analysis.normed.group.infinite_sum ⟷ Mathlib.Analysis.Normed.Group.InfiniteSum

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

@@ -5,7 +5,7 @@ Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
 -/
 import Algebra.BigOperators.Intervals
 import Analysis.Normed.Group.Basic
-import Topology.Instances.Nnreal
+import Topology.Instances.NNReal
 
 #align_import analysis.normed.group.infinite_sum from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 
@@ -45,7 +45,7 @@ theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔
       ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε :=
   by
-  rw [cauchySeq_finset_iff_vanishing, nhds_basis_ball.forall_iff]
+  rw [cauchySeq_finset_iff_sum_vanishing, nhds_basis_ball.forall_iff]
   · simp only [ball_zero_eq, Set.mem_setOf_eq]
   · rintro s t hst ⟨s', hs'⟩
     exact ⟨s', fun t' ht' => hst <| hs' _ ht'⟩

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

@@ -69,7 +69,7 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
   have : ∀ i ∈ t, ‖f i‖ ≤ g i := by
     intro i hi
     simp only [disjoint_left, mem_union, not_or, h.mem_to_finset, Set.mem_compl_iff,
-      Classical.not_not] at ht 
+      Classical.not_not] at ht
     exact (ht hi).2
   calc
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this

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

@@ -129,13 +129,13 @@ theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Su
 #align has_sum_iff_tendsto_nat_of_summable_norm hasSum_iff_tendsto_nat_of_summable_norm
 -/
 
-#print summable_of_norm_bounded /-
+#print Summable.of_norm_bounded /-
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
-theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
+theorem Summable.of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : Summable f := by rw [summable_iff_cauchySeq_finset];
   exact cauchySeq_finset_of_norm_bounded g hg h
-#align summable_of_norm_bounded summable_of_norm_bounded
+#align summable_of_norm_bounded Summable.of_norm_bounded
 -/
 
 #print HasSum.norm_le_of_bounded /-
@@ -192,32 +192,32 @@ theorem nnnorm_tsum_le {f : ι → E} (hf : Summable fun i => ‖f i‖₊) : 
 
 variable [CompleteSpace E]
 
-#print summable_of_norm_bounded_eventually /-
+#print Summable.of_norm_bounded_eventually /-
 /-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
 real function `g` which is summable, then `f` is summable. -/
-theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
+theorem Summable.of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : Summable f :=
   summable_iff_cauchySeq_finset.2 <| cauchySeq_finset_of_norm_bounded_eventually hg h
-#align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventually
+#align summable_of_norm_bounded_eventually Summable.of_norm_bounded_eventually
 -/
 
-#print summable_of_nnnorm_bounded /-
-theorem summable_of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
+#print Summable.of_nnnorm_bounded /-
+theorem Summable.of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
     (h : ∀ i, ‖f i‖₊ ≤ g i) : Summable f :=
-  summable_of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
+  Summable.of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
     exact_mod_cast h i
-#align summable_of_nnnorm_bounded summable_of_nnnorm_bounded
+#align summable_of_nnnorm_bounded Summable.of_nnnorm_bounded
 -/
 
-#print summable_of_summable_norm /-
-theorem summable_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
-  summable_of_norm_bounded _ hf fun i => le_rfl
-#align summable_of_summable_norm summable_of_summable_norm
+#print Summable.of_norm /-
+theorem Summable.of_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
+  Summable.of_norm_bounded _ hf fun i => le_rfl
+#align summable_of_summable_norm Summable.of_norm
 -/
 
-#print summable_of_summable_nnnorm /-
-theorem summable_of_summable_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
-  summable_of_nnnorm_bounded _ hf fun i => le_rfl
-#align summable_of_summable_nnnorm summable_of_summable_nnnorm
+#print Summable.of_nnnorm /-
+theorem Summable.of_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
+  Summable.of_nnnorm_bounded _ hf fun i => le_rfl
+#align summable_of_summable_nnnorm Summable.of_nnnorm
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
 -/
-import Mathbin.Algebra.BigOperators.Intervals
-import Mathbin.Analysis.Normed.Group.Basic
-import Mathbin.Topology.Instances.Nnreal
+import Algebra.BigOperators.Intervals
+import Analysis.Normed.Group.Basic
+import Topology.Instances.Nnreal
 
 #align_import analysis.normed.group.infinite_sum from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.normed.group.infinite_sum
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Intervals
 import Mathbin.Analysis.Normed.Group.Basic
 import Mathbin.Topology.Instances.Nnreal
 
+#align_import analysis.normed.group.infinite_sum from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Infinite sums in (semi)normed groups
 

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

@@ -43,6 +43,7 @@ open Finset Filter Metric
 
 variable {ι α E F : Type _} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
 
+#print cauchySeq_finset_iff_vanishing_norm /-
 theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔
       ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε :=
@@ -52,12 +53,16 @@ theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
   · rintro s t hst ⟨s', hs'⟩
     exact ⟨s', fun t' ht' => hst <| hs' _ ht'⟩
 #align cauchy_seq_finset_iff_vanishing_norm cauchySeq_finset_iff_vanishing_norm
+-/
 
+#print summable_iff_vanishing_norm /-
 theorem summable_iff_vanishing_norm [CompleteSpace E] {f : ι → E} :
     Summable f ↔ ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε := by
   rw [summable_iff_cauchySeq_finset, cauchySeq_finset_iff_vanishing_norm]
 #align summable_iff_vanishing_norm summable_iff_vanishing_norm
+-/
 
+#print cauchySeq_finset_of_norm_bounded_eventually /-
 theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → ℝ} (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : CauchySeq fun s => ∑ i in s, f i :=
   by
@@ -74,12 +79,16 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     _ ≤ ‖∑ i in t, g i‖ := (le_abs_self _)
     _ < ε := hs _ (ht.mono_right le_sup_left)
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
+-/
 
+#print cauchySeq_finset_of_norm_bounded /-
 theorem cauchySeq_finset_of_norm_bounded {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : CauchySeq fun s : Finset ι => ∑ i in s, f i :=
   cauchySeq_finset_of_norm_bounded_eventually hg <| eventually_of_forall h
 #align cauchy_seq_finset_of_norm_bounded cauchySeq_finset_of_norm_bounded
+-/
 
+#print cauchySeq_range_of_norm_bounded /-
 /-- A version of the **direct comparison test** for conditionally convergent series.
 See `cauchy_seq_finset_of_norm_bounded` for the same statement about absolutely convergent ones. -/
 theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
@@ -96,12 +105,16 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
     _ ≤ ‖∑ k in _, g k‖ := (le_abs_self _)
     _ < ε := hg
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
+-/
 
+#print cauchySeq_finset_of_summable_norm /-
 theorem cauchySeq_finset_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) :
     CauchySeq fun s : Finset ι => ∑ a in s, f a :=
   cauchySeq_finset_of_norm_bounded _ hf fun i => le_rfl
 #align cauchy_seq_finset_of_summable_norm cauchySeq_finset_of_summable_norm
+-/
 
+#print hasSum_of_subseq_of_summable /-
 /-- If a function `f` is summable in norm, and along some sequence of finsets exhausting the space
 its sum is converging to a limit `a`, then this holds along all finsets, i.e., `f` is summable
 with sum `a`. -/
@@ -110,6 +123,7 @@ theorem hasSum_of_subseq_of_summable {f : ι → E} (hf : Summable fun a => ‖f
     (ha : Tendsto (fun b => ∑ i in s b, f i) p (𝓝 a)) : HasSum f a :=
   tendsto_nhds_of_cauchySeq_of_subseq (cauchySeq_finset_of_summable_norm hf) hs ha
 #align has_sum_of_subseq_of_summable hasSum_of_subseq_of_summable
+-/
 
 #print hasSum_iff_tendsto_nat_of_summable_norm /-
 theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Summable fun i => ‖f i‖) :
@@ -118,18 +132,23 @@ theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Su
 #align has_sum_iff_tendsto_nat_of_summable_norm hasSum_iff_tendsto_nat_of_summable_norm
 -/
 
+#print summable_of_norm_bounded /-
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : Summable f := by rw [summable_iff_cauchySeq_finset];
   exact cauchySeq_finset_of_norm_bounded g hg h
 #align summable_of_norm_bounded summable_of_norm_bounded
+-/
 
+#print HasSum.norm_le_of_bounded /-
 theorem HasSum.norm_le_of_bounded {f : ι → E} {g : ι → ℝ} {a : E} {b : ℝ} (hf : HasSum f a)
     (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b :=
   le_of_tendsto_of_tendsto' hf.norm hg fun s => norm_sum_le_of_le _ fun i hi => h i
 #align has_sum.norm_le_of_bounded HasSum.norm_le_of_bounded
+-/
 
+#print tsum_of_norm_bounded /-
 /-- Quantitative result associated to the direct comparison test for series:  If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖ ≤ g i`, then `‖∑' i, f i‖ ≤ ∑' i, g i`. Note that we do not
 assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
@@ -141,14 +160,18 @@ theorem tsum_of_norm_bounded {f : ι → E} {g : ι → ℝ} {a : ℝ} (hg : Has
   · rw [tsum_eq_zero_of_not_summable hf, norm_zero]
     exact ge_of_tendsto' hg fun s => sum_nonneg fun i hi => (norm_nonneg _).trans (h i)
 #align tsum_of_norm_bounded tsum_of_norm_bounded
+-/
 
+#print norm_tsum_le_tsum_norm /-
 /-- If `∑' i, ‖f i‖` is summable, then `‖∑' i, f i‖ ≤ (∑' i, ‖f i‖)`. Note that we do not assume
 that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
 theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖) :
     ‖∑' i, f i‖ ≤ ∑' i, ‖f i‖ :=
   tsum_of_norm_bounded hf.HasSum fun i => le_rfl
 #align norm_tsum_le_tsum_norm norm_tsum_le_tsum_norm
+-/
 
+#print tsum_of_nnnorm_bounded /-
 /-- Quantitative result associated to the direct comparison test for series: If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖₊ ≤ g i`, then `‖∑' i, f i‖₊ ≤ ∑' i, g i`. Note that we
 do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
@@ -159,34 +182,45 @@ theorem tsum_of_nnnorm_bounded {f : ι → E} {g : ι → ℝ≥0} {a : ℝ≥0}
   simp only [← NNReal.coe_le_coe, ← NNReal.hasSum_coe, coe_nnnorm] at *
   exact tsum_of_norm_bounded hg h
 #align tsum_of_nnnorm_bounded tsum_of_nnnorm_bounded
+-/
 
+#print nnnorm_tsum_le /-
 /-- If `∑' i, ‖f i‖₊` is summable, then `‖∑' i, f i‖₊ ≤ ∑' i, ‖f i‖₊`. Note that
 we do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
 space. -/
 theorem nnnorm_tsum_le {f : ι → E} (hf : Summable fun i => ‖f i‖₊) : ‖∑' i, f i‖₊ ≤ ∑' i, ‖f i‖₊ :=
   tsum_of_nnnorm_bounded hf.HasSum fun i => le_rfl
 #align nnnorm_tsum_le nnnorm_tsum_le
+-/
 
 variable [CompleteSpace E]
 
+#print summable_of_norm_bounded_eventually /-
 /-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
 real function `g` which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : Summable f :=
   summable_iff_cauchySeq_finset.2 <| cauchySeq_finset_of_norm_bounded_eventually hg h
 #align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventually
+-/
 
+#print summable_of_nnnorm_bounded /-
 theorem summable_of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
     (h : ∀ i, ‖f i‖₊ ≤ g i) : Summable f :=
   summable_of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
     exact_mod_cast h i
 #align summable_of_nnnorm_bounded summable_of_nnnorm_bounded
+-/
 
+#print summable_of_summable_norm /-
 theorem summable_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
   summable_of_norm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_norm summable_of_summable_norm
+-/
 
+#print summable_of_summable_nnnorm /-
 theorem summable_of_summable_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
   summable_of_nnnorm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_nnnorm summable_of_summable_nnnorm
+-/
 

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

@@ -73,7 +73,6 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this
     _ ≤ ‖∑ i in t, g i‖ := (le_abs_self _)
     _ < ε := hs _ (ht.mono_right le_sup_left)
-    
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
 
 theorem cauchySeq_finset_of_norm_bounded {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -96,7 +95,6 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
     _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)
     _ ≤ ‖∑ k in _, g k‖ := (le_abs_self _)
     _ < ε := hg
-    
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
 
 theorem cauchySeq_finset_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) :

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

@@ -67,7 +67,7 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
   have : ∀ i ∈ t, ‖f i‖ ≤ g i := by
     intro i hi
     simp only [disjoint_left, mem_union, not_or, h.mem_to_finset, Set.mem_compl_iff,
-      Classical.not_not] at ht
+      Classical.not_not] at ht 
     exact (ht hi).2
   calc
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this
@@ -90,7 +90,7 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
   refine' Metric.cauchySeq_iff'.2 fun ε hε => _
   refine' (Metric.cauchySeq_iff'.1 hg ε hε).imp fun N hg n hn => _
   specialize hg n hn
-  rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg⊢
+  rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg ⊢
   calc
     ‖∑ k in Ico N n, f k‖ ≤ ∑ k in _, ‖f k‖ := norm_sum_le _ _
     _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)

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

@@ -37,7 +37,7 @@ infinite series, absolute convergence, normed group
 -/
 
 
-open Classical BigOperators Topology NNReal
+open scoped Classical BigOperators Topology NNReal
 
 open Finset Filter Metric
 

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

@@ -43,12 +43,6 @@ open Finset Filter Metric
 
 variable {ι α E F : Type _} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
 
-/- warning: cauchy_seq_finset_iff_vanishing_norm -> cauchySeq_finset_iff_vanishing_norm is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, Iff (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.lattice.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (i : ι) => f i))) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => forall (t : Finset.{u1} ι), (Disjoint.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι) (Finset.orderBot.{u1} ι) t s) -> (LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) t (fun (i : ι) => f i))) ε))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_iff_vanishing_norm cauchySeq_finset_iff_vanishing_normₓ'. -/
 theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔
       ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε :=
@@ -59,23 +53,11 @@ theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     exact ⟨s', fun t' ht' => hst <| hs' _ ht'⟩
 #align cauchy_seq_finset_iff_vanishing_norm cauchySeq_finset_iff_vanishing_norm
 
-/- warning: summable_iff_vanishing_norm -> summable_iff_vanishing_norm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align summable_iff_vanishing_norm summable_iff_vanishing_normₓ'. -/
 theorem summable_iff_vanishing_norm [CompleteSpace E] {f : ι → E} :
     Summable f ↔ ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε := by
   rw [summable_iff_cauchySeq_finset, cauchySeq_finset_iff_vanishing_norm]
 #align summable_iff_vanishing_norm summable_iff_vanishing_norm
 
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 theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → ℝ} (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : CauchySeq fun s => ∑ i in s, f i :=
   by
@@ -94,23 +76,11 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_norm_bounded cauchySeq_finset_of_norm_boundedₓ'. -/
 theorem cauchySeq_finset_of_norm_bounded {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : CauchySeq fun s : Finset ι => ∑ i in s, f i :=
   cauchySeq_finset_of_norm_bounded_eventually hg <| eventually_of_forall h
 #align cauchy_seq_finset_of_norm_bounded cauchySeq_finset_of_norm_bounded
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_boundedₓ'. -/
 /-- A version of the **direct comparison test** for conditionally convergent series.
 See `cauchy_seq_finset_of_norm_bounded` for the same statement about absolutely convergent ones. -/
 theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
@@ -129,23 +99,11 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
     
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_summable_norm cauchySeq_finset_of_summable_normₓ'. -/
 theorem cauchySeq_finset_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) :
     CauchySeq fun s : Finset ι => ∑ a in s, f a :=
   cauchySeq_finset_of_norm_bounded _ hf fun i => le_rfl
 #align cauchy_seq_finset_of_summable_norm cauchySeq_finset_of_summable_norm
 
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-Case conversion may be inaccurate. Consider using '#align has_sum_of_subseq_of_summable hasSum_of_subseq_of_summableₓ'. -/
 /-- If a function `f` is summable in norm, and along some sequence of finsets exhausting the space
 its sum is converging to a limit `a`, then this holds along all finsets, i.e., `f` is summable
 with sum `a`. -/
@@ -162,12 +120,6 @@ theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Su
 #align has_sum_iff_tendsto_nat_of_summable_norm hasSum_iff_tendsto_nat_of_summable_norm
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align summable_of_norm_bounded summable_of_norm_boundedₓ'. -/
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -175,23 +127,11 @@ theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → 
   exact cauchySeq_finset_of_norm_bounded g hg h
 #align summable_of_norm_bounded summable_of_norm_bounded
 
-/- warning: has_sum.norm_le_of_bounded -> HasSum.norm_le_of_bounded is a dubious translation:
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-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : E} {b : Real}, (HasSum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f a) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g b) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) a) b)
-but is expected to have type
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : E} {b : Real}, (HasSum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f a) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g b) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) a) b)
-Case conversion may be inaccurate. Consider using '#align has_sum.norm_le_of_bounded HasSum.norm_le_of_boundedₓ'. -/
 theorem HasSum.norm_le_of_bounded {f : ι → E} {g : ι → ℝ} {a : E} {b : ℝ} (hf : HasSum f a)
     (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b :=
   le_of_tendsto_of_tendsto' hf.norm hg fun s => norm_sum_le_of_le _ fun i hi => h i
 #align has_sum.norm_le_of_bounded HasSum.norm_le_of_bounded
 
-/- warning: tsum_of_norm_bounded -> tsum_of_norm_bounded is a dubious translation:
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-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : Real}, (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g a) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) a)
-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> Real} {a : Real}, (HasSum.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g a) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) a)
-Case conversion may be inaccurate. Consider using '#align tsum_of_norm_bounded tsum_of_norm_boundedₓ'. -/
 /-- Quantitative result associated to the direct comparison test for series:  If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖ ≤ g i`, then `‖∑' i, f i‖ ≤ ∑' i, g i`. Note that we do not
 assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
@@ -204,12 +144,6 @@ theorem tsum_of_norm_bounded {f : ι → E} {g : ι → ℝ} {a : ℝ} (hg : Has
     exact ge_of_tendsto' hg fun s => sum_nonneg fun i hi => (norm_nonneg _).trans (h i)
 #align tsum_of_norm_bounded tsum_of_norm_bounded
 
-/- warning: norm_tsum_le_tsum_norm -> norm_tsum_le_tsum_norm is a dubious translation:
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-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u2} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i))))
-Case conversion may be inaccurate. Consider using '#align norm_tsum_le_tsum_norm norm_tsum_le_tsum_normₓ'. -/
 /-- If `∑' i, ‖f i‖` is summable, then `‖∑' i, f i‖ ≤ (∑' i, ‖f i‖)`. Note that we do not assume
 that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
 theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖) :
@@ -217,12 +151,6 @@ theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖)
   tsum_of_norm_bounded hf.HasSum fun i => le_rfl
 #align norm_tsum_le_tsum_norm norm_tsum_le_tsum_norm
 
-/- warning: tsum_of_nnnorm_bounded -> tsum_of_nnnorm_bounded is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) a)
-Case conversion may be inaccurate. Consider using '#align tsum_of_nnnorm_bounded tsum_of_nnnorm_boundedₓ'. -/
 /-- Quantitative result associated to the direct comparison test for series: If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖₊ ≤ g i`, then `‖∑' i, f i‖₊ ≤ ∑' i, g i`. Note that we
 do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
@@ -234,12 +162,6 @@ theorem tsum_of_nnnorm_bounded {f : ι → E} {g : ι → ℝ≥0} {a : ℝ≥0}
   exact tsum_of_norm_bounded hg h
 #align tsum_of_nnnorm_bounded tsum_of_nnnorm_bounded
 
-/- warning: nnnorm_tsum_le -> nnnorm_tsum_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))))
-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u2} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))))
-Case conversion may be inaccurate. Consider using '#align nnnorm_tsum_le nnnorm_tsum_leₓ'. -/
 /-- If `∑' i, ‖f i‖₊` is summable, then `‖∑' i, f i‖₊ ≤ ∑' i, ‖f i‖₊`. Note that
 we do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
 space. -/
@@ -249,12 +171,6 @@ theorem nnnorm_tsum_le {f : ι → E} (hf : Summable fun i => ‖f i‖₊) : 
 
 variable [CompleteSpace E]
 
-/- warning: summable_of_norm_bounded_eventually -> summable_of_norm_bounded_eventually is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E} (g : ι -> Real), (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (Filter.Eventually.{u2} ι (fun (i : ι) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) (Filter.cofinite.{u2} ι)) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
-Case conversion may be inaccurate. Consider using '#align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventuallyₓ'. -/
 /-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
 real function `g` which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -262,34 +178,16 @@ theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg
   summable_iff_cauchySeq_finset.2 <| cauchySeq_finset_of_norm_bounded_eventually hg h
 #align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventually
 
-/- warning: summable_of_nnnorm_bounded -> summable_of_nnnorm_bounded is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
-Case conversion may be inaccurate. Consider using '#align summable_of_nnnorm_bounded summable_of_nnnorm_boundedₓ'. -/
 theorem summable_of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
     (h : ∀ i, ‖f i‖₊ ≤ g i) : Summable f :=
   summable_of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
     exact_mod_cast h i
 #align summable_of_nnnorm_bounded summable_of_nnnorm_bounded
 
-/- warning: summable_of_summable_norm -> summable_of_summable_norm is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f a))) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f a))) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
-Case conversion may be inaccurate. Consider using '#align summable_of_summable_norm summable_of_summable_normₓ'. -/
 theorem summable_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
   summable_of_norm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_norm summable_of_summable_norm
 
-/- warning: summable_of_summable_nnnorm -> summable_of_summable_nnnorm is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (a : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f a))) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
-but is expected to have type
-  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E}, (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (a : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f a))) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
-Case conversion may be inaccurate. Consider using '#align summable_of_summable_nnnorm summable_of_summable_nnnormₓ'. -/
 theorem summable_of_summable_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
   summable_of_nnnorm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_nnnorm summable_of_summable_nnnorm

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

@@ -171,9 +171,7 @@ Case conversion may be inaccurate. Consider using '#align summable_of_norm_bound
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
-    (h : ∀ i, ‖f i‖ ≤ g i) : Summable f :=
-  by
-  rw [summable_iff_cauchySeq_finset]
+    (h : ∀ i, ‖f i‖ ≤ g i) : Summable f := by rw [summable_iff_cauchySeq_finset];
   exact cauchySeq_finset_of_norm_bounded g hg h
 #align summable_of_norm_bounded summable_of_norm_bounded
 

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

@@ -221,7 +221,7 @@ theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖)
 
 /- warning: tsum_of_nnnorm_bounded -> tsum_of_nnnorm_bounded is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) a)
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) a)
 but is expected to have type
   forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) a)
 Case conversion may be inaccurate. Consider using '#align tsum_of_nnnorm_bounded tsum_of_nnnorm_boundedₓ'. -/
@@ -238,7 +238,7 @@ theorem tsum_of_nnnorm_bounded {f : ι → E} {g : ι → ℝ≥0} {a : ℝ≥0}
 
 /- warning: nnnorm_tsum_le -> nnnorm_tsum_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))))
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))))
 but is expected to have type
   forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u2} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))))
 Case conversion may be inaccurate. Consider using '#align nnnorm_tsum_le nnnorm_tsum_leₓ'. -/
@@ -266,7 +266,7 @@ theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg
 
 /- warning: summable_of_nnnorm_bounded -> summable_of_nnnorm_bounded is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
 but is expected to have type
   forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
 Case conversion may be inaccurate. Consider using '#align summable_of_nnnorm_bounded summable_of_nnnorm_boundedₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.normed.group.infinite_sum
-! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Instances.Nnreal
 /-!
 # Infinite sums in (semi)normed groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In a complete (semi)normed group,
 
 - `summable_iff_vanishing_norm`: a series `∑' i, f i` is summable if and only if for any `ε > 0`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -40,6 +40,12 @@ open Finset Filter Metric
 
 variable {ι α E F : Type _} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
 
+/- warning: cauchy_seq_finset_iff_vanishing_norm -> cauchySeq_finset_iff_vanishing_norm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, Iff (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.lattice.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (i : ι) => f i))) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => forall (t : Finset.{u1} ι), (Disjoint.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι) (Finset.orderBot.{u1} ι) t s) -> (LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) t (fun (i : ι) => f i))) ε))))
+but is expected to have type
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, Iff (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.instLatticeFinset.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (i : ι) => f i))) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => forall (t : Finset.{u1} ι), (Disjoint.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} ι) t s) -> (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) t (fun (i : ι) => f i))) ε))))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_iff_vanishing_norm cauchySeq_finset_iff_vanishing_normₓ'. -/
 theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔
       ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε :=
@@ -50,11 +56,23 @@ theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     exact ⟨s', fun t' ht' => hst <| hs' _ ht'⟩
 #align cauchy_seq_finset_iff_vanishing_norm cauchySeq_finset_iff_vanishing_norm
 
+/- warning: summable_iff_vanishing_norm -> summable_iff_vanishing_norm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, Iff (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f) (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => forall (t : Finset.{u1} ι), (Disjoint.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι) (Finset.orderBot.{u1} ι) t s) -> (LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) t (fun (i : ι) => f i))) ε))))
+but is expected to have type
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, Iff (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f) (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u1} (Finset.{u1} ι) (fun (s : Finset.{u1} ι) => forall (t : Finset.{u1} ι), (Disjoint.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} ι) t s) -> (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) t (fun (i : ι) => f i))) ε))))
+Case conversion may be inaccurate. Consider using '#align summable_iff_vanishing_norm summable_iff_vanishing_normₓ'. -/
 theorem summable_iff_vanishing_norm [CompleteSpace E] {f : ι → E} :
     Summable f ↔ ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε := by
   rw [summable_iff_cauchySeq_finset, cauchySeq_finset_iff_vanishing_norm]
 #align summable_iff_vanishing_norm summable_iff_vanishing_norm
 
+/- warning: cauchy_seq_finset_of_norm_bounded_eventually -> cauchySeq_finset_of_norm_bounded_eventually is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (Filter.Eventually.{u1} ι (fun (i : ι) => LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) (Filter.cofinite.{u1} ι)) -> (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.lattice.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (i : ι) => f i)))
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> Real}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (Filter.Eventually.{u2} ι (fun (i : ι) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) (Filter.cofinite.{u2} ι)) -> (CauchySeq.{u1, u2} E (Finset.{u2} ι) (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1)) (Lattice.toSemilatticeSup.{u2} (Finset.{u2} ι) (Finset.instLatticeFinset.{u2} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u2} ι a b)))) (fun (s : Finset.{u2} ι) => Finset.sum.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) s (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventuallyₓ'. -/
 theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → ℝ} (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : CauchySeq fun s => ∑ i in s, f i :=
   by
@@ -73,11 +91,23 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
 
+/- warning: cauchy_seq_finset_of_norm_bounded -> cauchySeq_finset_of_norm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} (g : ι -> Real), (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.lattice.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (i : ι) => f i)))
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} (g : ι -> Real), (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) -> (CauchySeq.{u1, u2} E (Finset.{u2} ι) (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1)) (Lattice.toSemilatticeSup.{u2} (Finset.{u2} ι) (Finset.instLatticeFinset.{u2} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u2} ι a b)))) (fun (s : Finset.{u2} ι) => Finset.sum.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) s (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_norm_bounded cauchySeq_finset_of_norm_boundedₓ'. -/
 theorem cauchySeq_finset_of_norm_bounded {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : CauchySeq fun s : Finset ι => ∑ i in s, f i :=
   cauchySeq_finset_of_norm_bounded_eventually hg <| eventually_of_forall h
 #align cauchy_seq_finset_of_norm_bounded cauchySeq_finset_of_norm_bounded
 
+/- warning: cauchy_seq_range_of_norm_bounded -> cauchySeq_range_of_norm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : Nat -> E} (g : Nat -> Real), (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (i : Nat) => g i))) -> (forall (i : Nat), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} E (SeminormedAddCommGroup.toHasNorm.{u1} E _inst_1) (f i)) (g i)) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1)) (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => f i)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : Nat -> E} (g : Nat -> Real), (CauchySeq.{0, 0} Real Nat (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (i : Nat) => g i))) -> (forall (i : Nat), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) -> (CauchySeq.{u1, 0} E Nat (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1)) (Lattice.toSemilatticeSup.{0} Nat Nat.instLatticeNat) (fun (n : Nat) => Finset.sum.{u1, 0} E Nat (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (Finset.range n) (fun (i : Nat) => f i)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_boundedₓ'. -/
 /-- A version of the **direct comparison test** for conditionally convergent series.
 See `cauchy_seq_finset_of_norm_bounded` for the same statement about absolutely convergent ones. -/
 theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
@@ -96,11 +126,23 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
     
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
 
+/- warning: cauchy_seq_finset_of_summable_norm -> cauchySeq_finset_of_summable_norm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f a))) -> (CauchySeq.{u2, u1} E (Finset.{u1} ι) (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1)) (Lattice.toSemilatticeSup.{u1} (Finset.{u1} ι) (Finset.lattice.{u1} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u1} ι a b)))) (fun (s : Finset.{u1} ι) => Finset.sum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) s (fun (a : ι) => f a)))
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f a))) -> (CauchySeq.{u1, u2} E (Finset.{u2} ι) (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1)) (Lattice.toSemilatticeSup.{u2} (Finset.{u2} ι) (Finset.instLatticeFinset.{u2} ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u2} ι a b)))) (fun (s : Finset.{u2} ι) => Finset.sum.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) s (fun (a : ι) => f a)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_finset_of_summable_norm cauchySeq_finset_of_summable_normₓ'. -/
 theorem cauchySeq_finset_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) :
     CauchySeq fun s : Finset ι => ∑ a in s, f a :=
   cauchySeq_finset_of_norm_bounded _ hf fun i => le_rfl
 #align cauchy_seq_finset_of_summable_norm cauchySeq_finset_of_summable_norm
 
+/- warning: has_sum_of_subseq_of_summable -> hasSum_of_subseq_of_summable is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {α : Type.{u2}} {E : Type.{u3}} [_inst_1 : SeminormedAddCommGroup.{u3} E] {f : ι -> E}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u3} E (SeminormedAddCommGroup.toHasNorm.{u3} E _inst_1) (f a))) -> (forall {s : α -> (Finset.{u1} ι)} {p : Filter.{u2} α} [_inst_3 : Filter.NeBot.{u2} α p], (Filter.Tendsto.{u2, u1} α (Finset.{u1} ι) s p (Filter.atTop.{u1} (Finset.{u1} ι) (PartialOrder.toPreorder.{u1} (Finset.{u1} ι) (Finset.partialOrder.{u1} ι)))) -> (forall {a : E}, (Filter.Tendsto.{u2, u3} α E (fun (b : α) => Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_1)) (s b) (fun (i : ι) => f i)) p (nhds.{u3} E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_1))) a)) -> (HasSum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E _inst_1)) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E _inst_1))) f a)))
+but is expected to have type
+  forall {ι : Type.{u3}} {α : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u3} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (f a))) -> (forall {s : α -> (Finset.{u3} ι)} {p : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α p], (Filter.Tendsto.{u1, u3} α (Finset.{u3} ι) s p (Filter.atTop.{u3} (Finset.{u3} ι) (PartialOrder.toPreorder.{u3} (Finset.{u3} ι) (Finset.partialOrder.{u3} ι)))) -> (forall {a : E}, (Filter.Tendsto.{u1, u2} α E (fun (b : α) => Finset.sum.{u2, u3} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (s b) (fun (i : ι) => f i)) p (nhds.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) a)) -> (HasSum.{u2, u3} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f a)))
+Case conversion may be inaccurate. Consider using '#align has_sum_of_subseq_of_summable hasSum_of_subseq_of_summableₓ'. -/
 /-- If a function `f` is summable in norm, and along some sequence of finsets exhausting the space
 its sum is converging to a limit `a`, then this holds along all finsets, i.e., `f` is summable
 with sum `a`. -/
@@ -110,11 +152,19 @@ theorem hasSum_of_subseq_of_summable {f : ι → E} (hf : Summable fun a => ‖f
   tendsto_nhds_of_cauchySeq_of_subseq (cauchySeq_finset_of_summable_norm hf) hs ha
 #align has_sum_of_subseq_of_summable hasSum_of_subseq_of_summable
 
+#print hasSum_iff_tendsto_nat_of_summable_norm /-
 theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Summable fun i => ‖f i‖) :
     HasSum f a ↔ Tendsto (fun n : ℕ => ∑ i in range n, f i) atTop (𝓝 a) :=
   ⟨fun h => h.tendsto_sum_nat, fun h => hasSum_of_subseq_of_summable hf tendsto_finset_range h⟩
 #align has_sum_iff_tendsto_nat_of_summable_norm hasSum_iff_tendsto_nat_of_summable_norm
+-/
 
+/- warning: summable_of_norm_bounded -> summable_of_norm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> Real), (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+but is expected to have type
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> Real), (Summable.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_norm_bounded summable_of_norm_boundedₓ'. -/
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -124,11 +174,23 @@ theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → 
   exact cauchySeq_finset_of_norm_bounded g hg h
 #align summable_of_norm_bounded summable_of_norm_bounded
 
+/- warning: has_sum.norm_le_of_bounded -> HasSum.norm_le_of_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : E} {b : Real}, (HasSum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f a) -> (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g b) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) a) b)
+but is expected to have type
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : E} {b : Real}, (HasSum.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f a) -> (HasSum.{0, u1} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g b) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_1) a) b)
+Case conversion may be inaccurate. Consider using '#align has_sum.norm_le_of_bounded HasSum.norm_le_of_boundedₓ'. -/
 theorem HasSum.norm_le_of_bounded {f : ι → E} {g : ι → ℝ} {a : E} {b : ℝ} (hf : HasSum f a)
     (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b :=
   le_of_tendsto_of_tendsto' hf.norm hg fun s => norm_sum_le_of_le _ fun i hi => h i
 #align has_sum.norm_le_of_bounded HasSum.norm_le_of_bounded
 
+/- warning: tsum_of_norm_bounded -> tsum_of_norm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> Real} {a : Real}, (HasSum.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g a) -> (forall (i : ι), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) a)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> Real} {a : Real}, (HasSum.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g a) -> (forall (i : ι), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) a)
+Case conversion may be inaccurate. Consider using '#align tsum_of_norm_bounded tsum_of_norm_boundedₓ'. -/
 /-- Quantitative result associated to the direct comparison test for series:  If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖ ≤ g i`, then `‖∑' i, f i‖ ≤ ∑' i, g i`. Note that we do not
 assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
@@ -141,6 +203,12 @@ theorem tsum_of_norm_bounded {f : ι → E} {g : ι → ℝ} {a : ℝ} (hg : Has
     exact ge_of_tendsto' hg fun s => sum_nonneg fun i hi => (norm_nonneg _).trans (h i)
 #align tsum_of_norm_bounded tsum_of_norm_bounded
 
+/- warning: norm_tsum_le_tsum_norm -> norm_tsum_le_tsum_norm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u1} Real Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i))))
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (i : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u2} Real Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ι (fun (i : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i))))
+Case conversion may be inaccurate. Consider using '#align norm_tsum_le_tsum_norm norm_tsum_le_tsum_normₓ'. -/
 /-- If `∑' i, ‖f i‖` is summable, then `‖∑' i, f i‖ ≤ (∑' i, ‖f i‖)`. Note that we do not assume
 that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete space. -/
 theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖) :
@@ -148,6 +216,12 @@ theorem norm_tsum_le_tsum_norm {f : ι → E} (hf : Summable fun i => ‖f i‖)
   tsum_of_norm_bounded hf.HasSum fun i => le_rfl
 #align norm_tsum_le_tsum_norm norm_tsum_le_tsum_norm
 
+/- warning: tsum_of_nnnorm_bounded -> tsum_of_nnnorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) a)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E} {g : ι -> NNReal} {a : NNReal}, (HasSum.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g a) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) a)
+Case conversion may be inaccurate. Consider using '#align tsum_of_nnnorm_bounded tsum_of_nnnorm_boundedₓ'. -/
 /-- Quantitative result associated to the direct comparison test for series: If `∑' i, g i` is
 summable, and for all `i`, `‖f i‖₊ ≤ g i`, then `‖∑' i, f i‖₊ ≤ ∑' i, g i`. Note that we
 do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
@@ -159,6 +233,12 @@ theorem tsum_of_nnnorm_bounded {f : ι → E} {g : ι → ℝ≥0} {a : ℝ≥0}
   exact tsum_of_norm_bounded hg h
 #align tsum_of_nnnorm_bounded tsum_of_nnnorm_bounded
 
+/- warning: nnnorm_tsum_le -> nnnorm_tsum_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (tsum.{u2, u1} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u1} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace ι (fun (i : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i))))
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] {f : ι -> E}, (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (tsum.{u1, u2} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) ι (fun (i : ι) => f i))) (tsum.{0, u2} NNReal (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal ι (fun (i : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i))))
+Case conversion may be inaccurate. Consider using '#align nnnorm_tsum_le nnnorm_tsum_leₓ'. -/
 /-- If `∑' i, ‖f i‖₊` is summable, then `‖∑' i, f i‖₊ ≤ ∑' i, ‖f i‖₊`. Note that
 we do not assume that `∑' i, f i` is summable, and it might not be the case if `α` is not a complete
 space. -/
@@ -168,6 +248,12 @@ theorem nnnorm_tsum_le {f : ι → E} (hf : Summable fun i => ‖f i‖₊) : 
 
 variable [CompleteSpace E]
 
+/- warning: summable_of_norm_bounded_eventually -> summable_of_norm_bounded_eventually is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> Real), (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (Filter.Eventually.{u1} ι (fun (i : ι) => LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f i)) (g i)) (Filter.cofinite.{u1} ι)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E} (g : ι -> Real), (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) g) -> (Filter.Eventually.{u2} ι (fun (i : ι) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f i)) (g i)) (Filter.cofinite.{u2} ι)) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventuallyₓ'. -/
 /-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
 real function `g` which is summable, then `f` is summable. -/
 theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -175,16 +261,34 @@ theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg
   summable_iff_cauchySeq_finset.2 <| cauchySeq_finset_of_norm_bounded_eventually hg h
 #align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventually
 
+/- warning: summable_of_nnnorm_bounded -> summable_of_nnnorm_bounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f i)) (g i)) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E} (g : ι -> NNReal), (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal g) -> (forall (i : ι), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f i)) (g i)) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_nnnorm_bounded summable_of_nnnorm_boundedₓ'. -/
 theorem summable_of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
     (h : ∀ i, ‖f i‖₊ ≤ g i) : Summable f :=
   summable_of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
     exact_mod_cast h i
 #align summable_of_nnnorm_bounded summable_of_nnnorm_bounded
 
+/- warning: summable_of_summable_norm -> summable_of_summable_norm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, (Summable.{0, u1} Real ι Real.addCommMonoid (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_1) (f a))) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E}, (Summable.{0, u2} Real ι Real.instAddCommMonoidReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (fun (a : ι) => Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_1) (f a))) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_summable_norm summable_of_summable_normₓ'. -/
 theorem summable_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
   summable_of_norm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_norm summable_of_summable_norm
 
+/- warning: summable_of_summable_nnnorm -> summable_of_summable_nnnorm is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} E] [_inst_3 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))] {f : ι -> E}, (Summable.{0, u1} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)) NNReal.topologicalSpace (fun (a : ι) => NNNorm.nnnorm.{u2} E (SeminormedAddGroup.toNNNorm.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_1)) (f a))) -> (Summable.{u2, u1} E ι (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_1)) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_1))) f)
+but is expected to have type
+  forall {ι : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} E] [_inst_3 : CompleteSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))] {f : ι -> E}, (Summable.{0, u2} NNReal ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal instNNRealStrictOrderedSemiring)) NNReal.instTopologicalSpaceNNReal (fun (a : ι) => NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E _inst_1)) (f a))) -> (Summable.{u1, u2} E ι (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_1)) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align summable_of_summable_nnnorm summable_of_summable_nnnormₓ'. -/
 theorem summable_of_summable_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
   summable_of_nnnorm_bounded _ hf fun i => le_rfl
 #align summable_of_summable_nnnorm summable_of_summable_nnnorm

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.normed.group.infinite_sum
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.Algebra.BigOperators.Intervals
 import Mathbin.Analysis.Normed.Group.Basic
 import Mathbin.Topology.Instances.Nnreal
 

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

@@ -67,7 +67,7 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     exact (ht hi).2
   calc
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this
-    _ ≤ ‖∑ i in t, g i‖ := le_abs_self _
+    _ ≤ ‖∑ i in t, g i‖ := (le_abs_self _)
     _ < ε := hs _ (ht.mono_right le_sup_left)
     
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
@@ -89,8 +89,8 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
   rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg⊢
   calc
     ‖∑ k in Ico N n, f k‖ ≤ ∑ k in _, ‖f k‖ := norm_sum_le _ _
-    _ ≤ ∑ k in _, g k := sum_le_sum fun x _ => hf x
-    _ ≤ ‖∑ k in _, g k‖ := le_abs_self _
+    _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)
+    _ ≤ ‖∑ k in _, g k‖ := (le_abs_self _)
     _ < ε := hg
     
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -64,7 +64,7 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     exact (ht hi).2
   calc
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this
-    _ ≤ ‖∑ i in t, g i‖ := (le_abs_self _)
+    _ ≤ ‖∑ i in t, g i‖ := le_abs_self _
     _ < ε := hs _ (ht.mono_right le_sup_left)
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
 
@@ -84,8 +84,8 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
   rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg ⊢
   calc
     ‖∑ k in Ico N n, f k‖ ≤ ∑ k in _, ‖f k‖ := norm_sum_le _ _
-    _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)
-    _ ≤ ‖∑ k in _, g k‖ := (le_abs_self _)
+    _ ≤ ∑ k in _, g k := sum_le_sum fun x _ => hf x
+    _ ≤ ‖∑ k in _, g k‖ := le_abs_self _
     _ < ε := hg
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
 

@@ -18,7 +18,7 @@ In a complete (semi)normed group,
   there exists a finite set `s` such that the sum `∑ i in t, f i` over any finite set `t` disjoint
   with `s` has norm less than `ε`;
 
-- `summable_of_norm_bounded`, `summable_of_norm_bounded_eventually`: if `‖f i‖` is bounded above by
+- `summable_of_norm_bounded`, `Summable.of_norm_bounded_eventually`: if `‖f i‖` is bounded above by
   a summable series `∑' i, g i`, then `∑' i, f i` is summable as well; the same is true if the
   inequality hold only off some finite set.
 

Last year, YaelDillies made a pull request to mathlib3 that unfortunately never got merged in: https://github.com/leanprover-community/mathlib/pull/18405. This is the mathlib4 version of that pull request.

We define arbitrarily indexed products in a commutative monoid with a topology. This is done by "multiplicativizing" the currently existing definitions and theorems about arbitrarily indexed sums. That is, the existing code is rewritten in the multiplicative setting, and the original definitions and theorems are recovered using @[to_additive]. Please see this thread on Zulip for information on why this approach was chosen: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Infinite.20products

As YaelDillies wrote in the description of https://github.com/leanprover-community/mathlib/pull/18405, there are a few small technical issues that arise when directly "multiplicativizing" theorems in this way:

• I have renamed cauchySeq_finset_iff_vanishing to cauchySeq_finset_iff_sum_vanishing to make the name multiplicativizable. This is slightly different from the name cauchy_seq_finset_sum_iff_vanishing that YaelDillies used, and it is meant to parallel the existing name cauchySeq_finset_iff_tsum_vanishing.
• Currently, on master, there is a theorem called tsum_sum about taking the tsum of a sum, and a theorem called tsum_prod about taking a tsum on a product of two index sets. I have called the multiplicative versions tprod_of_prod and tprod_prod. This is slightly different from the names tprod_prod'' and tprod_prod that YaelDillies used. eric-wieser suggested renaming tsum_prod to tsum_prod_index to get around this issue, which I can do in a separate pull request.

@@ -40,7 +40,7 @@ variable {ι α E F : Type*} [SeminormedAddCommGroup E] [SeminormedAddCommGroup
 theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔
       ∀ ε > (0 : ℝ), ∃ s : Finset ι, ∀ t, Disjoint t s → ‖∑ i in t, f i‖ < ε := by
-  rw [cauchySeq_finset_iff_vanishing, nhds_basis_ball.forall_iff]
+  rw [cauchySeq_finset_iff_sum_vanishing, nhds_basis_ball.forall_iff]
   · simp only [ball_zero_eq, Set.mem_setOf_eq]
   · rintro s t hst ⟨s', hs'⟩
     exact ⟨s', fun t' ht' => hst <| hs' _ ht'⟩

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.

@@ -110,11 +110,11 @@ theorem hasSum_iff_tendsto_nat_of_summable_norm {f : ℕ → E} {a : E} (hf : Su
 
 /-- The direct comparison test for series:  if the norm of `f` is bounded by a real function `g`
 which is summable, then `f` is summable. -/
-theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
+theorem Summable.of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ i, ‖f i‖ ≤ g i) : Summable f := by
   rw [summable_iff_cauchySeq_finset]
   exact cauchySeq_finset_of_norm_bounded g hg h
-#align summable_of_norm_bounded summable_of_norm_bounded
+#align summable_of_norm_bounded Summable.of_norm_bounded
 
 theorem HasSum.norm_le_of_bounded {f : ι → E} {g : ι → ℝ} {a : E} {b : ℝ} (hf : HasSum f a)
     (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b := by
@@ -160,21 +160,26 @@ variable [CompleteSpace E]
 
 /-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
 real function `g` which is summable, then `f` is summable. -/
-theorem summable_of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
+theorem Summable.of_norm_bounded_eventually {f : ι → E} (g : ι → ℝ) (hg : Summable g)
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : Summable f :=
   summable_iff_cauchySeq_finset.2 <| cauchySeq_finset_of_norm_bounded_eventually hg h
-#align summable_of_norm_bounded_eventually summable_of_norm_bounded_eventually
+#align summable_of_norm_bounded_eventually Summable.of_norm_bounded_eventually
 
-theorem summable_of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
+/-- Variant of the direct comparison test for series:  if the norm of `f` is eventually bounded by a
+real function `g` which is summable, then `f` is summable. -/
+theorem Summable.of_norm_bounded_eventually_nat {f : ℕ → E} (g : ℕ → ℝ) (hg : Summable g)
+    (h : ∀ᶠ i in atTop, ‖f i‖ ≤ g i) : Summable f :=
+  .of_norm_bounded_eventually g hg <| Nat.cofinite_eq_atTop ▸ h
+
+theorem Summable.of_nnnorm_bounded {f : ι → E} (g : ι → ℝ≥0) (hg : Summable g)
     (h : ∀ i, ‖f i‖₊ ≤ g i) : Summable f :=
-  summable_of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) fun i => by
-    exact_mod_cast h i
-#align summable_of_nnnorm_bounded summable_of_nnnorm_bounded
+  .of_norm_bounded (fun i => (g i : ℝ)) (NNReal.summable_coe.2 hg) h
+#align summable_of_nnnorm_bounded Summable.of_nnnorm_bounded
 
-theorem summable_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
-  summable_of_norm_bounded _ hf fun _i => le_rfl
-#align summable_of_summable_norm summable_of_summable_norm
+theorem Summable.of_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) : Summable f :=
+  .of_norm_bounded _ hf fun _i => le_rfl
+#align summable_of_summable_norm Summable.of_norm
 
-theorem summable_of_summable_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
-  summable_of_nnnorm_bounded _ hf fun _i => le_rfl
-#align summable_of_summable_nnnorm summable_of_summable_nnnorm
+theorem Summable.of_nnnorm {f : ι → E} (hf : Summable fun a => ‖f a‖₊) : Summable f :=
+  .of_nnnorm_bounded _ hf fun _i => le_rfl
+#align summable_of_summable_nnnorm Summable.of_nnnorm

@@ -31,7 +31,7 @@ infinite series, absolute convergence, normed group
 -/
 
 
-open Classical BigOperators Topology NNReal
+open BigOperators Topology NNReal
 
 open Finset Filter Metric
 
@@ -55,6 +55,7 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     (h : ∀ᶠ i in cofinite, ‖f i‖ ≤ g i) : CauchySeq fun s => ∑ i in s, f i := by
   refine' cauchySeq_finset_iff_vanishing_norm.2 fun ε hε => _
   rcases summable_iff_vanishing_norm.1 hg ε hε with ⟨s, hs⟩
+  classical
   refine' ⟨s ∪ h.toFinset, fun t ht => _⟩
   have : ∀ i ∈ t, ‖f i‖ ≤ g i := by
     intro i hi
@@ -116,8 +117,8 @@ theorem summable_of_norm_bounded [CompleteSpace E] {f : ι → E} (g : ι → 
 #align summable_of_norm_bounded summable_of_norm_bounded
 
 theorem HasSum.norm_le_of_bounded {f : ι → E} {g : ι → ℝ} {a : E} {b : ℝ} (hf : HasSum f a)
-    (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b :=
-  le_of_tendsto_of_tendsto' hf.norm hg fun _s => norm_sum_le_of_le _ fun i _hi => h i
+    (hg : HasSum g b) (h : ∀ i, ‖f i‖ ≤ g i) : ‖a‖ ≤ b := by
+  classical exact le_of_tendsto_of_tendsto' hf.norm hg fun _s ↦ norm_sum_le_of_le _ fun i _hi ↦ h i
 #align has_sum.norm_le_of_bounded HasSum.norm_le_of_bounded
 
 /-- Quantitative result associated to the direct comparison test for series:  If `∑' i, g i` is
@@ -128,7 +129,7 @@ theorem tsum_of_norm_bounded {f : ι → E} {g : ι → ℝ} {a : ℝ} (hg : Has
   by_cases hf : Summable f
   · exact hf.hasSum.norm_le_of_bounded hg h
   · rw [tsum_eq_zero_of_not_summable hf, norm_zero]
-    exact ge_of_tendsto' hg fun s => sum_nonneg fun i _hi => (norm_nonneg _).trans (h i)
+    classical exact ge_of_tendsto' hg fun s => sum_nonneg fun i _hi => (norm_nonneg _).trans (h i)
 #align tsum_of_norm_bounded tsum_of_norm_bounded
 
 /-- If `∑' i, ‖f i‖` is summable, then `‖∑' i, f i‖ ≤ (∑' i, ‖f i‖)`. Note that we do not assume

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

This has nice performance benefits.

@@ -35,7 +35,7 @@ open Classical BigOperators Topology NNReal
 
 open Finset Filter Metric
 
-variable {ι α E F : Type _} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
+variable {ι α E F : Type*} [SeminormedAddCommGroup E] [SeminormedAddCommGroup F]
 
 theorem cauchySeq_finset_iff_vanishing_norm {f : ι → E} :
     (CauchySeq fun s : Finset ι => ∑ i in s, f i) ↔

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.normed.group.infinite_sum
-! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Intervals
 import Mathlib.Analysis.Normed.Group.Basic
 import Mathlib.Topology.Instances.NNReal
 
+#align_import analysis.normed.group.infinite_sum from "leanprover-community/mathlib"@"9a59dcb7a2d06bf55da57b9030169219980660cd"
+
 /-!
 # Infinite sums in (semi)normed groups
 

Changes are of the form

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

@@ -83,7 +83,7 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
   refine' Metric.cauchySeq_iff'.2 fun ε hε => _
   refine' (Metric.cauchySeq_iff'.1 hg ε hε).imp fun N hg n hn => _
   specialize hg n hn
-  rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg⊢
+  rw [dist_eq_norm, ← sum_Ico_eq_sub _ hn] at hg ⊢
   calc
     ‖∑ k in Ico N n, f k‖ ≤ ∑ k in _, ‖f k‖ := norm_sum_le _ _
     _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)

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.)

@@ -68,7 +68,6 @@ theorem cauchySeq_finset_of_norm_bounded_eventually {f : ι → E} {g : ι → 
     ‖∑ i in t, f i‖ ≤ ∑ i in t, g i := norm_sum_le_of_le _ this
     _ ≤ ‖∑ i in t, g i‖ := (le_abs_self _)
     _ < ε := hs _ (ht.mono_right le_sup_left)
-
 #align cauchy_seq_finset_of_norm_bounded_eventually cauchySeq_finset_of_norm_bounded_eventually
 
 theorem cauchySeq_finset_of_norm_bounded {f : ι → E} (g : ι → ℝ) (hg : Summable g)
@@ -90,7 +89,6 @@ theorem cauchySeq_range_of_norm_bounded {f : ℕ → E} (g : ℕ → ℝ)
     _ ≤ ∑ k in _, g k := (sum_le_sum fun x _ => hf x)
     _ ≤ ‖∑ k in _, g k‖ := (le_abs_self _)
     _ < ε := hg
-
 #align cauchy_seq_range_of_norm_bounded cauchySeq_range_of_norm_bounded
 
 theorem cauchySeq_finset_of_summable_norm {f : ι → E} (hf : Summable fun a => ‖f a‖) :