 ⟨1, fun x hx ↦ _⟩
     simp [div_le_iff (zero_lt_one.trans_le hx), inv_mul_cancel (zero_lt_one.trans_le hx).ne',
       (Nat.ceil_lt_add_one (mul_nonneg ha (zero_le_one.trans hx))).le, add_mul]
 #align tendsto_nat_ceil_mul_div_at_top tendsto_nat_ceil_mul_div_atTop
 
-theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
+theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x ↦ (⌈x⌉₊ : R) / x) atTop (𝓝 1) := by
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop
 

This PR proves the Akra-Bazzi theorem, which gives the asymptotic order of divide-and-conquer recurrences of the form

T n = (∑ i in Fin k, a i * T (r i n)) + g n

where T : ℕ → ℝ, and where r i n is close to b i * n for a set of coefficients b : Fin k → ℝ. These recurrences arise mainly in the analysis of divide-and-conquer algorithms such as mergesort or Strassen's algorithm for matrix multiplication.

Note that the traditional proof first proves a continuous version (i.e. for T : ℝ → ℝ) and then discretizes it to get a version that is relevant for algorithms. Here we prove the discrete version directly, which shortens the proof considerably.

@@ -595,6 +595,11 @@ theorem tendsto_nat_floor_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSe
   Nat.floor_mono.tendsto_atTop_atTop fun x => ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
 #align tendsto_nat_floor_at_top tendsto_nat_floor_atTop
 
+lemma tendsto_nat_floor_mul_atTop {α : Type _} [LinearOrderedSemifield α] [FloorSemiring α]
+    [Archimedean α] (a : α) (ha : 0 < a) : Tendsto (fun (x:ℕ) => ⌊a * x⌋₊) atTop atTop :=
+  Tendsto.comp tendsto_nat_floor_atTop
+    <| Tendsto.const_mul_atTop ha tendsto_nat_cast_atTop_atTop
+
 variable {R : Type*} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :

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

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

@@ -564,8 +564,8 @@ theorem tendsto_factorial_div_pow_self_atTop :
   tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds
     (tendsto_const_div_atTop_nhds_0_nat 1)
     (eventually_of_forall fun n =>
-      div_nonneg (by exact_mod_cast n.factorial_pos.le)
-        (pow_nonneg (by exact_mod_cast n.zero_le) _))
+      div_nonneg (mod_cast n.factorial_pos.le)
+        (pow_nonneg (mod_cast n.zero_le) _))
     (by
       refine' (eventually_gt_atTop 0).mono fun n hn => _
       rcases Nat.exists_eq_succ_of_ne_zero hn.ne.symm with ⟨k, rfl⟩
@@ -574,11 +574,11 @@ theorem tendsto_factorial_div_pow_self_atTop :
         Finset.prod_range_succ']
       simp only [prod_range_succ', one_mul, Nat.cast_add, zero_add, Nat.cast_one]
       refine'
-            mul_le_of_le_one_left (inv_nonneg.mpr <| by exact_mod_cast hn.le) (prod_le_one _ _) <;>
+            mul_le_of_le_one_left (inv_nonneg.mpr <| mod_cast hn.le) (prod_le_one _ _) <;>
           intro x hx <;>
         rw [Finset.mem_range] at hx
       · refine' mul_nonneg _ (inv_nonneg.mpr _) <;> norm_cast <;> linarith
-      · refine' (div_le_one <| by exact_mod_cast hn).mpr _
+      · refine' (div_le_one <| mod_cast hn).mpr _
         norm_cast
         linarith)
 #align tendsto_factorial_div_pow_self_at_top tendsto_factorial_div_pow_self_atTop

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.

@@ -255,9 +255,8 @@ theorem tsum_geometric_inv_two : (∑' n : ℕ, (2 : ℝ)⁻¹ ^ n) = 2 :=
 theorem tsum_geometric_inv_two_ge (n : ℕ) :
     (∑' i, ite (n ≤ i) ((2 : ℝ)⁻¹ ^ i) 0) = 2 * 2⁻¹ ^ n := by
   have A : Summable fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0 := by
-    apply summable_of_nonneg_of_le _ _ summable_geometric_two <;>
-      · intro i
-        by_cases hi : n ≤ i <;> simp [hi]; apply pow_nonneg; exact zero_le_two
+    simpa only [← piecewise_eq_indicator, one_div]
+      using summable_geometric_two.indicator {i | n ≤ i}
   have B : ((Finset.range n).sum fun i : ℕ => ite (n ≤ i) ((2⁻¹ : ℝ) ^ i) 0) = 0 :=
     Finset.sum_eq_zero fun i hi =>
       ite_eq_right_iff.2 fun h => (lt_irrefl _ ((Finset.mem_range.1 hi).trans_le h)).elim
@@ -459,9 +458,7 @@ end LeGeometric
 /-- A series whose terms are bounded by the terms of a converging geometric series converges. -/
 theorem summable_one_div_pow_of_le {m : ℝ} {f : ℕ → ℕ} (hm : 1 < m) (fi : ∀ i, i ≤ f i) :
     Summable fun i => 1 / m ^ f i := by
-  refine'
-    summable_of_nonneg_of_le (fun a => one_div_nonneg.mpr (pow_nonneg (zero_le_one.trans hm.le) _))
-      (fun a => _)
+  refine .of_nonneg_of_le (fun a => by positivity) (fun a => ?_)
       (summable_geometric_of_lt_1 (one_div_nonneg.mpr (zero_le_one.trans hm.le))
         ((one_div_lt (zero_lt_one.trans hm) zero_lt_one).mpr (one_div_one.le.trans_lt hm)))
   rw [div_pow, one_pow]

New lemmas / instances

• An archimedean ordered semiring is directed upwards.
• Filter.hasAntitoneBasis_atTop;
• Filter.HasAntitoneBasis.iInf_principal;

Fix typos

• Docstrings: "if the agree" -> "if they agree".
• ProbabilityTheory.measure_eq_zero_or_one_of_indepSetCat_self -> ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self.

Weaken typeclass assumptions

From a semilattice to a directed type

• MeasureTheory.tendsto_measure_iUnion;
• MeasureTheory.tendsto_measure_iInter;
• Monotone.directed_le, Monotone.directed_ge;
• Antitone.directed_le, Antitone.directed_ge;
• directed_of_sup, renamed to directed_of_isDirected_le;
• directed_of_inf, renamed to directed_of_isDirected_ge;

From a strict ordered semiring to an ordered semiring

• tendsto_nat_cast_atTop_atTop;
• Filter.Eventually.nat_cast_atTop;
• atTop_hasAntitoneBasis_of_archimedean;

@@ -639,7 +639,6 @@ theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atT
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop
 
 lemma Nat.tendsto_div_const_atTop {n : ℕ} (hn : n ≠ 0) : Tendsto (λ x ↦ x / n) atTop atTop := by
-  simp_rw [←@Nat.floor_div_eq_div ℚ]
-  exact tendsto_nat_floor_atTop.comp (tendsto_nat_cast_atTop_atTop.atTop_div_const $ by positivity)
+  rw [Tendsto, map_div_atTop_eq_nat n hn.bot_lt]
 
 end

Fixes the nonterminal simps identified by #7496

@@ -269,7 +269,7 @@ theorem hasSum_geometric_two' (a : ℝ) : HasSum (fun n : ℕ => a / 2 / 2 ^ n)
   convert HasSum.mul_left (a / 2)
       (hasSum_geometric_of_lt_1 (le_of_lt one_half_pos) one_half_lt_one) using 1
   · funext n
-    simp
+    simp only [one_div, inv_pow]
     rfl
   · norm_num
 #align has_sum_geometric_two' hasSum_geometric_two'

@@ -294,9 +294,9 @@ theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n :
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
-theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
+theorem tsum_geometric_nnreal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
-#align tsum_geometric_nnreal tsum_geometric_nNReal
+#align tsum_geometric_nnreal tsum_geometric_nnreal
 
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/

and a few lemmas missing from Order.Filter.AtTopBot.

@@ -638,4 +638,8 @@ theorem tendsto_nat_ceil_div_atTop : Tendsto (fun x => (⌈x⌉₊ : R) / x) atT
   simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)
 #align tendsto_nat_ceil_div_at_top tendsto_nat_ceil_div_atTop
 
+lemma Nat.tendsto_div_const_atTop {n : ℕ} (hn : n ≠ 0) : Tendsto (λ x ↦ x / n) atTop atTop := by
+  simp_rw [←@Nat.floor_div_eq_div ℚ]
+  exact tendsto_nat_floor_atTop.comp (tendsto_nat_cast_atTop_atTop.atTop_div_const $ by positivity)
+
 end

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

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

@@ -33,7 +33,7 @@ theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻
 #align tendsto_inverse_at_top_nhds_0_nat tendsto_inverse_atTop_nhds_0_nat
 
 theorem tendsto_const_div_atTop_nhds_0_nat (C : ℝ) : Tendsto (fun n : ℕ => C / n) atTop (𝓝 0) := by
-  simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
+  simpa only [mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat
 #align tendsto_const_div_at_top_nhds_0_nat tendsto_const_div_atTop_nhds_0_nat
 
 theorem NNReal.tendsto_inverse_atTop_nhds_0_nat :
@@ -76,7 +76,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [Topolo
   · exact fun n : ℕ => 1 / (1 + x / n)
   · field_simp [Nat.cast_ne_zero.mpr hn]
   · have : 𝓝 (1 : 𝕜) = 𝓝 (1 / (1 + x * (0 : 𝕜))) := by
-      rw [MulZeroClass.mul_zero, add_zero, div_one]
+      rw [mul_zero, add_zero, div_one]
     rw [this]
     refine' tendsto_const_nhds.div (tendsto_const_nhds.add _) (by simp)
     simp_rw [div_eq_mul_inv]

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

This has nice performance benefits.

@@ -26,7 +26,7 @@ open Classical Set Function Filter Finset Metric
 
 open Classical Topology Nat BigOperators uniformity NNReal ENNReal
 
-variable {α : Type _} {β : Type _} {ι : Type _}
+variable {α : Type*} {β : Type*} {ι : Type*}
 
 theorem tendsto_inverse_atTop_nhds_0_nat : Tendsto (fun n : ℕ => (n : ℝ)⁻¹) atTop (𝓝 0) :=
   tendsto_inv_atTop_zero.comp tendsto_nat_cast_atTop_atTop
@@ -53,13 +53,13 @@ theorem tendsto_one_div_add_atTop_nhds_0_nat :
   (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
-theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type _) [Semiring 𝕜] [Algebra ℝ≥0 𝕜]
+theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ≥0 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
     Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
   convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp tendsto_inverse_atTop_nhds_0_nat
   rw [map_zero]
 
-theorem tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type _) [Semiring 𝕜] [Algebra ℝ 𝕜]
+theorem tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type*) [Semiring 𝕜] [Algebra ℝ 𝕜]
     [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
     Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ => (n : ℝ)⁻¹) atTop (nhds 0) :=
   NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat 𝕜
@@ -69,7 +69,7 @@ algebra over `ℝ`, e.g., `ℂ`).
 
 TODO: introduce a typeclass saying that `1 / n` tends to 0 at top, making it possible to get this
 statement simultaneously on `ℚ`, `ℝ` and `ℂ`. -/
-theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
+theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type*} [DivisionRing 𝕜] [TopologicalSpace 𝕜]
     [CharZero 𝕜] [Algebra ℝ 𝕜] [ContinuousSMul ℝ 𝕜] [TopologicalDivisionRing 𝕜] (x : 𝕜) :
     Tendsto (fun n : ℕ => (n : 𝕜) / (n + x)) atTop (𝓝 1) := by
   refine' Tendsto.congr' ((eventually_ne_atTop 0).mp (eventually_of_forall fun n hn => _)) _
@@ -107,7 +107,7 @@ theorem Nat.tendsto_pow_atTop_atTop_of_one_lt {m : ℕ} (h : 1 < m) :
   tsub_add_cancel_of_le (le_of_lt h) ▸ tendsto_add_one_pow_atTop_atTop_of_pos (tsub_pos_of_lt h)
 #align nat.tendsto_pow_at_top_at_top_of_one_lt Nat.tendsto_pow_atTop_atTop_of_one_lt
 
-theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 ≤ r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) :=
   h₁.eq_or_lt.elim
@@ -118,7 +118,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
       (tendsto_inv_atTop_zero.comp this).congr fun n => by simp)
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
 
-@[simp] theorem tendsto_pow_atTop_nhds_0_iff {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+@[simp] theorem tendsto_pow_atTop_nhds_0_iff {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) ↔ |r| < 1 := by
   rw [tendsto_zero_iff_abs_tendsto_zero]
@@ -134,7 +134,7 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
       exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
   · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_0_of_lt_1 (abs_nonneg r)) h
 
-theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type*} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=
   tendsto_inf.2
@@ -142,7 +142,7 @@ theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedFie
       tendsto_principal.2 <| eventually_of_forall fun _ => pow_pos h₁ _⟩
 #align tendsto_pow_at_top_nhds_within_0_of_lt_1 tendsto_pow_atTop_nhdsWithin_0_of_lt_1
 
-theorem uniformity_basis_dist_pow_of_lt_1 {α : Type _} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
+theorem uniformity_basis_dist_pow_of_lt_1 {α : Type*} [PseudoMetricSpace α] {r : ℝ} (h₀ : 0 < r)
     (h₁ : r < 1) :
     (uniformity α).HasBasis (fun _ : ℕ => True) fun k => { p : α × α | dist p.1 p.2 < r ^ k } :=
   Metric.mk_uniformity_basis (fun _ _ => pow_pos h₀ _) fun _ ε0 =>
@@ -229,7 +229,7 @@ theorem summable_geometric_two : Summable fun n : ℕ => ((1 : ℝ) / 2) ^ n :=
   ⟨_, hasSum_geometric_two⟩
 #align summable_geometric_two summable_geometric_two
 
-theorem summable_geometric_two_encode {ι : Type _} [Encodable ι] :
+theorem summable_geometric_two_encode {ι : Type*} [Encodable ι] :
     Summable fun i : ι => (1 / 2 : ℝ) ^ Encodable.encode i :=
   summable_geometric_two.comp_injective Encodable.encode_injective
 #align summable_geometric_two_encode summable_geometric_two_encode
@@ -487,7 +487,7 @@ def posSumOfEncodable {ε : ℝ} (hε : 0 < ε) (ι) [Encodable ι] :
     exact le_rfl
 #align pos_sum_of_encodable posSumOfEncodable
 
-theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
+theorem Set.Countable.exists_pos_hasSum_le {ι : Type*} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ, (∀ i, 0 < ε' i) ∧ ∃ c, HasSum (fun i : s => ε' i) c ∧ c ≤ ε := by
   haveI := hs.toEncodable
   rcases posSumOfEncodable hε s with ⟨f, hf0, ⟨c, hfc, hcε⟩⟩
@@ -498,7 +498,7 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
   · simpa only [Subtype.coe_prop, dif_pos, Subtype.coe_eta]
 #align set.countable.exists_pos_has_sum_le Set.Countable.exists_pos_hasSum_le
 
-theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
+theorem Set.Countable.exists_pos_forall_sum_le {ι : Type*} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ,
     (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → ∑ i in t, ε' i ≤ ε := by
   rcases hs.exists_pos_hasSum_le hε with ⟨ε', hpos, c, hε'c, hcε⟩
@@ -593,12 +593,12 @@ theorem tendsto_factorial_div_pow_self_atTop :
 
 section
 
-theorem tendsto_nat_floor_atTop {α : Type _} [LinearOrderedSemiring α] [FloorSemiring α] :
+theorem tendsto_nat_floor_atTop {α : Type*} [LinearOrderedSemiring α] [FloorSemiring α] :
     Tendsto (fun x : α => ⌊x⌋₊) atTop atTop :=
   Nat.floor_mono.tendsto_atTop_atTop fun x => ⟨max 0 (x + 1), by simp [Nat.le_floor_iff]⟩
 #align tendsto_nat_floor_at_top tendsto_nat_floor_atTop
 
-variable {R : Type _} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
+variable {R : Type*} [TopologicalSpace R] [LinearOrderedField R] [OrderTopology R] [FloorRing R]
 
 theorem tendsto_nat_floor_mul_div_atTop {a : R} (ha : 0 ≤ a) :
     Tendsto (fun x => (⌊a * x⌋₊ : R) / x) atTop (𝓝 a) := by

This PR introduces a single new lemma about the limit of 1 / n as n → ∞ in the complex numbers. It has been placed in a new file to avoid import creep: the obvious file in which to put it (Analysis.SpecificLimits.Basic) does not have the required imports.

Note that this is a prerequisite for an upcoming PR for the Hadamard three-line theorem. Finally, thanks to Patrick Massot for supplying the actual proof on Zulip a while back!

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

@@ -53,6 +53,17 @@ theorem tendsto_one_div_add_atTop_nhds_0_nat :
   (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
+theorem NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type _) [Semiring 𝕜] [Algebra ℝ≥0 𝕜]
+    [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ≥0 𝕜] :
+    Tendsto (algebraMap ℝ≥0 𝕜 ∘ fun n : ℕ => (n : ℝ≥0)⁻¹) atTop (nhds 0) := by
+  convert (continuous_algebraMap ℝ≥0 𝕜).continuousAt.tendsto.comp tendsto_inverse_atTop_nhds_0_nat
+  rw [map_zero]
+
+theorem tendsto_algebraMap_inverse_atTop_nhds_0_nat (𝕜 : Type _) [Semiring 𝕜] [Algebra ℝ 𝕜]
+    [TopologicalSpace 𝕜] [TopologicalSemiring 𝕜] [ContinuousSMul ℝ 𝕜] :
+    Tendsto (algebraMap ℝ 𝕜 ∘ fun n : ℕ => (n : ℝ)⁻¹) atTop (nhds 0) :=
+  NNReal.tendsto_algebraMap_inverse_atTop_nhds_0_nat 𝕜
+
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.specific_limits.basic
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GeomSum
 import Mathlib.Order.Filter.Archimedean
@@ -14,6 +9,8 @@ import Mathlib.Order.Iterate
 import Mathlib.Topology.Instances.ENNReal
 import Mathlib.Topology.Algebra.Algebra
 
+#align_import analysis.specific_limits.basic from "leanprover-community/mathlib"@"57ac39bd365c2f80589a700f9fbb664d3a1a30c2"
+
 /-!
 # A collection of specific limit computations
 

Add lemma tendsto_pow_atTop_nhds_0_iff_lt_1 showing the reverse implication of tendsto_pow_atTop_nhds_0_of_lt_1: if the geometric progression of an element in an Archimedean field tends to 0, the element is strictly less than 1.

@@ -110,6 +110,22 @@ theorem tendsto_pow_atTop_nhds_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 
       (tendsto_inv_atTop_zero.comp this).congr fun n => by simp)
 #align tendsto_pow_at_top_nhds_0_of_lt_1 tendsto_pow_atTop_nhds_0_of_lt_1
 
+@[simp] theorem tendsto_pow_atTop_nhds_0_iff {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
+    [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} :
+    Tendsto (fun n : ℕ => r ^ n) atTop (𝓝 0) ↔ |r| < 1 := by
+  rw [tendsto_zero_iff_abs_tendsto_zero]
+  refine ⟨fun h ↦ by_contra (fun hr_le ↦ ?_), fun h ↦ ?_⟩
+  · by_cases hr : 1 = |r|
+    · replace h : Tendsto (fun n : ℕ ↦ |r|^n) atTop (𝓝 0) := by simpa only [← abs_pow, h]
+      simp only [hr.symm, one_pow] at h
+      exact zero_ne_one <| tendsto_nhds_unique h tendsto_const_nhds
+    · apply @not_tendsto_nhds_of_tendsto_atTop 𝕜 ℕ _ _ _ _ atTop _ (fun n ↦ |r| ^ n) _ 0 _
+      refine (pow_strictMono_right $ lt_of_le_of_ne (le_of_not_lt hr_le)
+        hr).monotone.tendsto_atTop_atTop (fun b ↦ ?_)
+      obtain ⟨n, hn⟩ := (pow_unbounded_of_one_lt b (lt_of_le_of_ne (le_of_not_lt hr_le) hr))
+      exacts [⟨n, le_of_lt hn⟩, by simpa only [← abs_pow]]
+  · simpa only [← abs_pow] using (tendsto_pow_atTop_nhds_0_of_lt_1 (abs_nonneg r)) h
+
 theorem tendsto_pow_atTop_nhdsWithin_0_of_lt_1 {𝕜 : Type _} [LinearOrderedField 𝕜] [Archimedean 𝕜]
     [TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜} (h₁ : 0 < r) (h₂ : r < 1) :
     Tendsto (fun n : ℕ => r ^ n) atTop (𝓝[>] 0) :=

• 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

@@ -193,7 +193,7 @@ theorem summable_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) :
   ⟨_, hasSum_geometric_of_lt_1 h₁ h₂⟩
 #align summable_geometric_of_lt_1 summable_geometric_of_lt_1
 
-theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_of_lt_1 {r : ℝ} (h₁ : 0 ≤ r) (h₂ : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (hasSum_geometric_of_lt_1 h₁ h₂).tsum_eq
 #align tsum_geometric_of_lt_1 tsum_geometric_of_lt_1
 
@@ -254,7 +254,7 @@ theorem summable_geometric_two' (a : ℝ) : Summable fun n : ℕ => a / 2 / 2 ^
   ⟨a, hasSum_geometric_two' a⟩
 #align summable_geometric_two' summable_geometric_two'
 
-theorem tsum_geometric_two' (a : ℝ) : (∑' n : ℕ, a / 2 / 2 ^ n) = a :=
+theorem tsum_geometric_two' (a : ℝ) : ∑' n : ℕ, a / 2 / 2 ^ n = a :=
   (hasSum_geometric_two' a).tsum_eq
 #align tsum_geometric_two' tsum_geometric_two'
 
@@ -270,14 +270,14 @@ theorem NNReal.summable_geometric {r : ℝ≥0} (hr : r < 1) : Summable fun n :
   ⟨_, NNReal.hasSum_geometric hr⟩
 #align nnreal.summable_geometric NNReal.summable_geometric
 
-theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ :=
+theorem tsum_geometric_nNReal {r : ℝ≥0} (hr : r < 1) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ :=
   (NNReal.hasSum_geometric hr).tsum_eq
 #align tsum_geometric_nnreal tsum_geometric_nNReal
 
 /-- The series `pow r` converges to `(1-r)⁻¹`. For `r < 1` the RHS is a finite number,
 and for `1 ≤ r` the RHS equals `∞`. -/
 @[simp]
-theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r)⁻¹ := by
+theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : ∑' n : ℕ, r ^ n = (1 - r)⁻¹ := by
   cases' lt_or_le r 1 with hr hr
   · rcases ENNReal.lt_iff_exists_coe.1 hr with ⟨r, rfl, hr'⟩
     norm_cast at *
@@ -476,7 +476,7 @@ theorem Set.Countable.exists_pos_hasSum_le {ι : Type _} {s : Set ι} (hs : s.Co
 
 theorem Set.Countable.exists_pos_forall_sum_le {ι : Type _} {s : Set ι} (hs : s.Countable) {ε : ℝ}
     (hε : 0 < ε) : ∃ ε' : ι → ℝ,
-    (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → (∑ i in t, ε' i) ≤ ε := by
+    (∀ i, 0 < ε' i) ∧ ∀ t : Finset ι, ↑t ⊆ s → ∑ i in t, ε' i ≤ ε := by
   rcases hs.exists_pos_hasSum_le hε with ⟨ε', hpos, c, hε'c, hcε⟩
   refine' ⟨ε', hpos, fun t ht => _⟩
   rw [← sum_subtype_of_mem _ ht]
@@ -510,7 +510,7 @@ theorem exists_pos_sum_of_countable {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Cou
 #align ennreal.exists_pos_sum_of_countable ENNReal.exists_pos_sum_of_countable
 
 theorem exists_pos_sum_of_countable' {ε : ℝ≥0∞} (hε : ε ≠ 0) (ι) [Countable ι] :
-    ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ (∑' i, ε' i) < ε :=
+    ∃ ε' : ι → ℝ≥0∞, (∀ i, 0 < ε' i) ∧ ∑' i, ε' i < ε :=
   let ⟨δ, δpos, hδ⟩ := exists_pos_sum_of_countable hε ι
   ⟨fun i => δ i, fun i => ENNReal.coe_pos.2 (δpos i), hδ⟩
 #align ennreal.exists_pos_sum_of_countable' ENNReal.exists_pos_sum_of_countable'

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

@@ -288,7 +288,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
       (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
     calc
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
-      _ ≤ ∑ i in range n, r ^ i := sum_le_sum fun k _ => one_le_pow_of_one_le' hr k
+      _ ≤ ∑ i in range n, r ^ i := by gcongr; apply one_le_pow_of_one_le' hr
 #align ennreal.tsum_geometric ENNReal.tsum_geometric
 
 end Geometric

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>

@@ -56,7 +56,6 @@ theorem tendsto_one_div_add_atTop_nhds_0_nat :
   (tendsto_add_atTop_iff_nat 1).2 (_root_.tendsto_const_div_atTop_nhds_0_nat 1)
 #align tendsto_one_div_add_at_top_nhds_0_nat tendsto_one_div_add_atTop_nhds_0_nat
 
-set_option synthInstance.etaExperiment true in -- porting note: gets around lean4#2074
 /-- The limit of `n / (n + x)` is 1, for any constant `x` (valid in `ℝ` or any topological division
 algebra over `ℝ`, e.g., `ℂ`).
 

@@ -75,7 +75,7 @@ theorem tendsto_coe_nat_div_add_atTop {𝕜 : Type _} [DivisionRing 𝕜] [Topol
     simp_rw [div_eq_mul_inv]
     refine' tendsto_const_nhds.mul _
     have := ((continuous_algebraMap ℝ 𝕜).tendsto _).comp tendsto_inverse_atTop_nhds_0_nat
-    rw [map_zero, tendsto_atTop'] at this
+    rw [map_zero, Filter.tendsto_atTop'] at this
     refine' Iff.mpr tendsto_atTop' _
     intros
     simp_all only [comp_apply, map_inv₀, map_natCast]

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -284,7 +284,7 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
     norm_cast at *
     convert ENNReal.tsum_coe_eq (NNReal.hasSum_geometric hr)
     rw [ENNReal.coe_inv <| ne_of_gt <| tsub_pos_iff_lt.2 hr, coe_sub, coe_one]
-  · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_supᵢ_nat, supᵢ_eq_top]
+  · rw [tsub_eq_zero_iff_le.mpr hr, ENNReal.inv_zero, ENNReal.tsum_eq_iSup_nat, iSup_eq_top]
     refine' fun a ha =>
       (ENNReal.exists_nat_gt (lt_top_iff_ne_top.1 ha)).imp fun n hn => lt_of_lt_of_le hn _
     calc

This PR fixes two things:

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

@@ -290,7 +290,6 @@ theorem ENNReal.tsum_geometric (r : ℝ≥0∞) : (∑' n : ℕ, r ^ n) = (1 - r
     calc
       (n : ℝ≥0∞) = ∑ i in range n, 1 := by rw [sum_const, nsmul_one, card_range]
       _ ≤ ∑ i in range n, r ^ i := sum_le_sum fun k _ => one_le_pow_of_one_le' hr k
-
 #align ennreal.tsum_geometric ENNReal.tsum_geometric
 
 end Geometric

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp>