algebra.big_operators.intervals ⟷ Mathlib.Algebra.BigOperators.Intervals

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

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Algebra.BigOperators.Basic
-import Mathbin.Algebra.Module.Basic
-import Mathbin.Data.Nat.Interval
+import Algebra.BigOperators.Basic
+import Algebra.Module.Basic
+import Data.Nat.Interval
 import Mathbin.Tactic.Linarith.Default
 
 #align_import algebra.big_operators.intervals from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"

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

@@ -2,17 +2,14 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module algebra.big_operators.intervals
-! leanprover-community/mathlib commit 68d1483e8a718ec63219f0e227ca3f0140361086
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Basic
 import Mathbin.Algebra.Module.Basic
 import Mathbin.Data.Nat.Interval
 import Mathbin.Tactic.Linarith.Default
 
+#align_import algebra.big_operators.intervals from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
+
 /-!
 # Results about big operators over intervals
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -252,7 +252,7 @@ theorem prod_range_add_one_eq_factorial : ∀ n : ℕ, ∏ x in range n, (x + 1)
 #align finset.prod_range_add_one_eq_factorial Finset.prod_range_add_one_eq_factorial
 -/
 
-section GaussSum
+section gaussSum
 
 #print Finset.sum_range_id_mul_two /-
 /-- Gauss' summation formula -/
@@ -274,7 +274,7 @@ theorem sum_range_id (n : ℕ) : ∑ i in range n, i = n * (n - 1) / 2 := by
 #align finset.sum_range_id Finset.sum_range_id
 -/
 
-end GaussSum
+end gaussSum
 
 end Generic
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -146,9 +146,9 @@ theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
 -/
 
-#print Finset.prod_range_sub_prod_range /-
+#print Finset.prod_range_div_prod_range /-
 @[to_additive]
-theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
+theorem prod_range_div_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
     (∏ k in range m, f k) / ∏ k in range n, f k = ∏ k in (range m).filterₓ fun k => n ≤ k, f k :=
   by
   rw [← prod_Ico_eq_div f hnm]
@@ -156,7 +156,7 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
   apply Finset.ext
   simp only [mem_Ico, mem_filter, mem_range, *]
   tauto
-#align finset.prod_range_sub_prod_range Finset.prod_range_sub_prod_range
+#align finset.prod_range_sub_prod_range Finset.prod_range_div_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 -/
 

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

@@ -35,13 +35,16 @@ variable {α : Type u} {β : Type v} {γ : Type w} {s₂ s₁ s : Finset α} {a
 
 variable [CommMonoid β]
 
+#print Finset.prod_Ico_add' /-
 @[to_additive]
 theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → β) (a b c : α) : ∏ x in Ico a b, f (x + c) = ∏ x in Ico (a + c) (b + c), f x := by
   rw [← map_add_right_Ico, Prod_map]; rfl
 #align finset.prod_Ico_add' Finset.prod_Ico_add'
 #align finset.sum_Ico_add' Finset.sum_Ico_add'
+-/
 
+#print Finset.prod_Ico_add /-
 @[to_additive]
 theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → β) (a b c : α) : ∏ x in Ico a b, f (c + x) = ∏ x in Ico (a + c) (b + c), f x :=
@@ -50,40 +53,52 @@ theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locally
   simp_rw [add_comm]
 #align finset.prod_Ico_add Finset.prod_Ico_add
 #align finset.sum_Ico_add Finset.sum_Ico_add
+-/
 
+#print Finset.sum_Ico_succ_top /-
 theorem sum_Ico_succ_top {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a ≤ b) (f : ℕ → δ) :
     ∑ k in Ico a (b + 1), f k = ∑ k in Ico a b, f k + f b := by
   rw [Nat.Ico_succ_right_eq_insert_Ico hab, sum_insert right_not_mem_Ico, add_comm]
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
+-/
 
+#print Finset.prod_Ico_succ_top /-
 @[to_additive]
 theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
     ∏ k in Ico a (b + 1), f k = (∏ k in Ico a b, f k) * f b :=
   @sum_Ico_succ_top (Additive β) _ _ _ hab _
 #align finset.prod_Ico_succ_top Finset.prod_Ico_succ_top
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
+-/
 
+#print Finset.sum_eq_sum_Ico_succ_bot /-
 theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a < b) (f : ℕ → δ) :
     ∑ k in Ico a b, f k = f a + ∑ k in Ico (a + 1) b, f k :=
   by
   have ha : a ∉ Ico (a + 1) b := by simp
   rw [← sum_insert ha, Nat.Ico_insert_succ_left hab]
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
+-/
 
+#print Finset.prod_eq_prod_Ico_succ_bot /-
 @[to_additive]
 theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
     ∏ k in Ico a b, f k = f a * ∏ k in Ico (a + 1) b, f k :=
   @sum_eq_sum_Ico_succ_bot (Additive β) _ _ _ hab _
 #align finset.prod_eq_prod_Ico_succ_bot Finset.prod_eq_prod_Ico_succ_bot
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
+-/
 
+#print Finset.prod_Ico_consecutive /-
 @[to_additive]
 theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     (∏ i in Ico m n, f i) * ∏ i in Ico n k, f i = ∏ i in Ico m k, f i :=
   Ico_union_Ico_eq_Ico hmn hnk ▸ Eq.symm <| prod_union <| Ico_disjoint_Ico_consecutive m n k
 #align finset.prod_Ico_consecutive Finset.prod_Ico_consecutive
 #align finset.sum_Ico_consecutive Finset.sum_Ico_consecutive
+-/
 
+#print Finset.prod_Ioc_consecutive /-
 @[to_additive]
 theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     (∏ i in Ioc m n, f i) * ∏ i in Ioc n k, f i = ∏ i in Ioc m k, f i :=
@@ -93,35 +108,45 @@ theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk
   exact lt_irrefl _ ((mem_Ioc.1 h'x).1.trans_le (mem_Ioc.1 hx).2)
 #align finset.prod_Ioc_consecutive Finset.prod_Ioc_consecutive
 #align finset.sum_Ioc_consecutive Finset.sum_Ioc_consecutive
+-/
 
+#print Finset.prod_Ioc_succ_top /-
 @[to_additive]
 theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
     ∏ k in Ioc a (b + 1), f k = (∏ k in Ioc a b, f k) * f (b + 1) := by
   rw [← prod_Ioc_consecutive _ hab (Nat.le_succ b), Nat.Ioc_succ_singleton, prod_singleton]
 #align finset.prod_Ioc_succ_top Finset.prod_Ioc_succ_top
 #align finset.sum_Ioc_succ_top Finset.sum_Ioc_succ_top
+-/
 
+#print Finset.prod_range_mul_prod_Ico /-
 @[to_additive]
 theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
     (∏ k in range m, f k) * ∏ k in Ico m n, f k = ∏ k in range n, f k :=
   Nat.Ico_zero_eq_range ▸ Nat.Ico_zero_eq_range ▸ prod_Ico_consecutive f m.zero_le h
 #align finset.prod_range_mul_prod_Ico Finset.prod_range_mul_prod_Ico
 #align finset.sum_range_add_sum_Ico Finset.sum_range_add_sum_Ico
+-/
 
+#print Finset.prod_Ico_eq_mul_inv /-
 @[to_additive]
 theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     ∏ k in Ico m n, f k = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
   eq_mul_inv_iff_mul_eq.2 <| by rw [mul_comm] <;> exact prod_range_mul_prod_Ico f h
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
 #align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
+-/
 
+#print Finset.prod_Ico_eq_div /-
 @[to_additive]
 theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     ∏ k in Ico m n, f k = (∏ k in range n, f k) / ∏ k in range m, f k := by
   simpa only [div_eq_mul_inv] using prod_Ico_eq_mul_inv f h
 #align finset.prod_Ico_eq_div Finset.prod_Ico_eq_div
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
+-/
 
+#print Finset.prod_range_sub_prod_range /-
 @[to_additive]
 theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
     (∏ k in range m, f k) / ∏ k in range n, f k = ∏ k in (range m).filterₓ fun k => n ≤ k, f k :=
@@ -133,7 +158,9 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
   tauto
 #align finset.prod_range_sub_prod_range Finset.prod_range_sub_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
+-/
 
+#print Finset.sum_Ico_Ico_comm /-
 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
 theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
     ∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j =
@@ -149,7 +176,9 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
       refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
     linarith
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
+-/
 
+#print Finset.prod_Ico_eq_prod_range /-
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     ∏ k in Ico m n, f k = ∏ k in range (n - m), f (m + k) :=
@@ -160,7 +189,9 @@ theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     rw [Ico_eq_empty_of_le h, tsub_eq_zero_iff_le.mpr h, range_zero, prod_empty, prod_empty]
 #align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_range
 #align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
+-/
 
+#print Finset.prod_Ico_reflect /-
 theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
     ∏ j in Ico k m, f (n - j) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   by
@@ -175,11 +206,14 @@ theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1
     rw [← tsub_tsub_cancel_of_le (this _ im), Hij, tsub_tsub_cancel_of_le (this _ jm)]
   · simp [Ico_eq_empty_of_le, tsub_le_tsub_left, hkm]
 #align finset.prod_Ico_reflect Finset.prod_Ico_reflect
+-/
 
+#print Finset.sum_Ico_reflect /-
 theorem sum_Ico_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
     (h : m ≤ n + 1) : ∑ j in Ico k m, f (n - j) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
 #align finset.sum_Ico_reflect Finset.sum_Ico_reflect
+-/
 
 #print Finset.prod_range_reflect /-
 theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
@@ -200,6 +234,7 @@ theorem sum_range_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (n :
 #align finset.sum_range_reflect Finset.sum_range_reflect
 -/
 
+#print Finset.prod_Ico_id_eq_factorial /-
 @[simp]
 theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, ∏ x in Ico 1 (n + 1), x = n !
   | 0 => rfl
@@ -207,6 +242,7 @@ theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, ∏ x in Ico 1 (n + 1), x = n !
     rw [prod_Ico_succ_top <| Nat.succ_le_succ <| zero_le n, Nat.factorial_succ,
       prod_Ico_id_eq_factorial n, Nat.succ_eq_add_one, mul_comm]
 #align finset.prod_Ico_id_eq_factorial Finset.prod_Ico_id_eq_factorial
+-/
 
 #print Finset.prod_range_add_one_eq_factorial /-
 @[simp]
@@ -252,30 +288,38 @@ section Group
 
 variable [CommGroup β]
 
+#print Finset.prod_range_succ_div_prod /-
 @[to_additive]
 theorem prod_range_succ_div_prod : (∏ i in range (n + 1), f i) / ∏ i in range n, f i = f n :=
   div_eq_iff_eq_mul'.mpr <| prod_range_succ f n
 #align finset.prod_range_succ_div_prod Finset.prod_range_succ_div_prod
 #align finset.sum_range_succ_sub_sum Finset.sum_range_succ_sub_sum
+-/
 
+#print Finset.prod_range_succ_div_top /-
 @[to_additive]
 theorem prod_range_succ_div_top : (∏ i in range (n + 1), f i) / f n = ∏ i in range n, f i :=
   div_eq_iff_eq_mul.mpr <| prod_range_succ f n
 #align finset.prod_range_succ_div_top Finset.prod_range_succ_div_top
 #align finset.sum_range_succ_sub_top Finset.sum_range_succ_sub_top
+-/
 
+#print Finset.prod_Ico_div_bot /-
 @[to_additive]
 theorem prod_Ico_div_bot (hmn : m < n) : (∏ i in Ico m n, f i) / f m = ∏ i in Ico (m + 1) n, f i :=
   div_eq_iff_eq_mul'.mpr <| prod_eq_prod_Ico_succ_bot hmn _
 #align finset.prod_Ico_div_bot Finset.prod_Ico_div_bot
 #align finset.sum_Ico_sub_bot Finset.sum_Ico_sub_bot
+-/
 
+#print Finset.prod_Ico_succ_div_top /-
 @[to_additive]
 theorem prod_Ico_succ_div_top (hmn : m ≤ n) :
     (∏ i in Ico m (n + 1), f i) / f n = ∏ i in Ico m n, f i :=
   div_eq_iff_eq_mul.mpr <| prod_Ico_succ_top hmn _
 #align finset.prod_Ico_succ_div_top Finset.prod_Ico_succ_div_top
 #align finset.sum_Ico_succ_sub_top Finset.sum_Ico_succ_sub_top
+-/
 
 end Group
 
@@ -287,10 +331,10 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] (f : ℕ → R) (
 
 open Finset
 
--- mathport name: «exprG »
 -- The partial sum of `g`, starting from zero
 local notation "G " n:80 => ∑ i in range n, g i
 
+#print Finset.sum_Ico_by_parts /-
 /-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
 theorem sum_Ico_by_parts (hmn : m < n) :
     ∑ i in Ico m n, f i • g i =
@@ -321,9 +365,11 @@ theorem sum_Ico_by_parts (hmn : m < n) :
   simp_rw [this, sum_neg_distrib, sum_range_succ, smul_add]
   abel
 #align finset.sum_Ico_by_parts Finset.sum_Ico_by_parts
+-/
 
 variable (n)
 
+#print Finset.sum_range_by_parts /-
 /-- **Summation by parts** for ranges -/
 theorem sum_range_by_parts :
     ∑ i in range n, f i • g i =
@@ -335,6 +381,7 @@ theorem sum_range_by_parts :
     rw [range_eq_Ico, sum_Ico_by_parts f g (Nat.pos_of_ne_zero hn), sum_range_zero, smul_zero,
       sub_zero, range_eq_Ico]
 #align finset.sum_range_by_parts Finset.sum_range_by_parts
+-/
 
 end Module
 

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

@@ -37,14 +37,14 @@ variable [CommMonoid β]
 
 @[to_additive]
 theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
-    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x := by
+    (f : α → β) (a b c : α) : ∏ x in Ico a b, f (x + c) = ∏ x in Ico (a + c) (b + c), f x := by
   rw [← map_add_right_Ico, Prod_map]; rfl
 #align finset.prod_Ico_add' Finset.prod_Ico_add'
 #align finset.sum_Ico_add' Finset.sum_Ico_add'
 
 @[to_additive]
 theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
-    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (c + x)) = ∏ x in Ico (a + c) (b + c), f x :=
+    (f : α → β) (a b c : α) : ∏ x in Ico a b, f (c + x) = ∏ x in Ico (a + c) (b + c), f x :=
   by
   convert prod_Ico_add' f a b c
   simp_rw [add_comm]
@@ -52,19 +52,19 @@ theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locally
 #align finset.sum_Ico_add Finset.sum_Ico_add
 
 theorem sum_Ico_succ_top {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a ≤ b) (f : ℕ → δ) :
-    (∑ k in Ico a (b + 1), f k) = (∑ k in Ico a b, f k) + f b := by
+    ∑ k in Ico a (b + 1), f k = ∑ k in Ico a b, f k + f b := by
   rw [Nat.Ico_succ_right_eq_insert_Ico hab, sum_insert right_not_mem_Ico, add_comm]
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
 @[to_additive]
 theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
-    (∏ k in Ico a (b + 1), f k) = (∏ k in Ico a b, f k) * f b :=
+    ∏ k in Ico a (b + 1), f k = (∏ k in Ico a b, f k) * f b :=
   @sum_Ico_succ_top (Additive β) _ _ _ hab _
 #align finset.prod_Ico_succ_top Finset.prod_Ico_succ_top
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
 theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a < b) (f : ℕ → δ) :
-    (∑ k in Ico a b, f k) = f a + ∑ k in Ico (a + 1) b, f k :=
+    ∑ k in Ico a b, f k = f a + ∑ k in Ico (a + 1) b, f k :=
   by
   have ha : a ∉ Ico (a + 1) b := by simp
   rw [← sum_insert ha, Nat.Ico_insert_succ_left hab]
@@ -72,21 +72,21 @@ theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (ha
 
 @[to_additive]
 theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
-    (∏ k in Ico a b, f k) = f a * ∏ k in Ico (a + 1) b, f k :=
+    ∏ k in Ico a b, f k = f a * ∏ k in Ico (a + 1) b, f k :=
   @sum_eq_sum_Ico_succ_bot (Additive β) _ _ _ hab _
 #align finset.prod_eq_prod_Ico_succ_bot Finset.prod_eq_prod_Ico_succ_bot
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
 
 @[to_additive]
 theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
-    ((∏ i in Ico m n, f i) * ∏ i in Ico n k, f i) = ∏ i in Ico m k, f i :=
+    (∏ i in Ico m n, f i) * ∏ i in Ico n k, f i = ∏ i in Ico m k, f i :=
   Ico_union_Ico_eq_Ico hmn hnk ▸ Eq.symm <| prod_union <| Ico_disjoint_Ico_consecutive m n k
 #align finset.prod_Ico_consecutive Finset.prod_Ico_consecutive
 #align finset.sum_Ico_consecutive Finset.sum_Ico_consecutive
 
 @[to_additive]
 theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
-    ((∏ i in Ioc m n, f i) * ∏ i in Ioc n k, f i) = ∏ i in Ioc m k, f i :=
+    (∏ i in Ioc m n, f i) * ∏ i in Ioc n k, f i = ∏ i in Ioc m k, f i :=
   by
   rw [← Ioc_union_Ioc_eq_Ioc hmn hnk, prod_union]
   apply disjoint_left.2 fun x hx h'x => _
@@ -96,35 +96,35 @@ theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk
 
 @[to_additive]
 theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
-    (∏ k in Ioc a (b + 1), f k) = (∏ k in Ioc a b, f k) * f (b + 1) := by
+    ∏ k in Ioc a (b + 1), f k = (∏ k in Ioc a b, f k) * f (b + 1) := by
   rw [← prod_Ioc_consecutive _ hab (Nat.le_succ b), Nat.Ioc_succ_singleton, prod_singleton]
 #align finset.prod_Ioc_succ_top Finset.prod_Ioc_succ_top
 #align finset.sum_Ioc_succ_top Finset.sum_Ioc_succ_top
 
 @[to_additive]
 theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
-    ((∏ k in range m, f k) * ∏ k in Ico m n, f k) = ∏ k in range n, f k :=
+    (∏ k in range m, f k) * ∏ k in Ico m n, f k = ∏ k in range n, f k :=
   Nat.Ico_zero_eq_range ▸ Nat.Ico_zero_eq_range ▸ prod_Ico_consecutive f m.zero_le h
 #align finset.prod_range_mul_prod_Ico Finset.prod_range_mul_prod_Ico
 #align finset.sum_range_add_sum_Ico Finset.sum_range_add_sum_Ico
 
 @[to_additive]
 theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
-    (∏ k in Ico m n, f k) = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
+    ∏ k in Ico m n, f k = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
   eq_mul_inv_iff_mul_eq.2 <| by rw [mul_comm] <;> exact prod_range_mul_prod_Ico f h
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
 #align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
 
 @[to_additive]
 theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
-    (∏ k in Ico m n, f k) = (∏ k in range n, f k) / ∏ k in range m, f k := by
+    ∏ k in Ico m n, f k = (∏ k in range n, f k) / ∏ k in range m, f k := by
   simpa only [div_eq_mul_inv] using prod_Ico_eq_mul_inv f h
 #align finset.prod_Ico_eq_div Finset.prod_Ico_eq_div
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
 
 @[to_additive]
 theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
-    ((∏ k in range m, f k) / ∏ k in range n, f k) = ∏ k in (range m).filterₓ fun k => n ≤ k, f k :=
+    (∏ k in range m, f k) / ∏ k in range n, f k = ∏ k in (range m).filterₓ fun k => n ≤ k, f k :=
   by
   rw [← prod_Ico_eq_div f hnm]
   congr
@@ -136,7 +136,7 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
 
 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
 theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
-    (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
+    ∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j =
       ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a (j + 1), f i j :=
   by
   rw [Finset.sum_sigma', Finset.sum_sigma']
@@ -152,7 +152,7 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
 
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
-    (∏ k in Ico m n, f k) = ∏ k in range (n - m), f (m + k) :=
+    ∏ k in Ico m n, f k = ∏ k in range (n - m), f (m + k) :=
   by
   by_cases h : m ≤ n
   · rw [← Nat.Ico_zero_eq_range, prod_Ico_add, zero_add, tsub_add_cancel_of_le h]
@@ -162,7 +162,7 @@ theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
 #align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
 
 theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
-    (∏ j in Ico k m, f (n - j)) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j :=
+    ∏ j in Ico k m, f (n - j) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   by
   have : ∀ i < m, i ≤ n := by
     intro i hi
@@ -177,13 +177,13 @@ theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1
 #align finset.prod_Ico_reflect Finset.prod_Ico_reflect
 
 theorem sum_Ico_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
-    (h : m ≤ n + 1) : (∑ j in Ico k m, f (n - j)) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
+    (h : m ≤ n + 1) : ∑ j in Ico k m, f (n - j) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
 #align finset.sum_Ico_reflect Finset.sum_Ico_reflect
 
 #print Finset.prod_range_reflect /-
 theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
-    (∏ j in range n, f (n - 1 - j)) = ∏ j in range n, f j :=
+    ∏ j in range n, f (n - 1 - j) = ∏ j in range n, f j :=
   by
   cases n
   · simp
@@ -195,13 +195,13 @@ theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
 
 #print Finset.sum_range_reflect /-
 theorem sum_range_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (n : ℕ) :
-    (∑ j in range n, f (n - 1 - j)) = ∑ j in range n, f j :=
+    ∑ j in range n, f (n - 1 - j) = ∑ j in range n, f j :=
   @prod_range_reflect (Multiplicative δ) _ f n
 #align finset.sum_range_reflect Finset.sum_range_reflect
 -/
 
 @[simp]
-theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n !
+theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, ∏ x in Ico 1 (n + 1), x = n !
   | 0 => rfl
   | n + 1 => by
     rw [prod_Ico_succ_top <| Nat.succ_le_succ <| zero_le n, Nat.factorial_succ,
@@ -210,7 +210,7 @@ theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n
 
 #print Finset.prod_range_add_one_eq_factorial /-
 @[simp]
-theorem prod_range_add_one_eq_factorial : ∀ n : ℕ, (∏ x in range n, x + 1) = n !
+theorem prod_range_add_one_eq_factorial : ∀ n : ℕ, ∏ x in range n, (x + 1) = n !
   | 0 => rfl
   | n + 1 => by simp [Finset.range_succ, prod_range_add_one_eq_factorial n]
 #align finset.prod_range_add_one_eq_factorial Finset.prod_range_add_one_eq_factorial
@@ -222,10 +222,10 @@ section GaussSum
 /-- Gauss' summation formula -/
 theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1) :=
   calc
-    (∑ i in range n, i) * 2 = (∑ i in range n, i) + ∑ i in range n, n - 1 - i := by
+    (∑ i in range n, i) * 2 = ∑ i in range n, i + ∑ i in range n, (n - 1 - i) := by
       rw [sum_range_reflect (fun i => i) n, mul_two]
-    _ = ∑ i in range n, i + (n - 1 - i) := sum_add_distrib.symm
-    _ = ∑ i in range n, n - 1 :=
+    _ = ∑ i in range n, (i + (n - 1 - i)) := sum_add_distrib.symm
+    _ = ∑ i in range n, (n - 1) :=
       (sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi)
     _ = n * (n - 1) := by rw [sum_const, card_range, Nat.nsmul_eq_mul]
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two
@@ -233,7 +233,7 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
 
 #print Finset.sum_range_id /-
 /-- Gauss' summation formula -/
-theorem sum_range_id (n : ℕ) : (∑ i in range n, i) = n * (n - 1) / 2 := by
+theorem sum_range_id (n : ℕ) : ∑ i in range n, i = n * (n - 1) / 2 := by
   rw [← sum_range_id_mul_two n, Nat.mul_div_cancel] <;> exact by decide
 #align finset.sum_range_id Finset.sum_range_id
 -/
@@ -253,7 +253,7 @@ section Group
 variable [CommGroup β]
 
 @[to_additive]
-theorem prod_range_succ_div_prod : ((∏ i in range (n + 1), f i) / ∏ i in range n, f i) = f n :=
+theorem prod_range_succ_div_prod : (∏ i in range (n + 1), f i) / ∏ i in range n, f i = f n :=
   div_eq_iff_eq_mul'.mpr <| prod_range_succ f n
 #align finset.prod_range_succ_div_prod Finset.prod_range_succ_div_prod
 #align finset.sum_range_succ_sub_sum Finset.sum_range_succ_sub_sum
@@ -293,16 +293,16 @@ local notation "G " n:80 => ∑ i in range n, g i
 
 /-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
 theorem sum_Ico_by_parts (hmn : m < n) :
-    (∑ i in Ico m n, f i • g i) =
+    ∑ i in Ico m n, f i • g i =
       f (n - 1) • G n - f m • G m - ∑ i in Ico m (n - 1), (f (i + 1) - f i) • G (i + 1) :=
   by
-  have h₁ : (∑ i in Ico (m + 1) n, f i • G i) = ∑ i in Ico m (n - 1), f (i + 1) • G (i + 1) :=
+  have h₁ : ∑ i in Ico (m + 1) n, f i • G i = ∑ i in Ico m (n - 1), f (i + 1) • G (i + 1) :=
     by
     conv in n => rw [← Nat.sub_add_cancel (Nat.one_le_of_lt hmn)]
     rw [← sum_Ico_add']
   have h₂ :
-    (∑ i in Ico (m + 1) n, f i • G (i + 1)) =
-      (∑ i in Ico m (n - 1), f i • G (i + 1)) + f (n - 1) • G n - f m • G (m + 1) :=
+    ∑ i in Ico (m + 1) n, f i • G (i + 1) =
+      ∑ i in Ico m (n - 1), f i • G (i + 1) + f (n - 1) • G n - f m • G (m + 1) :=
     by
     rw [← sum_Ico_sub_bot _ hmn, ← sum_Ico_succ_sub_top _ (Nat.le_pred_of_lt hmn),
       Nat.sub_add_cancel (pos_of_gt hmn), sub_add_cancel]
@@ -326,7 +326,7 @@ variable (n)
 
 /-- **Summation by parts** for ranges -/
 theorem sum_range_by_parts :
-    (∑ i in range n, f i • g i) =
+    ∑ i in range n, f i • g i =
       f (n - 1) • G n - ∑ i in range (n - 1), (f (i + 1) - f i) • G (i + 1) :=
   by
   by_cases hn : n = 0

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

@@ -228,7 +228,6 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
     _ = ∑ i in range n, n - 1 :=
       (sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi)
     _ = n * (n - 1) := by rw [sum_const, card_range, Nat.nsmul_eq_mul]
-    
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two
 -/
 

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

@@ -141,8 +141,8 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
   by
   rw [Finset.sum_sigma', Finset.sum_sigma']
   refine'
-            Finset.sum_bij' (fun (x : Σi : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σi : ℕ, ℕ)) _ (fun _ _ => rfl)
-              (fun (x : Σi : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σi : ℕ, ℕ)) _ (by rintro ⟨⟩ _ <;> rfl)
+            Finset.sum_bij' (fun (x : Σ i : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ i : ℕ, ℕ)) _ (fun _ _ => rfl)
+              (fun (x : Σ i : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ i : ℕ, ℕ)) _ (by rintro ⟨⟩ _ <;> rfl)
               (by rintro ⟨⟩ _ <;> rfl) <;>
           simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
         rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>

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

@@ -25,7 +25,7 @@ We prove results about big operators over intervals (mostly the `ℕ`-valued `Ic
 
 universe u v w
 
-open BigOperators Nat
+open scoped BigOperators Nat
 
 namespace Finset
 

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

@@ -35,12 +35,6 @@ variable {α : Type u} {β : Type v} {γ : Type w} {s₂ s₁ s : Finset α} {a
 
 variable [CommMonoid β]
 
-/- warning: finset.prod_Ico_add' -> Finset.prod_Ico_add' is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) x c))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
-Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_add' Finset.prod_Ico_add'ₓ'. -/
 @[to_additive]
 theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → β) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x := by
@@ -48,12 +42,6 @@ theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locall
 #align finset.prod_Ico_add' Finset.prod_Ico_add'
 #align finset.sum_Ico_add' Finset.sum_Ico_add'
 
-/- warning: finset.prod_Ico_add -> Finset.prod_Ico_add is a dubious translation:
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 @[to_additive]
 theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → β) (a b c : α) : (∏ x in Ico a b, f (c + x)) = ∏ x in Ico (a + c) (b + c), f x :=
@@ -63,23 +51,11 @@ theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locally
 #align finset.prod_Ico_add Finset.prod_Ico_add
 #align finset.sum_Ico_add Finset.sum_Ico_add
 
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 theorem sum_Ico_succ_top {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a ≤ b) (f : ℕ → δ) :
     (∑ k in Ico a (b + 1), f k) = (∑ k in Ico a b, f k) + f b := by
   rw [Nat.Ico_succ_right_eq_insert_Ico hab, sum_insert right_not_mem_Ico, add_comm]
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
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 @[to_additive]
 theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
     (∏ k in Ico a (b + 1), f k) = (∏ k in Ico a b, f k) * f b :=
@@ -87,12 +63,6 @@ theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
 #align finset.prod_Ico_succ_top Finset.prod_Ico_succ_top
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
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 theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a < b) (f : ℕ → δ) :
     (∑ k in Ico a b, f k) = f a + ∑ k in Ico (a + 1) b, f k :=
   by
@@ -100,12 +70,6 @@ theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (ha
   rw [← sum_insert ha, Nat.Ico_insert_succ_left hab]
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
 
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 @[to_additive]
 theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
     (∏ k in Ico a b, f k) = f a * ∏ k in Ico (a + 1) b, f k :=
@@ -113,12 +77,6 @@ theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
 #align finset.prod_eq_prod_Ico_succ_bot Finset.prod_eq_prod_Ico_succ_bot
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
 
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 @[to_additive]
 theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     ((∏ i in Ico m n, f i) * ∏ i in Ico n k, f i) = ∏ i in Ico m k, f i :=
@@ -126,12 +84,6 @@ theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk
 #align finset.prod_Ico_consecutive Finset.prod_Ico_consecutive
 #align finset.sum_Ico_consecutive Finset.sum_Ico_consecutive
 
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 @[to_additive]
 theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     ((∏ i in Ioc m n, f i) * ∏ i in Ioc n k, f i) = ∏ i in Ioc m k, f i :=
@@ -142,12 +94,6 @@ theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk
 #align finset.prod_Ioc_consecutive Finset.prod_Ioc_consecutive
 #align finset.sum_Ioc_consecutive Finset.sum_Ioc_consecutive
 
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 @[to_additive]
 theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
     (∏ k in Ioc a (b + 1), f k) = (∏ k in Ioc a b, f k) * f (b + 1) := by
@@ -155,12 +101,6 @@ theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
 #align finset.prod_Ioc_succ_top Finset.prod_Ioc_succ_top
 #align finset.sum_Ioc_succ_top Finset.sum_Ioc_succ_top
 
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 @[to_additive]
 theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
     ((∏ k in range m, f k) * ∏ k in Ico m n, f k) = ∏ k in range n, f k :=
@@ -168,12 +108,6 @@ theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
 #align finset.prod_range_mul_prod_Ico Finset.prod_range_mul_prod_Ico
 #align finset.sum_range_add_sum_Ico Finset.sum_range_add_sum_Ico
 
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 @[to_additive]
 theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     (∏ k in Ico m n, f k) = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
@@ -181,12 +115,6 @@ theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n :
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
 #align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
 
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 @[to_additive]
 theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     (∏ k in Ico m n, f k) = (∏ k in range n, f k) / ∏ k in range m, f k := by
@@ -194,12 +122,6 @@ theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ
 #align finset.prod_Ico_eq_div Finset.prod_Ico_eq_div
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
 
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 @[to_additive]
 theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
     ((∏ k in range m, f k) / ∏ k in range n, f k) = ∏ k in (range m).filterₓ fun k => n ≤ k, f k :=
@@ -212,12 +134,6 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
 #align finset.prod_range_sub_prod_range Finset.prod_range_sub_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 
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 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
 theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
     (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
@@ -234,12 +150,6 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
     linarith
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
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 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     (∏ k in Ico m n, f k) = ∏ k in range (n - m), f (m + k) :=
@@ -251,12 +161,6 @@ theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
 #align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_range
 #align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
 
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 theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
     (∏ j in Ico k m, f (n - j)) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   by
@@ -272,12 +176,6 @@ theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1
   · simp [Ico_eq_empty_of_le, tsub_le_tsub_left, hkm]
 #align finset.prod_Ico_reflect Finset.prod_Ico_reflect
 
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 theorem sum_Ico_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
     (h : m ≤ n + 1) : (∑ j in Ico k m, f (n - j)) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
@@ -302,12 +200,6 @@ theorem sum_range_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (n :
 #align finset.sum_range_reflect Finset.sum_range_reflect
 -/
 
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 @[simp]
 theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n !
   | 0 => rfl
@@ -361,48 +253,24 @@ section Group
 
 variable [CommGroup β]
 
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 @[to_additive]
 theorem prod_range_succ_div_prod : ((∏ i in range (n + 1), f i) / ∏ i in range n, f i) = f n :=
   div_eq_iff_eq_mul'.mpr <| prod_range_succ f n
 #align finset.prod_range_succ_div_prod Finset.prod_range_succ_div_prod
 #align finset.sum_range_succ_sub_sum Finset.sum_range_succ_sub_sum
 
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 @[to_additive]
 theorem prod_range_succ_div_top : (∏ i in range (n + 1), f i) / f n = ∏ i in range n, f i :=
   div_eq_iff_eq_mul.mpr <| prod_range_succ f n
 #align finset.prod_range_succ_div_top Finset.prod_range_succ_div_top
 #align finset.sum_range_succ_sub_top Finset.sum_range_succ_sub_top
 
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 @[to_additive]
 theorem prod_Ico_div_bot (hmn : m < n) : (∏ i in Ico m n, f i) / f m = ∏ i in Ico (m + 1) n, f i :=
   div_eq_iff_eq_mul'.mpr <| prod_eq_prod_Ico_succ_bot hmn _
 #align finset.prod_Ico_div_bot Finset.prod_Ico_div_bot
 #align finset.sum_Ico_sub_bot Finset.sum_Ico_sub_bot
 
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 @[to_additive]
 theorem prod_Ico_succ_div_top (hmn : m ≤ n) :
     (∏ i in Ico m (n + 1), f i) / f n = ∏ i in Ico m n, f i :=
@@ -424,9 +292,6 @@ open Finset
 -- The partial sum of `g`, starting from zero
 local notation "G " n:80 => ∑ i in range n, g i
 
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-<too large>
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 /-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
 theorem sum_Ico_by_parts (hmn : m < n) :
     (∑ i in Ico m n, f i • g i) =
@@ -460,12 +325,6 @@ theorem sum_Ico_by_parts (hmn : m < n) :
 
 variable (n)
 
-/- warning: finset.sum_range_by_parts -> Finset.sum_range_by_parts is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finset.sum_range_by_parts Finset.sum_range_by_partsₓ'. -/
 /-- **Summation by parts** for ranges -/
 theorem sum_range_by_parts :
     (∑ i in range n, f i • g i) =

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

@@ -43,10 +43,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_add' Finset.prod_Ico_add'ₓ'. -/
 @[to_additive]
 theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
-    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x :=
-  by
-  rw [← map_add_right_Ico, Prod_map]
-  rfl
+    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x := by
+  rw [← map_add_right_Ico, Prod_map]; rfl
 #align finset.prod_Ico_add' Finset.prod_Ico_add'
 #align finset.sum_Ico_add' Finset.sum_Ico_add'
 

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

@@ -427,10 +427,7 @@ open Finset
 local notation "G " n:80 => ∑ i in range n, g i
 
 /- warning: finset.sum_Ico_by_parts -> Finset.sum_Ico_by_parts is a dubious translation:
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-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) {m : Nat} {n : Nat}, (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f m) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range m) (fun (i : Nat) => g i)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => g i))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align finset.sum_Ico_by_parts Finset.sum_Ico_by_partsₓ'. -/
 /-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
 theorem sum_Ico_by_parts (hmn : m < n) :

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

@@ -37,7 +37,7 @@ variable [CommMonoid β]
 
 /- warning: finset.prod_Ico_add' -> Finset.prod_Ico_add' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) x c))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) x c))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) x c))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
 Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_add' Finset.prod_Ico_add'ₓ'. -/
@@ -52,7 +52,7 @@ theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locall
 
 /- warning: finset.prod_Ico_add -> Finset.prod_Ico_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) c x))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) c x))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoid.{u2} β] [_inst_2 : OrderedCancelAddCommMonoid.{u1} α] [_inst_3 : ExistsAddOfLE.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2)))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)))] [_inst_4 : LocallyFiniteOrder.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2))] (f : α -> β) (a : α) (b : α) (c : α), Eq.{succ u2} β (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 a b) (fun (x : α) => f (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) c x))) (Finset.prod.{u2, u1} β α _inst_1 (Finset.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α _inst_2)) _inst_4 (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddRightCancelMonoid.toAddMonoid.{u1} α (AddCancelMonoid.toAddRightCancelMonoid.{u1} α (AddCancelCommMonoid.toAddCancelMonoid.{u1} α (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} α _inst_2))))))) b c)) (fun (x : α) => f x))
 Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_add Finset.prod_Ico_addₓ'. -/
@@ -214,7 +214,12 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
 #align finset.prod_range_sub_prod_range Finset.prod_range_sub_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 
-#print Finset.sum_Ico_Ico_comm /-
+/- warning: finset.sum_Ico_Ico_comm -> Finset.sum_Ico_Ico_comm is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} M] (a : Nat) (b : Nat) (f : Nat -> Nat -> M), Eq.{succ u1} M (Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder a b) (fun (i : Nat) => Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder i b) (fun (j : Nat) => f i j))) (Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder a b) (fun (j : Nat) => Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder a (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) j (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => f i j)))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} M] (a : Nat) (b : Nat) (f : Nat -> Nat -> M), Eq.{succ u1} M (Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring a b) (fun (i : Nat) => Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring i b) (fun (j : Nat) => f i j))) (Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring a b) (fun (j : Nat) => Finset.sum.{u1, 0} M Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring a (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) j (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => f i j)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_commₓ'. -/
 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
 theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
     (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
@@ -230,9 +235,13 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
       refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
     linarith
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
--/
 
-#print Finset.prod_Ico_eq_prod_range /-
+/- warning: finset.prod_Ico_eq_prod_range -> Finset.prod_Ico_eq_prod_range is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : CommMonoid.{u1} β] (f : Nat -> β) (m : Nat) (n : Nat), Eq.{succ u1} β (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (k : Nat) => f k)) (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.range (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n m)) (fun (k : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m k)))
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : CommMonoid.{u1} β] (f : Nat -> β) (m : Nat) (n : Nat), Eq.{succ u1} β (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (k : Nat) => f k)) (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.range (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n m)) (fun (k : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m k)))
+Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_rangeₓ'. -/
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     (∏ k in Ico m n, f k) = ∏ k in range (n - m), f (m + k) :=
@@ -243,9 +252,13 @@ theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     rw [Ico_eq_empty_of_le h, tsub_eq_zero_iff_le.mpr h, range_zero, prod_empty, prod_empty]
 #align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_range
 #align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
--/
 
-#print Finset.prod_Ico_reflect /-
+/- warning: finset.prod_Ico_reflect -> Finset.prod_Ico_reflect is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} [_inst_1 : CommMonoid.{u1} β] (f : Nat -> β) (k : Nat) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} β (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k m) (fun (j : Nat) => f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n j))) (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) m) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) k)) (fun (j : Nat) => f j)))
+but is expected to have type
+  forall {β : Type.{u1}} [_inst_1 : CommMonoid.{u1} β] (f : Nat -> β) (k : Nat) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u1} β (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k m) (fun (j : Nat) => f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n j))) (Finset.prod.{u1, 0} β Nat _inst_1 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) m) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) k)) (fun (j : Nat) => f j)))
+Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_reflect Finset.prod_Ico_reflectₓ'. -/
 theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
     (∏ j in Ico k m, f (n - j)) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   by
@@ -260,14 +273,17 @@ theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1
     rw [← tsub_tsub_cancel_of_le (this _ im), Hij, tsub_tsub_cancel_of_le (this _ jm)]
   · simp [Ico_eq_empty_of_le, tsub_le_tsub_left, hkm]
 #align finset.prod_Ico_reflect Finset.prod_Ico_reflect
--/
 
-#print Finset.sum_Ico_reflect /-
+/- warning: finset.sum_Ico_reflect -> Finset.sum_Ico_reflect is a dubious translation:
+lean 3 declaration is
+  forall {δ : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} δ] (f : Nat -> δ) (k : Nat) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} δ (Finset.sum.{u1, 0} δ Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder k m) (fun (j : Nat) => f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n j))) (Finset.sum.{u1, 0} δ Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) m) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) k)) (fun (j : Nat) => f j)))
+but is expected to have type
+  forall {δ : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} δ] (f : Nat -> δ) (k : Nat) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u1} δ (Finset.sum.{u1, 0} δ Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring k m) (fun (j : Nat) => f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n j))) (Finset.sum.{u1, 0} δ Nat _inst_2 (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) m) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) k)) (fun (j : Nat) => f j)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_Ico_reflect Finset.sum_Ico_reflectₓ'. -/
 theorem sum_Ico_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
     (h : m ≤ n + 1) : (∑ j in Ico k m, f (n - j)) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
 #align finset.sum_Ico_reflect Finset.sum_Ico_reflect
--/
 
 #print Finset.prod_range_reflect /-
 theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
@@ -288,7 +304,12 @@ theorem sum_range_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (n :
 #align finset.sum_range_reflect Finset.sum_range_reflect
 -/
 
-#print Finset.prod_Ico_id_eq_factorial /-
+/- warning: finset.prod_Ico_id_eq_factorial -> Finset.prod_Ico_id_eq_factorial is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Nat (Finset.prod.{0, 0} Nat Nat Nat.commMonoid (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (x : Nat) => x)) (Nat.factorial n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Nat (Finset.prod.{0, 0} Nat Nat Nat.commMonoid (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x : Nat) => x)) (Nat.factorial n)
+Case conversion may be inaccurate. Consider using '#align finset.prod_Ico_id_eq_factorial Finset.prod_Ico_id_eq_factorialₓ'. -/
 @[simp]
 theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n !
   | 0 => rfl
@@ -296,7 +317,6 @@ theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n
     rw [prod_Ico_succ_top <| Nat.succ_le_succ <| zero_le n, Nat.factorial_succ,
       prod_Ico_id_eq_factorial n, Nat.succ_eq_add_one, mul_comm]
 #align finset.prod_Ico_id_eq_factorial Finset.prod_Ico_id_eq_factorial
--/
 
 #print Finset.prod_range_add_one_eq_factorial /-
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -408,7 +408,7 @@ local notation "G " n:80 => ∑ i in range n, g i
 
 /- warning: finset.sum_Ico_by_parts -> Finset.sum_Ico_by_parts is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) {m : Nat} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt m n) -> (Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f m) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range m) (fun (i : Nat) => g i)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => g i))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) {m : Nat} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt m n) -> (Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f m) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range m) (fun (i : Nat) => g i)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => g i))))))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) {m : Nat} {n : Nat}, (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f m) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range m) (fun (i : Nat) => g i)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => g i))))))
 Case conversion may be inaccurate. Consider using '#align finset.sum_Ico_by_parts Finset.sum_Ico_by_partsₓ'. -/
@@ -447,7 +447,7 @@ variable (n)
 
 /- warning: finset.sum_range_by_parts -> Finset.sum_range_by_parts is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) (n : Nat), Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => g i)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) (n : Nat), Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toHasSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (i : Nat) => g i)))))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (f : Nat -> R) (g : Nat -> M) (n : Nat), Eq.{succ u2} M (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f i) (g i))) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (f (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range n) (fun (i : Nat) => g i))) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (f i)) (Finset.sum.{u2, 0} M Nat (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.range (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Nat) => g i)))))
 Case conversion may be inaccurate. Consider using '#align finset.sum_range_by_parts Finset.sum_range_by_partsₓ'. -/

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

@@ -316,7 +316,7 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
       rw [sum_range_reflect (fun i => i) n, mul_two]
     _ = ∑ i in range n, i + (n - 1 - i) := sum_add_distrib.symm
     _ = ∑ i in range n, n - 1 :=
-      sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi
+      (sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi)
     _ = n * (n - 1) := by rw [sum_const, card_range, Nat.nsmul_eq_mul]
     
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two

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

These · are scoping when there is a single active goal.

These were found using a modification of the linter at #12339.

@@ -295,7 +295,7 @@ lemma prod_range_diag_flip (n : ℕ) (f : ℕ → ℕ → M) :
       Nat.lt_succ_iff, le_add_iff_nonneg_right, Nat.zero_le, and_true, and_imp, imp_self,
       implies_true, Sigma.forall, forall_const, add_tsub_cancel_of_le, Sigma.mk.inj_iff,
       add_tsub_cancel_left, heq_eq_eq]
-  · exact fun a b han hba ↦ lt_of_le_of_lt hba han
+  exact fun a b han hba ↦ lt_of_le_of_lt hba han
 #align sum_range_diag_flip Finset.sum_range_diag_flip
 
 end Generic

and Data.Finset.LocallyFinite not depend on Finset.sum too

@@ -72,6 +72,22 @@ lemma prod_Iio_mul_eq_prod_Iic (a : α) : (∏ x in Iio a, f x) * f a = ∏ x in
 end LocallyFiniteOrderBot
 end PartialOrder
 
+section LinearOrder
+variable [Fintype α] [LinearOrder α] [LocallyFiniteOrderTop α] [LocallyFiniteOrderBot α]
+  [CommMonoid M]
+
+@[to_additive]
+lemma prod_prod_Ioi_mul_eq_prod_prod_off_diag (f : α → α → M) :
+    ∏ i, ∏ j in Ioi i, f j i * f i j = ∏ i, ∏ j in {i}ᶜ, f j i := by
+  simp_rw [← Ioi_disjUnion_Iio, prod_disjUnion, prod_mul_distrib]
+  congr 1
+  rw [prod_sigma', prod_sigma']
+  refine' prod_nbij' (fun i ↦ ⟨i.2, i.1⟩) (fun i ↦ ⟨i.2, i.1⟩) _ _ _ _ _ <;> simp
+#align finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag
+#align finset.sum_sum_Ioi_add_eq_sum_sum_off_diag Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag
+
+end LinearOrder
+
 section Generic
 variable [CommMonoid M] {s₂ s₁ s : Finset α} {a : α} {g f : α → M}
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -287,7 +287,6 @@ end Generic
 section Nat
 
 variable {M : Type*}
-
 variable (f g : ℕ → M) {m n : ℕ}
 
 section Group

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

@@ -173,7 +173,7 @@ theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
   simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
   rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
   refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
-  linarith
+  omega
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
 /-- The two ways of summing over `(i, j)` in the range `a ≤ i < j < b` are equal. -/
@@ -186,7 +186,7 @@ theorem sum_Ico_Ico_comm' {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
   simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
   rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
   refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
-  linarith
+  omega
 
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → M) (m n : ℕ) :

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

@@ -163,7 +163,7 @@ theorem prod_range_div_prod_range {α : Type*} [CommGroup α] {f : ℕ → α} {
 #align finset.prod_range_sub_prod_range Finset.prod_range_div_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 
-/-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
+/-- The two ways of summing over `(i, j)` in the range `a ≤ i ≤ j < b` are equal. -/
 theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
     (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
       ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a (j + 1), f i j := by
@@ -176,6 +176,18 @@ theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
   linarith
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
+/-- The two ways of summing over `(i, j)` in the range `a ≤ i < j < b` are equal. -/
+theorem sum_Ico_Ico_comm' {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
+    (∑ i in Finset.Ico a b, ∑ j in Finset.Ico (i + 1) b, f i j) =
+      ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a j, f i j := by
+  rw [Finset.sum_sigma', Finset.sum_sigma']
+  refine' sum_nbij' (fun x ↦ ⟨x.2, x.1⟩) (fun x ↦ ⟨x.2, x.1⟩) _ _ (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
+    (fun _ _ ↦ rfl) <;>
+  simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
+  rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
+  refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
+  linarith
+
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → M) (m n : ℕ) :
     ∏ k in Ico m n, f k = ∏ k in range (n - m), f (m + k) := by

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

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
 import Mathlib.Algebra.BigOperators.Basic
-import Mathlib.Algebra.Module.Basic
 import Mathlib.Data.Nat.Interval
 import Mathlib.Tactic.Linarith
 
@@ -258,6 +257,19 @@ theorem sum_range_id (n : ℕ) : ∑ i in range n, i = n * (n - 1) / 2 := by
 
 end GaussSum
 
+@[to_additive]
+lemma prod_range_diag_flip (n : ℕ) (f : ℕ → ℕ → M) :
+    (∏ m in range n, ∏ k in range (m + 1), f k (m - k)) =
+      ∏ m in range n, ∏ k in range (n - m), f m k := by
+  rw [prod_sigma', prod_sigma']
+  refine prod_nbij' (fun a ↦ ⟨a.2, a.1 - a.2⟩) (fun a ↦ ⟨a.1 + a.2, a.1⟩) ?_ ?_ ?_ ?_ ?_ <;>
+    simp (config := { contextual := true }) only [mem_sigma, mem_range, lt_tsub_iff_left,
+      Nat.lt_succ_iff, le_add_iff_nonneg_right, Nat.zero_le, and_true, and_imp, imp_self,
+      implies_true, Sigma.forall, forall_const, add_tsub_cancel_of_le, Sigma.mk.inj_iff,
+      add_tsub_cancel_left, heq_eq_eq]
+  · exact fun a b han hba ↦ lt_of_le_of_lt hba han
+#align sum_range_diag_flip Finset.sum_range_diag_flip
+
 end Generic
 
 section Nat
@@ -298,68 +310,4 @@ theorem prod_Ico_succ_div_top (hmn : m ≤ n) :
 end Group
 
 end Nat
-
-section Module
-
-variable {R M : Type*} [Ring R] [AddCommGroup M] [Module R M] (f : ℕ → R) (g : ℕ → M) {m n : ℕ}
-
-open Finset
-
--- The partial sum of `g`, starting from zero
-local notation "G " n:80 => ∑ i in range n, g i
-
-/-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
-theorem sum_Ico_by_parts (hmn : m < n) :
-    ∑ i in Ico m n, f i • g i =
-      f (n - 1) • G n - f m • G m - ∑ i in Ico m (n - 1), (f (i + 1) - f i) • G (i + 1) := by
-  have h₁ : (∑ i in Ico (m + 1) n, f i • G i) = ∑ i in Ico m (n - 1), f (i + 1) • G (i + 1) := by
-    rw [← Nat.sub_add_cancel (Nat.one_le_of_lt hmn), ← sum_Ico_add']
-    simp only [ge_iff_le, tsub_le_iff_right, add_le_iff_nonpos_left, nonpos_iff_eq_zero,
-      tsub_eq_zero_iff_le, add_tsub_cancel_right]
-  have h₂ :
-    (∑ i in Ico (m + 1) n, f i • G (i + 1)) =
-      (∑ i in Ico m (n - 1), f i • G (i + 1)) + f (n - 1) • G n - f m • G (m + 1) := by
-    rw [← sum_Ico_sub_bot _ hmn, ← sum_Ico_succ_sub_top _ (Nat.le_sub_one_of_lt hmn),
-      Nat.sub_add_cancel (pos_of_gt hmn), sub_add_cancel]
-  rw [sum_eq_sum_Ico_succ_bot hmn]
-  -- porting note: the following used to be done with `conv`
-  have h₃: (Finset.sum (Ico (m + 1) n) fun i => f i • g i) =
-             (Finset.sum (Ico (m + 1) n) fun i =>
-                f i • ((Finset.sum (Finset.range (i + 1)) g) -
-                        (Finset.sum (Finset.range i) g))) := by
-    congr; funext; rw [← sum_range_succ_sub_sum g]
-  rw [h₃]
-  simp_rw [smul_sub, sum_sub_distrib, h₂, h₁]
-  -- porting note: the following used to be done with `conv`
-  have h₄ : ((((Finset.sum (Ico m (n - 1)) fun i => f i • Finset.sum (range (i + 1)) fun i => g i) +
-      f (n - 1) • Finset.sum (range n) fun i => g i) -
-      f m • Finset.sum (range (m + 1)) fun i => g i) -
-      Finset.sum (Ico m (n - 1)) fun i => f (i + 1) • Finset.sum (range (i + 1)) fun i => g i) =
-      f (n - 1) • (range n).sum g - f m • (range (m + 1)).sum g +
-      Finset.sum (Ico m (n - 1)) (fun i => f i • (range (i + 1)).sum g -
-      f (i + 1) • (range (i + 1)).sum g) := by
-    rw [← add_sub, add_comm, ← add_sub, ← sum_sub_distrib]
-  rw [h₄]
-  have : ∀ i, f i • G (i + 1) - f (i + 1) • G (i + 1) = -((f (i + 1) - f i) • G (i + 1)) := by
-    intro i
-    rw [sub_smul]
-    abel
-  simp_rw [this, sum_neg_distrib, sum_range_succ, smul_add]
-  abel
-#align finset.sum_Ico_by_parts Finset.sum_Ico_by_parts
-
-variable (n)
-
-/-- **Summation by parts** for ranges -/
-theorem sum_range_by_parts :
-    ∑ i in range n, f i • g i =
-      f (n - 1) • G n - ∑ i in range (n - 1), (f (i + 1) - f i) • G (i + 1) := by
-  by_cases hn : n = 0
-  · simp [hn]
-  · rw [range_eq_Ico, sum_Ico_by_parts f g (Nat.pos_of_ne_zero hn), sum_range_zero, smul_zero,
-      sub_zero, range_eq_Ico]
-#align finset.sum_range_by_parts Finset.sum_range_by_parts
-
-end Module
-
 end Finset

From LeanCamCombi

@@ -13,26 +13,72 @@ import Mathlib.Tactic.Linarith
 /-!
 # Results about big operators over intervals
 
-We prove results about big operators over intervals (mostly the `ℕ`-valued `Ico m n`).
+We prove results about big operators over intervals.
 -/
 
-
-universe u v w
-
-open BigOperators
 open Nat
+open scoped BigOperators
+
+variable {α M : Type*}
 
 namespace Finset
+section PartialOrder
+variable [PartialOrder α] [CommMonoid M] {f : α → M} {a b : α}
 
-section Generic
+section LocallyFiniteOrder
+variable [LocallyFiniteOrder α]
+
+@[to_additive]
+lemma mul_prod_Ico_eq_prod_Icc (h : a ≤ b) : f b * ∏ x in Ico a b, f x = ∏ x in Icc a b, f x := by
+  rw [Icc_eq_cons_Ico h, prod_cons]
+
+@[to_additive]
+lemma prod_Ico_mul_eq_prod_Icc (h : a ≤ b) : (∏ x in Ico a b, f x) * f b = ∏ x in Icc a b, f x := by
+  rw [mul_comm, mul_prod_Ico_eq_prod_Icc h]
+
+@[to_additive]
+lemma mul_prod_Ioc_eq_prod_Icc (h : a ≤ b) : f a * ∏ x in Ioc a b, f x = ∏ x in Icc a b, f x := by
+  rw [Icc_eq_cons_Ioc h, prod_cons]
+
+@[to_additive]
+lemma prod_Ioc_mul_eq_prod_Icc (h : a ≤ b) : (∏ x in Ioc a b, f x) * f a = ∏ x in Icc a b, f x := by
+  rw [mul_comm, mul_prod_Ioc_eq_prod_Icc h]
+
+end LocallyFiniteOrder
 
-variable {α : Type u} {β : Type v} {γ : Type w} {s₂ s₁ s : Finset α} {a : α} {g f : α → β}
+section LocallyFiniteOrderTop
+variable [LocallyFiniteOrderTop α]
 
-variable [CommMonoid β]
+@[to_additive]
+lemma mul_prod_Ioi_eq_prod_Ici (a : α) : f a * ∏ x in Ioi a, f x = ∏ x in Ici a, f x := by
+  rw [Ici_eq_cons_Ioi, prod_cons]
+
+@[to_additive]
+lemma prod_Ioi_mul_eq_prod_Ici (a : α) : (∏ x in Ioi a, f x) * f a = ∏ x in Ici a, f x := by
+  rw [mul_comm, mul_prod_Ioi_eq_prod_Ici]
+
+end LocallyFiniteOrderTop
+
+section LocallyFiniteOrderBot
+variable [LocallyFiniteOrderBot α]
+
+@[to_additive]
+lemma mul_prod_Iio_eq_prod_Iic (a : α) : f a * ∏ x in Iio a, f x = ∏ x in Iic a, f x := by
+  rw [Iic_eq_cons_Iio, prod_cons]
+
+@[to_additive]
+lemma prod_Iio_mul_eq_prod_Iic (a : α) : (∏ x in Iio a, f x) * f a = ∏ x in Iic a, f x := by
+  rw [mul_comm, mul_prod_Iio_eq_prod_Iic]
+
+end LocallyFiniteOrderBot
+end PartialOrder
+
+section Generic
+variable [CommMonoid M] {s₂ s₁ s : Finset α} {a : α} {g f : α → M}
 
 @[to_additive]
 theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
-    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x := by
+    (f : α → M) (a b c : α) : (∏ x in Ico a b, f (x + c)) = ∏ x in Ico (a + c) (b + c), f x := by
   rw [← map_add_right_Ico, prod_map]
   rfl
 #align finset.prod_Ico_add' Finset.prod_Ico_add'
@@ -40,21 +86,21 @@ theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locall
 
 @[to_additive]
 theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
-    (f : α → β) (a b c : α) : (∏ x in Ico a b, f (c + x)) = ∏ x in Ico (a + c) (b + c), f x := by
+    (f : α → M) (a b c : α) : (∏ x in Ico a b, f (c + x)) = ∏ x in Ico (a + c) (b + c), f x := by
   convert prod_Ico_add' f a b c using 2
   rw [add_comm]
 #align finset.prod_Ico_add Finset.prod_Ico_add
 #align finset.sum_Ico_add Finset.sum_Ico_add
 
 @[to_additive]
-theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
+theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → M) :
     (∏ k in Ico a (b + 1), f k) = (∏ k in Ico a b, f k) * f b := by
   rw [Nat.Ico_succ_right_eq_insert_Ico hab, prod_insert right_not_mem_Ico, mul_comm]
 #align finset.prod_Ico_succ_top Finset.prod_Ico_succ_top
 #align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
 @[to_additive]
-theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
+theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → M) :
     ∏ k in Ico a b, f k = f a * ∏ k in Ico (a + 1) b, f k := by
   have ha : a ∉ Ico (a + 1) b := by simp
   rw [← prod_insert ha, Nat.Ico_insert_succ_left hab]
@@ -62,14 +108,14 @@ theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
 #align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
 
 @[to_additive]
-theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
+theorem prod_Ico_consecutive (f : ℕ → M) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     ((∏ i in Ico m n, f i) * ∏ i in Ico n k, f i) = ∏ i in Ico m k, f i :=
   Ico_union_Ico_eq_Ico hmn hnk ▸ Eq.symm (prod_union (Ico_disjoint_Ico_consecutive m n k))
 #align finset.prod_Ico_consecutive Finset.prod_Ico_consecutive
 #align finset.sum_Ico_consecutive Finset.sum_Ico_consecutive
 
 @[to_additive]
-theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
+theorem prod_Ioc_consecutive (f : ℕ → M) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :
     ((∏ i in Ioc m n, f i) * ∏ i in Ioc n k, f i) = ∏ i in Ioc m k, f i := by
   rw [← Ioc_union_Ioc_eq_Ioc hmn hnk, prod_union]
   apply disjoint_left.2 fun x hx h'x => _
@@ -79,14 +125,14 @@ theorem prod_Ioc_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk
 #align finset.sum_Ioc_consecutive Finset.sum_Ioc_consecutive
 
 @[to_additive]
-theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
+theorem prod_Ioc_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → M) :
     (∏ k in Ioc a (b + 1), f k) = (∏ k in Ioc a b, f k) * f (b + 1) := by
   rw [← prod_Ioc_consecutive _ hab (Nat.le_succ b), Nat.Ioc_succ_singleton, prod_singleton]
 #align finset.prod_Ioc_succ_top Finset.prod_Ioc_succ_top
 #align finset.sum_Ioc_succ_top Finset.sum_Ioc_succ_top
 
 @[to_additive]
-theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
+theorem prod_range_mul_prod_Ico (f : ℕ → M) {m n : ℕ} (h : m ≤ n) :
     ((∏ k in range m, f k) * ∏ k in Ico m n, f k) = ∏ k in range n, f k :=
   Nat.Ico_zero_eq_range ▸ Nat.Ico_zero_eq_range ▸ prod_Ico_consecutive f m.zero_le h
 #align finset.prod_range_mul_prod_Ico Finset.prod_range_mul_prod_Ico
@@ -132,7 +178,7 @@ theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
 @[to_additive]
-theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
+theorem prod_Ico_eq_prod_range (f : ℕ → M) (m n : ℕ) :
     ∏ k in Ico m n, f k = ∏ k in range (n - m), f (m + k) := by
   by_cases h : m ≤ n
   · rw [← Nat.Ico_zero_eq_range, prod_Ico_add, zero_add, tsub_add_cancel_of_le h]
@@ -141,7 +187,7 @@ theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
 #align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_range
 #align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
 
-theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
+theorem prod_Ico_reflect (f : ℕ → M) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
     (∏ j in Ico k m, f (n - j)) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j := by
   have : ∀ i < m, i ≤ n := by
     intro i hi
@@ -164,7 +210,7 @@ theorem sum_Ico_reflect {δ : Type*} [AddCommMonoid δ] (f : ℕ → δ) (k : 
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
 #align finset.sum_Ico_reflect Finset.sum_Ico_reflect
 
-theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
+theorem prod_range_reflect (f : ℕ → M) (n : ℕ) :
     (∏ j in range n, f (n - 1 - j)) = ∏ j in range n, f j := by
   cases n
   · simp
@@ -216,13 +262,13 @@ end Generic
 
 section Nat
 
-variable {β : Type*}
+variable {M : Type*}
 
-variable (f g : ℕ → β) {m n : ℕ}
+variable (f g : ℕ → M) {m n : ℕ}
 
 section Group
 
-variable [CommGroup β]
+variable [CommGroup M]
 
 @[to_additive]
 theorem prod_range_succ_div_prod : ((∏ i in range (n + 1), f i) / ∏ i in range n, f i) = f n :=

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

@@ -123,10 +123,8 @@ theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
     (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
       ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a (j + 1), f i j := by
   rw [Finset.sum_sigma', Finset.sum_sigma']
-  refine'
-    Finset.sum_bij' (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (fun _ _ => rfl)
-      (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (by (rintro ⟨⟩ _; rfl))
-      (by (rintro ⟨⟩ _; rfl)) <;>
+  refine' sum_nbij' (fun x ↦ ⟨x.2, x.1⟩) (fun x ↦ ⟨x.2, x.1⟩) _ _ (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
+    (fun _ _ ↦ rfl) <;>
   simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
   rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
   refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>

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

@@ -294,7 +294,7 @@ theorem sum_Ico_by_parts (hmn : m < n) :
       f (n - 1) • (range n).sum g - f m • (range (m + 1)).sum g +
       Finset.sum (Ico m (n - 1)) (fun i => f i • (range (i + 1)).sum g -
       f (i + 1) • (range (i + 1)).sum g) := by
-    rw [← add_sub, add_comm, ←add_sub, ← sum_sub_distrib]
+    rw [← add_sub, add_comm, ← add_sub, ← sum_sub_distrib]
   rw [h₄]
   have : ∀ i, f i • G (i + 1) - f (i + 1) • G (i + 1) = -((f (i + 1) - f i) • G (i + 1)) := by
     intro i

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -199,8 +199,8 @@ section GaussSum
 /-- Gauss' summation formula -/
 theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1) :=
   calc
-    (∑ i in range n, i) * 2 = (∑ i in range n, i) + ∑ i in range n, (n - 1 - i) :=
-    by rw [sum_range_reflect (fun i => i) n, mul_two]
+    (∑ i in range n, i) * 2 = (∑ i in range n, i) + ∑ i in range n, (n - 1 - i) := by
+      rw [sum_range_reflect (fun i => i) n, mul_two]
     _ = ∑ i in range n, (i + (n - 1 - i)) := sum_add_distrib.symm
     _ = ∑ i in range n, (n - 1) :=
       sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_sub_one_of_lt <| mem_range.1 hi

@@ -203,7 +203,7 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
     by rw [sum_range_reflect (fun i => i) n, mul_two]
     _ = ∑ i in range n, (i + (n - 1 - i)) := sum_add_distrib.symm
     _ = ∑ i in range n, (n - 1) :=
-      sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi
+      sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_sub_one_of_lt <| mem_range.1 hi
     _ = n * (n - 1) := by rw [sum_const, card_range, Nat.nsmul_eq_mul]
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two
 
@@ -275,7 +275,7 @@ theorem sum_Ico_by_parts (hmn : m < n) :
   have h₂ :
     (∑ i in Ico (m + 1) n, f i • G (i + 1)) =
       (∑ i in Ico m (n - 1), f i • G (i + 1)) + f (n - 1) • G n - f m • G (m + 1) := by
-    rw [← sum_Ico_sub_bot _ hmn, ← sum_Ico_succ_sub_top _ (Nat.le_pred_of_lt hmn),
+    rw [← sum_Ico_sub_bot _ hmn, ← sum_Ico_succ_sub_top _ (Nat.le_sub_one_of_lt hmn),
       Nat.sub_add_cancel (pos_of_gt hmn), sub_add_cancel]
   rw [sum_eq_sum_Ico_succ_bot hmn]
   -- porting note: the following used to be done with `conv`

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

@@ -191,7 +191,7 @@ theorem prod_Ico_id_eq_factorial : ∀ n : ℕ, (∏ x in Ico 1 (n + 1), x) = n
 @[simp]
 theorem prod_range_add_one_eq_factorial : ∀ n : ℕ, (∏ x in range n, (x + 1)) = n !
   | 0 => rfl
-  | n + 1 => by simp [Finset.range_succ, prod_range_add_one_eq_factorial n]
+  | n + 1 => by simp [factorial, Finset.range_succ, prod_range_add_one_eq_factorial n]
 #align finset.prod_range_add_one_eq_factorial Finset.prod_range_add_one_eq_factorial
 
 section GaussSum

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

This has nice performance benefits.

@@ -93,21 +93,21 @@ theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
 #align finset.sum_range_add_sum_Ico Finset.sum_range_add_sum_Ico
 
 @[to_additive]
-theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
+theorem prod_Ico_eq_mul_inv {δ : Type*} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     ∏ k in Ico m n, f k = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
   eq_mul_inv_iff_mul_eq.2 <| by (rw [mul_comm]; exact prod_range_mul_prod_Ico f h)
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
 #align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
 
 @[to_additive]
-theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
+theorem prod_Ico_eq_div {δ : Type*} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
     ∏ k in Ico m n, f k = (∏ k in range n, f k) / ∏ k in range m, f k := by
   simpa only [div_eq_mul_inv] using prod_Ico_eq_mul_inv f h
 #align finset.prod_Ico_eq_div Finset.prod_Ico_eq_div
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
 
 @[to_additive]
-theorem prod_range_div_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
+theorem prod_range_div_prod_range {α : Type*} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
     ((∏ k in range m, f k) / ∏ k in range n, f k) =
     ∏ k in (range m).filter fun k => n ≤ k, f k := by
   rw [← prod_Ico_eq_div f hnm]
@@ -119,7 +119,7 @@ theorem prod_range_div_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 
 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/
-theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
+theorem sum_Ico_Ico_comm {M : Type*} [AddCommMonoid M] (a b : ℕ) (f : ℕ → ℕ → M) :
     (∑ i in Finset.Ico a b, ∑ j in Finset.Ico i b, f i j) =
       ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a (j + 1), f i j := by
   rw [Finset.sum_sigma', Finset.sum_sigma']
@@ -161,7 +161,7 @@ theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1
       this]
 #align finset.prod_Ico_reflect Finset.prod_Ico_reflect
 
-theorem sum_Ico_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
+theorem sum_Ico_reflect {δ : Type*} [AddCommMonoid δ] (f : ℕ → δ) (k : ℕ) {m n : ℕ}
     (h : m ≤ n + 1) : (∑ j in Ico k m, f (n - j)) = ∑ j in Ico (n + 1 - m) (n + 1 - k), f j :=
   @prod_Ico_reflect (Multiplicative δ) _ f k m n h
 #align finset.sum_Ico_reflect Finset.sum_Ico_reflect
@@ -175,7 +175,7 @@ theorem prod_range_reflect (f : ℕ → β) (n : ℕ) :
     simp
 #align finset.prod_range_reflect Finset.prod_range_reflect
 
-theorem sum_range_reflect {δ : Type _} [AddCommMonoid δ] (f : ℕ → δ) (n : ℕ) :
+theorem sum_range_reflect {δ : Type*} [AddCommMonoid δ] (f : ℕ → δ) (n : ℕ) :
     (∑ j in range n, f (n - 1 - j)) = ∑ j in range n, f j :=
   @prod_range_reflect (Multiplicative δ) _ f n
 #align finset.sum_range_reflect Finset.sum_range_reflect
@@ -218,7 +218,7 @@ end Generic
 
 section Nat
 
-variable {β : Type _}
+variable {β : Type*}
 
 variable (f g : ℕ → β) {m n : ℕ}
 
@@ -257,7 +257,7 @@ end Nat
 
 section Module
 
-variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] (f : ℕ → R) (g : ℕ → M) {m n : ℕ}
+variable {R M : Type*} [Ring R] [AddCommGroup M] [Module R M] (f : ℕ → R) (g : ℕ → M) {m n : ℕ}
 
 open Finset
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module algebra.big_operators.intervals
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Basic
 import Mathlib.Algebra.Module.Basic
 import Mathlib.Data.Nat.Interval
 import Mathlib.Tactic.Linarith
 
+#align_import algebra.big_operators.intervals from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
 /-!
 # Results about big operators over intervals
 

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

@@ -58,7 +58,7 @@ theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
 
 @[to_additive]
 theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
-    (∏ k in Ico a b, f k) = f a * ∏ k in Ico (a + 1) b, f k := by
+    ∏ k in Ico a b, f k = f a * ∏ k in Ico (a + 1) b, f k := by
   have ha : a ∉ Ico (a + 1) b := by simp
   rw [← prod_insert ha, Nat.Ico_insert_succ_left hab]
 #align finset.prod_eq_prod_Ico_succ_bot Finset.prod_eq_prod_Ico_succ_bot
@@ -97,14 +97,14 @@ theorem prod_range_mul_prod_Ico (f : ℕ → β) {m n : ℕ} (h : m ≤ n) :
 
 @[to_additive]
 theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
-    (∏ k in Ico m n, f k) = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
+    ∏ k in Ico m n, f k = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
   eq_mul_inv_iff_mul_eq.2 <| by (rw [mul_comm]; exact prod_range_mul_prod_Ico f h)
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
 #align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
 
 @[to_additive]
 theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
-    (∏ k in Ico m n, f k) = (∏ k in range n, f k) / ∏ k in range m, f k := by
+    ∏ k in Ico m n, f k = (∏ k in range n, f k) / ∏ k in range m, f k := by
   simpa only [div_eq_mul_inv] using prod_Ico_eq_mul_inv f h
 #align finset.prod_Ico_eq_div Finset.prod_Ico_eq_div
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
@@ -138,7 +138,7 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
 
 @[to_additive]
 theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
-    (∏ k in Ico m n, f k) = ∏ k in range (n - m), f (m + k) := by
+    ∏ k in Ico m n, f k = ∏ k in range (n - m), f (m + k) := by
   by_cases h : m ≤ n
   · rw [← Nat.Ico_zero_eq_range, prod_Ico_add, zero_add, tsub_add_cancel_of_le h]
   · replace h : n ≤ m := le_of_not_ge h
@@ -211,7 +211,7 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two
 
 /-- Gauss' summation formula -/
-theorem sum_range_id (n : ℕ) : (∑ i in range n, i) = n * (n - 1) / 2 := by
+theorem sum_range_id (n : ℕ) : ∑ i in range n, i = n * (n - 1) / 2 := by
   rw [← sum_range_id_mul_two n, Nat.mul_div_cancel _ zero_lt_two]
 #align finset.sum_range_id Finset.sum_range_id
 
@@ -269,7 +269,7 @@ local notation "G " n:80 => ∑ i in range n, g i
 
 /-- **Summation by parts**, also known as **Abel's lemma** or an **Abel transformation** -/
 theorem sum_Ico_by_parts (hmn : m < n) :
-    (∑ i in Ico m n, f i • g i) =
+    ∑ i in Ico m n, f i • g i =
       f (n - 1) • G n - f m • G m - ∑ i in Ico m (n - 1), (f (i + 1) - f i) • G (i + 1) := by
   have h₁ : (∑ i in Ico (m + 1) n, f i • G i) = ∑ i in Ico m (n - 1), f (i + 1) • G (i + 1) := by
     rw [← Nat.sub_add_cancel (Nat.one_le_of_lt hmn), ← sum_Ico_add']
@@ -311,7 +311,7 @@ variable (n)
 
 /-- **Summation by parts** for ranges -/
 theorem sum_range_by_parts :
-    (∑ i in range n, f i • g i) =
+    ∑ i in range n, f i • g i =
       f (n - 1) • G n - ∑ i in range (n - 1), (f (i + 1) - f i) • G (i + 1) := by
   by_cases hn : n = 0
   · simp [hn]

Introduced while making it multiplicative in leanprover-community/mathlib#13359

@@ -110,7 +110,7 @@ theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ
 #align finset.sum_Ico_eq_sub Finset.sum_Ico_eq_sub
 
 @[to_additive]
-theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
+theorem prod_range_div_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
     ((∏ k in range m, f k) / ∏ k in range n, f k) =
     ∏ k in (range m).filter fun k => n ≤ k, f k := by
   rw [← prod_Ico_eq_div f hnm]
@@ -118,7 +118,7 @@ theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α}
   apply Finset.ext
   simp only [mem_Ico, mem_filter, mem_range, *]
   tauto
-#align finset.prod_range_sub_prod_range Finset.prod_range_sub_prod_range
+#align finset.prod_range_sub_prod_range Finset.prod_range_div_prod_range
 #align finset.sum_range_sub_sum_range Finset.sum_range_sub_sum_range
 
 /-- The two ways of summing over `(i,j)` in the range `a<=i<=j<b` are equal. -/

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -111,8 +111,8 @@ theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ
 
 @[to_additive]
 theorem prod_range_sub_prod_range {α : Type _} [CommGroup α] {f : ℕ → α} {n m : ℕ} (hnm : n ≤ m) :
-    ((∏ k in range m, f k) / ∏ k in range n, f k) = ∏ k in (range m).filter fun k => n ≤ k, f k :=
-  by
+    ((∏ k in range m, f k) / ∏ k in range n, f k) =
+    ∏ k in (range m).filter fun k => n ≤ k, f k := by
   rw [← prod_Ico_eq_div f hnm]
   congr
   apply Finset.ext

This introduces a tactic congr! that is an analogue to mathlib 3's congr'. It is a more insistent version of congr that makes use of more congruence lemmas (including user congruence lemmas), propext, funext, and Subsingleton instances. It also has a feature to lift reflexive relations to equalities. Along with funext, the tactic does intros, allowing congr! to get access to function bodies; the introduced variables can be named using rename_i if needed.

This also modifies convert to use congr! rather than congr, which makes it work more like the mathlib3 version of the tactic.

@@ -44,8 +44,8 @@ theorem prod_Ico_add' [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locall
 @[to_additive]
 theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [LocallyFiniteOrder α]
     (f : α → β) (a b c : α) : (∏ x in Ico a b, f (c + x)) = ∏ x in Ico (a + c) (b + c), f x := by
-  convert prod_Ico_add' f a b c
-  simp_rw [add_comm]
+  convert prod_Ico_add' f a b c using 2
+  rw [add_comm]
 #align finset.prod_Ico_add Finset.prod_Ico_add
 #align finset.sum_Ico_add Finset.sum_Ico_add
 

• Force the user to specify whether the additive declaration already exists.
• Will raise a linter error if the user specified it wrongly
• Requested on Zulip

@@ -49,28 +49,20 @@ theorem prod_Ico_add [OrderedCancelAddCommMonoid α] [ExistsAddOfLE α] [Locally
 #align finset.prod_Ico_add Finset.prod_Ico_add
 #align finset.sum_Ico_add Finset.sum_Ico_add
 
-theorem sum_Ico_succ_top {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a ≤ b) (f : ℕ → δ) :
-    (∑ k in Ico a (b + 1), f k) = (∑ k in Ico a b, f k) + f b := by
-  rw [Nat.Ico_succ_right_eq_insert_Ico hab, sum_insert right_not_mem_Ico, add_comm]
-#align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
-
 @[to_additive]
 theorem prod_Ico_succ_top {a b : ℕ} (hab : a ≤ b) (f : ℕ → β) :
-    (∏ k in Ico a (b + 1), f k) = (∏ k in Ico a b, f k) * f b :=
-  @sum_Ico_succ_top (Additive β) _ _ _ hab _
+    (∏ k in Ico a (b + 1), f k) = (∏ k in Ico a b, f k) * f b := by
+  rw [Nat.Ico_succ_right_eq_insert_Ico hab, prod_insert right_not_mem_Ico, mul_comm]
 #align finset.prod_Ico_succ_top Finset.prod_Ico_succ_top
-
-theorem sum_eq_sum_Ico_succ_bot {δ : Type _} [AddCommMonoid δ] {a b : ℕ} (hab : a < b) (f : ℕ → δ) :
-    (∑ k in Ico a b, f k) = f a + ∑ k in Ico (a + 1) b, f k := by
-  have ha : a ∉ Ico (a + 1) b := by simp
-  rw [← sum_insert ha, Nat.Ico_insert_succ_left hab]
-#align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
+#align finset.sum_Ico_succ_top Finset.sum_Ico_succ_top
 
 @[to_additive]
 theorem prod_eq_prod_Ico_succ_bot {a b : ℕ} (hab : a < b) (f : ℕ → β) :
-    (∏ k in Ico a b, f k) = f a * ∏ k in Ico (a + 1) b, f k :=
-  @sum_eq_sum_Ico_succ_bot (Additive β) _ _ _ hab _
+    (∏ k in Ico a b, f k) = f a * ∏ k in Ico (a + 1) b, f k := by
+  have ha : a ∉ Ico (a + 1) b := by simp
+  rw [← prod_insert ha, Nat.Ico_insert_succ_left hab]
 #align finset.prod_eq_prod_Ico_succ_bot Finset.prod_eq_prod_Ico_succ_bot
+#align finset.sum_eq_sum_Ico_succ_bot Finset.sum_eq_sum_Ico_succ_bot
 
 @[to_additive]
 theorem prod_Ico_consecutive (f : ℕ → β) {m n k : ℕ} (hmn : m ≤ n) (hnk : n ≤ k) :

@@ -135,13 +135,13 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
       ∑ j in Finset.Ico a b, ∑ i in Finset.Ico a (j + 1), f i j := by
   rw [Finset.sum_sigma', Finset.sum_sigma']
   refine'
-            Finset.sum_bij' (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (fun _ _ => rfl)
-              (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (by (rintro ⟨⟩ _; rfl))
-              (by (rintro ⟨⟩ _; rfl)) <;>
-          simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
-        rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
-      refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
-    linarith
+    Finset.sum_bij' (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (fun _ _ => rfl)
+      (fun (x : Σ _ : ℕ, ℕ) _ => (⟨x.2, x.1⟩ : Σ _ : ℕ, ℕ)) _ (by (rintro ⟨⟩ _; rfl))
+      (by (rintro ⟨⟩ _; rfl)) <;>
+  simp only [Finset.mem_Ico, Sigma.forall, Finset.mem_sigma] <;>
+  rintro a b ⟨⟨h₁, h₂⟩, ⟨h₃, h₄⟩⟩ <;>
+  refine' ⟨⟨_, _⟩, ⟨_, _⟩⟩ <;>
+  linarith
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
 @[to_additive]
@@ -216,12 +216,11 @@ theorem sum_range_id_mul_two (n : ℕ) : (∑ i in range n, i) * 2 = n * (n - 1)
     _ = ∑ i in range n, (n - 1) :=
       sum_congr rfl fun i hi => add_tsub_cancel_of_le <| Nat.le_pred_of_lt <| mem_range.1 hi
     _ = n * (n - 1) := by rw [sum_const, card_range, Nat.nsmul_eq_mul]
-
 #align finset.sum_range_id_mul_two Finset.sum_range_id_mul_two
 
 /-- Gauss' summation formula -/
 theorem sum_range_id (n : ℕ) : (∑ i in range n, i) = n * (n - 1) / 2 := by
-  (rw [← sum_range_id_mul_two n, Nat.mul_div_cancel]; exact by decide)
+  rw [← sum_range_id_mul_two n, Nat.mul_div_cancel _ zero_lt_two]
 #align finset.sum_range_id Finset.sum_range_id
 
 end GaussSum
@@ -273,7 +272,6 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] (f : ℕ → R) (
 
 open Finset
 
--- mathport name: «exprG »
 -- The partial sum of `g`, starting from zero
 local notation "G " n:80 => ∑ i in range n, g i
 

@@ -108,7 +108,7 @@ theorem prod_Ico_eq_mul_inv {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n :
     (∏ k in Ico m n, f k) = (∏ k in range n, f k) * (∏ k in range m, f k)⁻¹ :=
   eq_mul_inv_iff_mul_eq.2 <| by (rw [mul_comm]; exact prod_range_mul_prod_Ico f h)
 #align finset.prod_Ico_eq_mul_inv Finset.prod_Ico_eq_mul_inv
-#align finset.sum_ico_eq_add_neg Finset.sum_Ico_eq_add_neg
+#align finset.sum_Ico_eq_add_neg Finset.sum_Ico_eq_add_neg
 
 @[to_additive]
 theorem prod_Ico_eq_div {δ : Type _} [CommGroup δ] (f : ℕ → δ) {m n : ℕ} (h : m ≤ n) :
@@ -145,14 +145,14 @@ theorem sum_Ico_Ico_comm {M : Type _} [AddCommMonoid M] (a b : ℕ) (f : ℕ →
 #align finset.sum_Ico_Ico_comm Finset.sum_Ico_Ico_comm
 
 @[to_additive]
-theorem prod_ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
+theorem prod_Ico_eq_prod_range (f : ℕ → β) (m n : ℕ) :
     (∏ k in Ico m n, f k) = ∏ k in range (n - m), f (m + k) := by
   by_cases h : m ≤ n
   · rw [← Nat.Ico_zero_eq_range, prod_Ico_add, zero_add, tsub_add_cancel_of_le h]
   · replace h : n ≤ m := le_of_not_ge h
     rw [Ico_eq_empty_of_le h, tsub_eq_zero_iff_le.mpr h, range_zero, prod_empty, prod_empty]
-#align finset.prod_Ico_eq_prod_range Finset.prod_ico_eq_prod_range
-#align finset.sum_Ico_eq_sum_range Finset.sum_ico_eq_sum_range
+#align finset.prod_Ico_eq_prod_range Finset.prod_Ico_eq_prod_range
+#align finset.sum_Ico_eq_sum_range Finset.sum_Ico_eq_sum_range
 
 theorem prod_Ico_reflect (f : ℕ → β) (k : ℕ) {m n : ℕ} (h : m ≤ n + 1) :
     (∏ j in Ico k m, f (n - j)) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j := by

@@ -22,7 +22,7 @@ We prove results about big operators over intervals (mostly the `ℕ`-valued `Ic
 
 universe u v w
 
--- open BigOperators -- porting note: notation is global for now
+open BigOperators
 open Nat
 
 namespace Finset

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