ring_theory.integral_domain ⟷ Mathlib.RingTheory.IntegralDomain

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
 -/
-import Data.Polynomial.RingDivision
+import Algebra.Polynomial.RingDivision
 import GroupTheory.SpecificGroups.Cyclic
 import Algebra.GeomSum
 

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

@@ -82,7 +82,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 #print Finset.exists_eq_pow_of_mul_eq_pow_of_coprime /-
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}

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

@@ -90,11 +90,11 @@ theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemir
     (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
   intro i hi
-  rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
+  rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod
   refine'
     exists_eq_pow_of_mul_eq_pow_of_coprime
       (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
-  rw [hij] at hj 
+  rw [hij] at hj
   exact (s.not_mem_erase _) hj
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
@@ -148,7 +148,7 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
   refine' le_trans _ (nth_roots n (f g₀)).toFinset_card_le
   apply card_le_card_of_inj_on f
   · intro g hg
-    rw [sep_def, mem_filter] at hg 
+    rw [sep_def, mem_filter] at hg
     rw [Multiset.mem_toFinset, mem_nth_roots hn, ← f.map_pow, hg.2]
   · intros; apply hf; assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
@@ -227,7 +227,7 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
     simp (config := { contextual := true }) only [mem_filter, one_mul, MonoidHom.map_mul, mem_univ,
       mul_right_inv, eq_self_iff_true, MonoidHom.map_mul_inv, and_self_iff, forall_true_iff]
   · simp only [mul_left_inj, imp_self, forall₂_true_iff]
-  · simp only [true_and_iff, mem_filter, mem_univ] at hg 
+  · simp only [true_and_iff, mem_filter, mem_univ] at hg
     simp only [hg, mem_filter, one_mul, MonoidHom.map_mul, mem_univ, mul_right_inv,
       eq_self_iff_true, exists_prop_of_true, MonoidHom.map_mul_inv, and_self_iff,
       mul_inv_cancel_right, inv_mul_cancel_right]
@@ -250,7 +250,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
     rw [MonoidHom.one_apply]
     cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
     rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
-      eq_comm] at hn 
+      eq_comm] at hn
   replace hx1 : (x : R) - 1 ≠ 0
   exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
   let c := (univ.filter fun g => f.to_hom_units g = 1).card

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

@@ -87,7 +87,15 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
-    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by classical
+    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
+  classical
+  intro i hi
+  rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
+  refine'
+    exists_eq_pow_of_mul_eq_pow_of_coprime
+      (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
+  rw [hij] at hj 
+  exact (s.not_mem_erase _) hj
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
 
@@ -150,6 +158,10 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
+  cases nonempty_fintype G
+  apply isCyclic_of_card_pow_eq_one_le
+  intro n hn
+  convert le_trans (card_nthRoots_subgroup_units f hf hn 1) (card_nth_roots n (f 1))
 #align is_cyclic_of_subgroup_is_domain isCyclic_of_subgroup_isDomain
 -/
 
@@ -225,15 +237,69 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
 #print sum_hom_units_eq_zero /-
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
-theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by classical
+theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
+  classical
+  obtain ⟨x, hx⟩ :
+    ∃ x : MonoidHom.range f.to_hom_units,
+      ∀ y : MonoidHom.range f.to_hom_units, y ∈ Submonoid.powers x
+  exact IsCyclic.exists_monoid_generator
+  have hx1 : x ≠ 1 := by
+    rintro rfl
+    apply hf
+    ext g
+    rw [MonoidHom.one_apply]
+    cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
+    rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
+      eq_comm] at hn 
+  replace hx1 : (x : R) - 1 ≠ 0
+  exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
+  let c := (univ.filter fun g => f.to_hom_units g = 1).card
+  calc
+    ∑ g : G, f g = ∑ g : G, f.to_hom_units g := rfl
+    _ =
+        ∑ u : Rˣ in univ.image f.to_hom_units,
+          (univ.filter fun g => f.to_hom_units g = u).card • u :=
+      (sum_comp (coe : Rˣ → R) f.to_hom_units)
+    _ = ∑ u : Rˣ in univ.image f.to_hom_units, c • u :=
+      (sum_congr rfl fun u hu => congr_arg₂ _ _ rfl)
+    -- remaining goal 1, proven below
+        _ =
+        ∑ b : MonoidHom.range f.to_hom_units, c • ↑b :=
+      (Finset.sum_subtype _ (by simp) _)
+    _ = c • ∑ b : MonoidHom.range f.to_hom_units, (b : R) := smul_sum.symm
+    _ = c • 0 := (congr_arg₂ _ rfl _)
+    -- remaining goal 2, proven below
+        _ =
+        0 :=
+      smul_zero _
+  · -- remaining goal 1
+    show (univ.filter fun g : G => f.to_hom_units g = u).card = c
+    apply card_fiber_eq_of_mem_range f.to_hom_units
+    · simpa only [mem_image, mem_univ, exists_prop_of_true, Set.mem_range] using hu
+    · exact ⟨1, f.to_hom_units.map_one⟩
+  -- remaining goal 2
+  show ∑ b : MonoidHom.range f.to_hom_units, (b : R) = 0
+  calc
+    ∑ b : MonoidHom.range f.to_hom_units, (b : R) = ∑ n in range (orderOf x), x ^ n :=
+      Eq.symm <|
+        sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
+          (by
+            simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow, Units.val_pow_eq_pow_val,
+              coe_coe])
+          (fun m n hm hn =>
+            pow_injOn_Iio_orderOf _ (by simpa only [mem_range] using hm)
+              (by simpa only [mem_range] using hn))
+          fun b hb =>
+          let ⟨n, hn⟩ := hx b
+          ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by rw [← pow_mod_orderOf, hn]⟩
+    _ = 0 := _
+  rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
+  norm_cast
+  simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 -/
 
 #print sum_hom_units /-
--- remaining goal 1, proven below
--- remaining goal 2, proven below
--- remaining goal 1
--- remaining goal 2
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/

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

@@ -87,15 +87,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
-    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
-  classical
-  intro i hi
-  rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
-  refine'
-    exists_eq_pow_of_mul_eq_pow_of_coprime
-      (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
-  rw [hij] at hj 
-  exact (s.not_mem_erase _) hj
+    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by classical
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
 
@@ -158,10 +150,6 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
-  cases nonempty_fintype G
-  apply isCyclic_of_card_pow_eq_one_le
-  intro n hn
-  convert le_trans (card_nthRoots_subgroup_units f hf hn 1) (card_nth_roots n (f 1))
 #align is_cyclic_of_subgroup_is_domain isCyclic_of_subgroup_isDomain
 -/
 
@@ -237,69 +225,15 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
 #print sum_hom_units_eq_zero /-
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
-theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
-  classical
-  obtain ⟨x, hx⟩ :
-    ∃ x : MonoidHom.range f.to_hom_units,
-      ∀ y : MonoidHom.range f.to_hom_units, y ∈ Submonoid.powers x
-  exact IsCyclic.exists_monoid_generator
-  have hx1 : x ≠ 1 := by
-    rintro rfl
-    apply hf
-    ext g
-    rw [MonoidHom.one_apply]
-    cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
-    rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
-      eq_comm] at hn 
-  replace hx1 : (x : R) - 1 ≠ 0
-  exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
-  let c := (univ.filter fun g => f.to_hom_units g = 1).card
-  calc
-    ∑ g : G, f g = ∑ g : G, f.to_hom_units g := rfl
-    _ =
-        ∑ u : Rˣ in univ.image f.to_hom_units,
-          (univ.filter fun g => f.to_hom_units g = u).card • u :=
-      (sum_comp (coe : Rˣ → R) f.to_hom_units)
-    _ = ∑ u : Rˣ in univ.image f.to_hom_units, c • u :=
-      (sum_congr rfl fun u hu => congr_arg₂ _ _ rfl)
-    -- remaining goal 1, proven below
-        _ =
-        ∑ b : MonoidHom.range f.to_hom_units, c • ↑b :=
-      (Finset.sum_subtype _ (by simp) _)
-    _ = c • ∑ b : MonoidHom.range f.to_hom_units, (b : R) := smul_sum.symm
-    _ = c • 0 := (congr_arg₂ _ rfl _)
-    -- remaining goal 2, proven below
-        _ =
-        0 :=
-      smul_zero _
-  · -- remaining goal 1
-    show (univ.filter fun g : G => f.to_hom_units g = u).card = c
-    apply card_fiber_eq_of_mem_range f.to_hom_units
-    · simpa only [mem_image, mem_univ, exists_prop_of_true, Set.mem_range] using hu
-    · exact ⟨1, f.to_hom_units.map_one⟩
-  -- remaining goal 2
-  show ∑ b : MonoidHom.range f.to_hom_units, (b : R) = 0
-  calc
-    ∑ b : MonoidHom.range f.to_hom_units, (b : R) = ∑ n in range (orderOf x), x ^ n :=
-      Eq.symm <|
-        sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
-          (by
-            simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow, Units.val_pow_eq_pow_val,
-              coe_coe])
-          (fun m n hm hn =>
-            pow_injOn_Iio_orderOf _ (by simpa only [mem_range] using hm)
-              (by simpa only [mem_range] using hn))
-          fun b hb =>
-          let ⟨n, hn⟩ := hx b
-          ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by rw [← pow_mod_orderOf, hn]⟩
-    _ = 0 := _
-  rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
-  norm_cast
-  simp [pow_orderOf_eq_one]
+theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by classical
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 -/
 
 #print sum_hom_units /-
+-- remaining goal 1, proven below
+-- remaining goal 2, proven below
+-- remaining goal 1
+-- remaining goal 2
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/

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

@@ -287,12 +287,11 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
             simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow, Units.val_pow_eq_pow_val,
               coe_coe])
           (fun m n hm hn =>
-            pow_injective_of_lt_orderOf _ (by simpa only [mem_range] using hm)
+            pow_injOn_Iio_orderOf _ (by simpa only [mem_range] using hm)
               (by simpa only [mem_range] using hn))
           fun b hb =>
           let ⟨n, hn⟩ := hx b
-          ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by
-            rw [← pow_eq_mod_orderOf, hn]⟩
+          ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by rw [← pow_mod_orderOf, hn]⟩
     _ = 0 := _
   rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
   norm_cast

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
 -/
-import Mathbin.Data.Polynomial.RingDivision
-import Mathbin.GroupTheory.SpecificGroups.Cyclic
-import Mathbin.Algebra.GeomSum
+import Data.Polynomial.RingDivision
+import GroupTheory.SpecificGroups.Cyclic
+import Algebra.GeomSum
 
 #align_import ring_theory.integral_domain from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 
@@ -82,7 +82,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 #print Finset.exists_eq_pow_of_mul_eq_pow_of_coprime /-
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.integral_domain
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.RingDivision
 import Mathbin.GroupTheory.SpecificGroups.Cyclic
 import Mathbin.Algebra.GeomSum
 
+#align_import ring_theory.integral_domain from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Integral domains
 
@@ -85,7 +82,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 #print Finset.exists_eq_pow_of_mul_eq_pow_of_coprime /-
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}

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

@@ -46,13 +46,17 @@ section CancelMonoidWithZero
 -- There doesn't seem to be a better home for these right now
 variable {M : Type _} [CancelMonoidWithZero M] [Finite M]
 
+#print mul_right_bijective_of_finite₀ /-
 theorem mul_right_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => a * b :=
   Finite.injective_iff_bijective.1 <| mul_right_injective₀ ha
 #align mul_right_bijective_of_finite₀ mul_right_bijective_of_finite₀
+-/
 
+#print mul_left_bijective_of_finite₀ /-
 theorem mul_left_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => b * a :=
   Finite.injective_iff_bijective.1 <| mul_left_injective₀ ha
 #align mul_left_bijective_of_finite₀ mul_left_bijective_of_finite₀
+-/
 
 #print Fintype.groupWithZeroOfCancel /-
 /-- Every finite nontrivial cancel_monoid_with_zero is a group_with_zero. -/
@@ -68,6 +72,7 @@ def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [Decidab
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel
 -/
 
+#print exists_eq_pow_of_mul_eq_pow_of_coprime /-
 theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {a b c : R} {n : ℕ} (cp : IsCoprime a b) (h : a * b = c ^ n) :
     ∃ d : R, a = d ^ n :=
@@ -78,8 +83,10 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
   exact
     dvd_add (dvd_mul_of_dvd_right (gcd_dvd_left _ _) _) (dvd_mul_of_dvd_right (gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+#print Finset.exists_eq_pow_of_mul_eq_pow_of_coprime /-
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
@@ -93,6 +100,7 @@ theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemir
   rw [hij] at hj 
   exact (s.not_mem_erase _) hj
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
+-/
 
 end CancelMonoidWithZero
 
@@ -135,6 +143,7 @@ end Ring
 
 variable [CommRing R] [IsDomain R] [Group G]
 
+#print card_nthRoots_subgroup_units /-
 theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective f) {n : ℕ}
     (hn : 0 < n) (g₀ : G) : ({g ∈ univ | g ^ n = g₀} : Finset G).card ≤ (nthRoots n (f g₀)).card :=
   by
@@ -146,7 +155,9 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
     rw [Multiset.mem_toFinset, mem_nth_roots hn, ← f.map_pow, hg.2]
   · intros; apply hf; assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
+-/
 
+#print isCyclic_of_subgroup_isDomain /-
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
@@ -155,6 +166,7 @@ theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective
   intro n hn
   convert le_trans (card_nthRoots_subgroup_units f hf hn 1) (card_nth_roots n (f 1))
 #align is_cyclic_of_subgroup_is_domain isCyclic_of_subgroup_isDomain
+-/
 
 /-- The unit group of a finite integral domain is cyclic.
 
@@ -167,6 +179,7 @@ section
 
 variable (S : Subgroup Rˣ) [Finite S]
 
+#print subgroup_units_cyclic /-
 /-- A finite subgroup of the units of an integral domain is cyclic. -/
 instance subgroup_units_cyclic : IsCyclic S :=
   by
@@ -174,6 +187,7 @@ instance subgroup_units_cyclic : IsCyclic S :=
   · simp
   · intros; simp
 #align subgroup_units_cyclic subgroup_units_cyclic
+-/
 
 end
 
@@ -185,6 +199,7 @@ open scoped Polynomial
 
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
 
+#print Polynomial.div_eq_quo_add_rem_div /-
 theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     ∃ q r : R[X], r.degree < g.degree ∧ (↑f : K) / ↑g = ↑q + ↑r / ↑g :=
   by
@@ -195,6 +210,7 @@ theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     norm_cast
     rw [add_comm, mul_comm, mod_by_monic_add_div f hg]
 #align polynomial.div_eq_quo_add_rem_div Polynomial.div_eq_quo_add_rem_div
+-/
 
 end Polynomial
 
@@ -202,6 +218,7 @@ end EuclideanDivision
 
 variable [Fintype G]
 
+#print card_fiber_eq_of_mem_range /-
 theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
     (univ.filterₓ fun g => f g = x).card = (univ.filterₓ fun g => f g = y).card :=
@@ -218,7 +235,9 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
       eq_self_iff_true, exists_prop_of_true, MonoidHom.map_mul_inv, and_self_iff,
       mul_inv_cancel_right, inv_mul_cancel_right]
 #align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_range
+-/
 
+#print sum_hom_units_eq_zero /-
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
 theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
@@ -282,7 +301,9 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
   norm_cast
   simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
+-/
 
+#print sum_hom_units /-
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/
@@ -293,6 +314,7 @@ theorem sum_hom_units (f : G →* R) [Decidable (f = 1)] :
   · simp [h, card_univ]
   · exact sum_hom_units_eq_zero f h
 #align sum_hom_units sum_hom_units
+-/
 
 end
 

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

@@ -83,7 +83,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
-    (hprod : (∏ i in s, f i) = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
+    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
   intro i hi
   rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
@@ -221,7 +221,7 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
 
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
-theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) = 0 := by
+theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
   classical
   obtain ⟨x, hx⟩ :
     ∃ x : MonoidHom.range f.to_hom_units,
@@ -239,7 +239,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
   exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
   let c := (univ.filter fun g => f.to_hom_units g = 1).card
   calc
-    (∑ g : G, f g) = ∑ g : G, f.to_hom_units g := rfl
+    ∑ g : G, f g = ∑ g : G, f.to_hom_units g := rfl
     _ =
         ∑ u : Rˣ in univ.image f.to_hom_units,
           (univ.filter fun g => f.to_hom_units g = u).card • u :=
@@ -262,9 +262,9 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
     · simpa only [mem_image, mem_univ, exists_prop_of_true, Set.mem_range] using hu
     · exact ⟨1, f.to_hom_units.map_one⟩
   -- remaining goal 2
-  show (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = 0
+  show ∑ b : MonoidHom.range f.to_hom_units, (b : R) = 0
   calc
-    (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = ∑ n in range (orderOf x), x ^ n :=
+    ∑ b : MonoidHom.range f.to_hom_units, (b : R) = ∑ n in range (orderOf x), x ^ n :=
       Eq.symm <|
         sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
           (by
@@ -287,7 +287,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/
 theorem sum_hom_units (f : G →* R) [Decidable (f = 1)] :
-    (∑ g : G, f g) = if f = 1 then Fintype.card G else 0 :=
+    ∑ g : G, f g = if f = 1 then Fintype.card G else 0 :=
   by
   split_ifs with h h
   · simp [h, card_univ]

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

@@ -256,7 +256,6 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
         _ =
         0 :=
       smul_zero _
-    
   · -- remaining goal 1
     show (univ.filter fun g : G => f.to_hom_units g = u).card = c
     apply card_fiber_eq_of_mem_range f.to_hom_units
@@ -279,7 +278,6 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
           ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by
             rw [← pow_eq_mod_orderOf, hn]⟩
     _ = 0 := _
-    
   rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
   norm_cast
   simp [pow_orderOf_eq_one]

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -79,7 +79,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
     dvd_add (dvd_mul_of_dvd_right (gcd_dvd_left _ _) _) (dvd_mul_of_dvd_right (gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))

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

@@ -85,13 +85,13 @@ theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemir
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
     (hprod : (∏ i in s, f i) = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
-    intro i hi
-    rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
-    refine'
-      exists_eq_pow_of_mul_eq_pow_of_coprime
-        (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
-    rw [hij] at hj 
-    exact (s.not_mem_erase _) hj
+  intro i hi
+  rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
+  refine'
+    exists_eq_pow_of_mul_eq_pow_of_coprime
+      (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
+  rw [hij] at hj 
+  exact (s.not_mem_erase _) hj
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
 
 end CancelMonoidWithZero
@@ -136,8 +136,7 @@ end Ring
 variable [CommRing R] [IsDomain R] [Group G]
 
 theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective f) {n : ℕ}
-    (hn : 0 < n) (g₀ : G) :
-    ({ g ∈ univ | g ^ n = g₀ } : Finset G).card ≤ (nthRoots n (f g₀)).card :=
+    (hn : 0 < n) (g₀ : G) : ({g ∈ univ | g ^ n = g₀} : Finset G).card ≤ (nthRoots n (f g₀)).card :=
   by
   haveI : DecidableEq R := Classical.decEq _
   refine' le_trans _ (nth_roots n (f g₀)).toFinset_card_le
@@ -151,10 +150,10 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
-    cases nonempty_fintype G
-    apply isCyclic_of_card_pow_eq_one_le
-    intro n hn
-    convert le_trans (card_nthRoots_subgroup_units f hf hn 1) (card_nth_roots n (f 1))
+  cases nonempty_fintype G
+  apply isCyclic_of_card_pow_eq_one_le
+  intro n hn
+  convert le_trans (card_nthRoots_subgroup_units f hf hn 1) (card_nth_roots n (f 1))
 #align is_cyclic_of_subgroup_is_domain isCyclic_of_subgroup_isDomain
 
 /-- The unit group of a finite integral domain is cyclic.
@@ -224,66 +223,66 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
 -/
 theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) = 0 := by
   classical
-    obtain ⟨x, hx⟩ :
-      ∃ x : MonoidHom.range f.to_hom_units,
-        ∀ y : MonoidHom.range f.to_hom_units, y ∈ Submonoid.powers x
-    exact IsCyclic.exists_monoid_generator
-    have hx1 : x ≠ 1 := by
-      rintro rfl
-      apply hf
-      ext g
-      rw [MonoidHom.one_apply]
-      cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
-      rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
-        eq_comm] at hn 
-    replace hx1 : (x : R) - 1 ≠ 0
-    exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
-    let c := (univ.filter fun g => f.to_hom_units g = 1).card
-    calc
-      (∑ g : G, f g) = ∑ g : G, f.to_hom_units g := rfl
-      _ =
-          ∑ u : Rˣ in univ.image f.to_hom_units,
-            (univ.filter fun g => f.to_hom_units g = u).card • u :=
-        (sum_comp (coe : Rˣ → R) f.to_hom_units)
-      _ = ∑ u : Rˣ in univ.image f.to_hom_units, c • u :=
-        (sum_congr rfl fun u hu => congr_arg₂ _ _ rfl)
-      -- remaining goal 1, proven below
-          _ =
-          ∑ b : MonoidHom.range f.to_hom_units, c • ↑b :=
-        (Finset.sum_subtype _ (by simp) _)
-      _ = c • ∑ b : MonoidHom.range f.to_hom_units, (b : R) := smul_sum.symm
-      _ = c • 0 := (congr_arg₂ _ rfl _)
-      -- remaining goal 2, proven below
-          _ =
-          0 :=
-        smul_zero _
-      
-    · -- remaining goal 1
-      show (univ.filter fun g : G => f.to_hom_units g = u).card = c
-      apply card_fiber_eq_of_mem_range f.to_hom_units
-      · simpa only [mem_image, mem_univ, exists_prop_of_true, Set.mem_range] using hu
-      · exact ⟨1, f.to_hom_units.map_one⟩
-    -- remaining goal 2
-    show (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = 0
-    calc
-      (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = ∑ n in range (orderOf x), x ^ n :=
-        Eq.symm <|
-          sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
-            (by
-              simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow, Units.val_pow_eq_pow_val,
-                coe_coe])
-            (fun m n hm hn =>
-              pow_injective_of_lt_orderOf _ (by simpa only [mem_range] using hm)
-                (by simpa only [mem_range] using hn))
-            fun b hb =>
-            let ⟨n, hn⟩ := hx b
-            ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by
-              rw [← pow_eq_mod_orderOf, hn]⟩
-      _ = 0 := _
-      
-    rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
-    norm_cast
-    simp [pow_orderOf_eq_one]
+  obtain ⟨x, hx⟩ :
+    ∃ x : MonoidHom.range f.to_hom_units,
+      ∀ y : MonoidHom.range f.to_hom_units, y ∈ Submonoid.powers x
+  exact IsCyclic.exists_monoid_generator
+  have hx1 : x ≠ 1 := by
+    rintro rfl
+    apply hf
+    ext g
+    rw [MonoidHom.one_apply]
+    cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
+    rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
+      eq_comm] at hn 
+  replace hx1 : (x : R) - 1 ≠ 0
+  exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
+  let c := (univ.filter fun g => f.to_hom_units g = 1).card
+  calc
+    (∑ g : G, f g) = ∑ g : G, f.to_hom_units g := rfl
+    _ =
+        ∑ u : Rˣ in univ.image f.to_hom_units,
+          (univ.filter fun g => f.to_hom_units g = u).card • u :=
+      (sum_comp (coe : Rˣ → R) f.to_hom_units)
+    _ = ∑ u : Rˣ in univ.image f.to_hom_units, c • u :=
+      (sum_congr rfl fun u hu => congr_arg₂ _ _ rfl)
+    -- remaining goal 1, proven below
+        _ =
+        ∑ b : MonoidHom.range f.to_hom_units, c • ↑b :=
+      (Finset.sum_subtype _ (by simp) _)
+    _ = c • ∑ b : MonoidHom.range f.to_hom_units, (b : R) := smul_sum.symm
+    _ = c • 0 := (congr_arg₂ _ rfl _)
+    -- remaining goal 2, proven below
+        _ =
+        0 :=
+      smul_zero _
+    
+  · -- remaining goal 1
+    show (univ.filter fun g : G => f.to_hom_units g = u).card = c
+    apply card_fiber_eq_of_mem_range f.to_hom_units
+    · simpa only [mem_image, mem_univ, exists_prop_of_true, Set.mem_range] using hu
+    · exact ⟨1, f.to_hom_units.map_one⟩
+  -- remaining goal 2
+  show (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = 0
+  calc
+    (∑ b : MonoidHom.range f.to_hom_units, (b : R)) = ∑ n in range (orderOf x), x ^ n :=
+      Eq.symm <|
+        sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
+          (by
+            simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow, Units.val_pow_eq_pow_val,
+              coe_coe])
+          (fun m n hm hn =>
+            pow_injective_of_lt_orderOf _ (by simpa only [mem_range] using hm)
+              (by simpa only [mem_range] using hn))
+          fun b hb =>
+          let ⟨n, hn⟩ := hx b
+          ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)), by
+            rw [← pow_eq_mod_orderOf, hn]⟩
+    _ = 0 := _
+    
+  rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
+  norm_cast
+  simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,

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

@@ -86,11 +86,11 @@ theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemir
     (hprod : (∏ i in s, f i) = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
     intro i hi
-    rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod
+    rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod 
     refine'
       exists_eq_pow_of_mul_eq_pow_of_coprime
         (IsCoprime.prod_right fun j hj => h i hi j (erase_subset i s hj) fun hij => _) hprod
-    rw [hij] at hj
+    rw [hij] at hj 
     exact (s.not_mem_erase _) hj
 #align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
 
@@ -143,9 +143,9 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
   refine' le_trans _ (nth_roots n (f g₀)).toFinset_card_le
   apply card_le_card_of_inj_on f
   · intro g hg
-    rw [sep_def, mem_filter] at hg
+    rw [sep_def, mem_filter] at hg 
     rw [Multiset.mem_toFinset, mem_nth_roots hn, ← f.map_pow, hg.2]
-  · intros ; apply hf; assumption
+  · intros; apply hf; assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
 
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
@@ -173,7 +173,7 @@ instance subgroup_units_cyclic : IsCyclic S :=
   by
   refine' isCyclic_of_subgroup_isDomain ⟨(coe : S → R), _, _⟩ (units.ext.comp Subtype.val_injective)
   · simp
-  · intros ; simp
+  · intros; simp
 #align subgroup_units_cyclic subgroup_units_cyclic
 
 end
@@ -214,7 +214,7 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
     simp (config := { contextual := true }) only [mem_filter, one_mul, MonoidHom.map_mul, mem_univ,
       mul_right_inv, eq_self_iff_true, MonoidHom.map_mul_inv, and_self_iff, forall_true_iff]
   · simp only [mul_left_inj, imp_self, forall₂_true_iff]
-  · simp only [true_and_iff, mem_filter, mem_univ] at hg
+  · simp only [true_and_iff, mem_filter, mem_univ] at hg 
     simp only [hg, mem_filter, one_mul, MonoidHom.map_mul, mem_univ, mul_right_inv,
       eq_self_iff_true, exists_prop_of_true, MonoidHom.map_mul_inv, and_self_iff,
       mul_inv_cancel_right, inv_mul_cancel_right]
@@ -235,7 +235,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
       rw [MonoidHom.one_apply]
       cases' hx ⟨f.to_hom_units g, g, rfl⟩ with n hn
       rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
-        eq_comm] at hn
+        eq_comm] at hn 
     replace hx1 : (x : R) - 1 ≠ 0
     exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
     let c := (univ.filter fun g => f.to_hom_units g = 1).card

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

@@ -39,7 +39,7 @@ section
 
 open Finset Polynomial Function
 
-open BigOperators Nat
+open scoped BigOperators Nat
 
 section CancelMonoidWithZero
 
@@ -182,7 +182,7 @@ section EuclideanDivision
 
 namespace Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
 

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

@@ -46,22 +46,10 @@ section CancelMonoidWithZero
 -- There doesn't seem to be a better home for these right now
 variable {M : Type _} [CancelMonoidWithZero M] [Finite M]
 
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-Case conversion may be inaccurate. Consider using '#align mul_right_bijective_of_finite₀ mul_right_bijective_of_finite₀ₓ'. -/
 theorem mul_right_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => a * b :=
   Finite.injective_iff_bijective.1 <| mul_right_injective₀ ha
 #align mul_right_bijective_of_finite₀ mul_right_bijective_of_finite₀
 
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 theorem mul_left_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => b * a :=
   Finite.injective_iff_bijective.1 <| mul_left_injective₀ ha
 #align mul_left_bijective_of_finite₀ mul_left_bijective_of_finite₀
@@ -80,12 +68,6 @@ def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [Decidab
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel
 -/
 
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-Case conversion may be inaccurate. Consider using '#align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprimeₓ'. -/
 theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {a b c : R} {n : ℕ} (cp : IsCoprime a b) (h : a * b = c ^ n) :
     ∃ d : R, a = d ^ n :=
@@ -97,12 +79,6 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
     dvd_add (dvd_mul_of_dvd_right (gcd_dvd_left _ _) _) (dvd_mul_of_dvd_right (gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 
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-Case conversion may be inaccurate. Consider using '#align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprimeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
@@ -159,9 +135,6 @@ end Ring
 
 variable [CommRing R] [IsDomain R] [Group G]
 
-/- warning: card_nth_roots_subgroup_units -> card_nthRoots_subgroup_units is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align card_nth_roots_subgroup_units card_nthRoots_subgroup_unitsₓ'. -/
 theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective f) {n : ℕ}
     (hn : 0 < n) (g₀ : G) :
     ({ g ∈ univ | g ^ n = g₀ } : Finset G).card ≤ (nthRoots n (f g₀)).card :=
@@ -175,12 +148,6 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
   · intros ; apply hf; assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
 
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 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
@@ -201,12 +168,6 @@ section
 
 variable (S : Subgroup Rˣ) [Finite S]
 
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-Case conversion may be inaccurate. Consider using '#align subgroup_units_cyclic subgroup_units_cyclicₓ'. -/
 /-- A finite subgroup of the units of an integral domain is cyclic. -/
 instance subgroup_units_cyclic : IsCyclic S :=
   by
@@ -225,9 +186,6 @@ open Polynomial
 
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
 
-/- warning: polynomial.div_eq_quo_add_rem_div -> Polynomial.div_eq_quo_add_rem_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.div_eq_quo_add_rem_div Polynomial.div_eq_quo_add_rem_divₓ'. -/
 theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     ∃ q r : R[X], r.degree < g.degree ∧ (↑f : K) / ↑g = ↑q + ↑r / ↑g :=
   by
@@ -245,9 +203,6 @@ end EuclideanDivision
 
 variable [Fintype G]
 
-/- warning: card_fiber_eq_of_mem_range -> card_fiber_eq_of_mem_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_rangeₓ'. -/
 theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
     (univ.filterₓ fun g => f g = x).card = (univ.filterₓ fun g => f g = y).card :=
@@ -265,12 +220,6 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
       mul_inv_cancel_right, inv_mul_cancel_right]
 #align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_range
 
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 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
 theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) = 0 := by
@@ -337,9 +286,6 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
     simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 
-/- warning: sum_hom_units -> sum_hom_units is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align sum_hom_units sum_hom_unitsₓ'. -/
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/

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

@@ -74,8 +74,7 @@ def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [Decidab
     ‹CancelMonoidWithZero
         M› with
     inv := fun a => if h : a = 0 then 0 else Fintype.bijInv (mul_right_bijective_of_finite₀ h) 1
-    mul_inv_cancel := fun a ha => by
-      simp [Inv.inv, dif_neg ha]
+    mul_inv_cancel := fun a ha => by simp [Inv.inv, dif_neg ha];
       exact Fintype.rightInverse_bijInv _ _
     inv_zero := by simp [Inv.inv, dif_pos rfl] }
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel
@@ -173,9 +172,7 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
   · intro g hg
     rw [sep_def, mem_filter] at hg
     rw [Multiset.mem_toFinset, mem_nth_roots hn, ← f.map_pow, hg.2]
-  · intros
-    apply hf
-    assumption
+  · intros ; apply hf; assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
 
 /- warning: is_cyclic_of_subgroup_is_domain -> isCyclic_of_subgroup_isDomain is a dubious translation:
@@ -215,8 +212,7 @@ instance subgroup_units_cyclic : IsCyclic S :=
   by
   refine' isCyclic_of_subgroup_isDomain ⟨(coe : S → R), _, _⟩ (units.ext.comp Subtype.val_injective)
   · simp
-  · intros
-    simp
+  · intros ; simp
 #align subgroup_units_cyclic subgroup_units_cyclic
 
 end

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
 
 ! This file was ported from Lean 3 source module ring_theory.integral_domain
-! leanprover-community/mathlib commit 6e70e0d419bf686784937d64ed4bfde866ff229e
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Algebra.GeomSum
 /-!
 # Integral domains
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Assorted theorems about integral domains.
 
 ## Main theorems
@@ -158,10 +161,7 @@ end Ring
 variable [CommRing R] [IsDomain R] [Group G]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align card_nth_roots_subgroup_units card_nthRoots_subgroup_unitsₓ'. -/
 theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective f) {n : ℕ}
     (hn : 0 < n) (g₀ : G) :
@@ -230,10 +230,7 @@ open Polynomial
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
 
 /- warning: polynomial.div_eq_quo_add_rem_div -> Polynomial.div_eq_quo_add_rem_div is a dubious translation:
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(CommRing.toCommSemiring.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (DivisionSemiring.toSemiring.{0} K (Semifield.toDivisionSemiring.{0} K (Field.toSemifield.{0} K _inst_4))) _inst_5) g)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.div_eq_quo_add_rem_div Polynomial.div_eq_quo_add_rem_divₓ'. -/
 theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     ∃ q r : R[X], r.degree < g.degree ∧ (↑f : K) / ↑g = ↑q + ↑r / ↑g :=
@@ -253,10 +250,7 @@ end EuclideanDivision
 variable [Fintype G]
 
 /- warning: card_fiber_eq_of_mem_range -> card_fiber_eq_of_mem_range is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_rangeₓ'. -/
 theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
@@ -348,10 +342,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 
 /- warning: sum_hom_units -> sum_hom_units is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align sum_hom_units sum_hom_unitsₓ'. -/
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -43,14 +43,27 @@ section CancelMonoidWithZero
 -- There doesn't seem to be a better home for these right now
 variable {M : Type _} [CancelMonoidWithZero M] [Finite M]
 
+/- warning: mul_right_bijective_of_finite₀ -> mul_right_bijective_of_finite₀ is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} M] [_inst_2 : Finite.{succ u1} M] {a : M}, (Ne.{succ u1} M a (OfNat.ofNat.{u1} M 0 (OfNat.mk.{u1} M 0 (Zero.zero.{u1} M (MulZeroClass.toHasZero.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1)))))))) -> (Function.Bijective.{succ u1, succ u1} M M (fun (b : M) => HMul.hMul.{u1, u1, u1} M M M (instHMul.{u1} M (MulZeroClass.toHasMul.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) a b))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} M] [_inst_2 : Finite.{succ u1} M] {a : M}, (Ne.{succ u1} M a (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (MonoidWithZero.toZero.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) -> (Function.Bijective.{succ u1, succ u1} M M (fun (b : M) => HMul.hMul.{u1, u1, u1} M M M (instHMul.{u1} M (MulZeroClass.toMul.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align mul_right_bijective_of_finite₀ mul_right_bijective_of_finite₀ₓ'. -/
 theorem mul_right_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => a * b :=
   Finite.injective_iff_bijective.1 <| mul_right_injective₀ ha
 #align mul_right_bijective_of_finite₀ mul_right_bijective_of_finite₀
 
+/- warning: mul_left_bijective_of_finite₀ -> mul_left_bijective_of_finite₀ is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} M] [_inst_2 : Finite.{succ u1} M] {a : M}, (Ne.{succ u1} M a (OfNat.ofNat.{u1} M 0 (OfNat.mk.{u1} M 0 (Zero.zero.{u1} M (MulZeroClass.toHasZero.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1)))))))) -> (Function.Bijective.{succ u1, succ u1} M M (fun (b : M) => HMul.hMul.{u1, u1, u1} M M M (instHMul.{u1} M (MulZeroClass.toHasMul.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) b a))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} M] [_inst_2 : Finite.{succ u1} M] {a : M}, (Ne.{succ u1} M a (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (MonoidWithZero.toZero.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) -> (Function.Bijective.{succ u1, succ u1} M M (fun (b : M) => HMul.hMul.{u1, u1, u1} M M M (instHMul.{u1} M (MulZeroClass.toMul.{u1} M (MulZeroOneClass.toMulZeroClass.{u1} M (MonoidWithZero.toMulZeroOneClass.{u1} M (CancelMonoidWithZero.toMonoidWithZero.{u1} M _inst_1))))) b a))
+Case conversion may be inaccurate. Consider using '#align mul_left_bijective_of_finite₀ mul_left_bijective_of_finite₀ₓ'. -/
 theorem mul_left_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => b * a :=
   Finite.injective_iff_bijective.1 <| mul_left_injective₀ ha
 #align mul_left_bijective_of_finite₀ mul_left_bijective_of_finite₀
 
+#print Fintype.groupWithZeroOfCancel /-
 /-- Every finite nontrivial cancel_monoid_with_zero is a group_with_zero. -/
 def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [DecidableEq M] [Fintype M]
     [Nontrivial M] : GroupWithZero M :=
@@ -63,7 +76,14 @@ def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [Decidab
       exact Fintype.rightInverse_bijInv _ _
     inv_zero := by simp [Inv.inv, dif_pos rfl] }
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel
+-/
 
+/- warning: exists_eq_pow_of_mul_eq_pow_of_coprime -> exists_eq_pow_of_mul_eq_pow_of_coprime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : CommSemiring.{u1} R] [_inst_4 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)] [_inst_5 : GCDMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R _inst_3 _inst_4)] [_inst_6 : Unique.{succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))] {a : R} {b : R} {c : R} {n : Nat}, (IsCoprime.{u1} R _inst_3 a b) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))))) a b) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) c n)) -> (Exists.{succ u1} R (fun (d : R) => Eq.{succ u1} R a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) d n)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_3 : CommSemiring.{u1} R] [_inst_4 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)] [_inst_5 : GCDMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R _inst_3 _inst_4)] [_inst_6 : Unique.{succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))] {a : R} {b : R} {c : R} {n : Nat}, (IsCoprime.{u1} R _inst_3 a b) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) a b) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) c n)) -> (Exists.{succ u1} R (fun (d : R) => Eq.{succ u1} R a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) d n)))
+Case conversion may be inaccurate. Consider using '#align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprimeₓ'. -/
 theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {a b c : R} {n : ℕ} (cp : IsCoprime a b) (h : a * b = c ^ n) :
     ∃ d : R, a = d ^ n :=
@@ -75,6 +95,12 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
     dvd_add (dvd_mul_of_dvd_right (gcd_dvd_left _ _) _) (dvd_mul_of_dvd_right (gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 
+/- warning: finset.exists_eq_pow_of_mul_eq_pow_of_coprime -> Finset.exists_eq_pow_of_mul_eq_pow_of_coprime is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_3 : CommSemiring.{u2} R] [_inst_4 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)] [_inst_5 : GCDMonoid.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R _inst_3 _inst_4)] [_inst_6 : Unique.{succ u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))))] {n : Nat} {c : R} {s : Finset.{u1} ι} {f : ι -> R}, (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (forall (j : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) j s) -> (Ne.{succ u1} ι i j) -> (IsCoprime.{u2} R _inst_3 (f i) (f j)))) -> (Eq.{succ u2} R (Finset.prod.{u2, u1} R ι (CommSemiring.toCommMonoid.{u2} R _inst_3) s (fun (i : ι) => f i)) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))))) c n)) -> (forall (i : ι), (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Exists.{succ u2} R (fun (d : R) => Eq.{succ u2} R (f i) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))))) d n))))
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_3 : CommSemiring.{u1} R] [_inst_4 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)] [_inst_5 : GCDMonoid.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R _inst_3 _inst_4)] [_inst_6 : Unique.{succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))] {n : Nat} {c : R} {s : Finset.{u2} ι} {f : ι -> R}, (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (forall (j : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Ne.{succ u2} ι i j) -> (IsCoprime.{u1} R _inst_3 (f i) (f j)))) -> (Eq.{succ u1} R (Finset.prod.{u1, u2} R ι (CommSemiring.toCommMonoid.{u1} R _inst_3) s (fun (i : ι) => f i)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) c n)) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Exists.{succ u1} R (fun (d : R) => Eq.{succ u1} R (f i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))))) d n))))
+Case conversion may be inaccurate. Consider using '#align finset.exists_eq_pow_of_mul_eq_pow_of_coprime Finset.exists_eq_pow_of_mul_eq_pow_of_coprimeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
@@ -98,6 +124,7 @@ section Ring
 
 variable [Ring R] [IsDomain R] [Fintype R]
 
+#print Fintype.divisionRingOfIsDomain /-
 /-- Every finite domain is a division ring.
 
 TODO: Prove Wedderburn's little theorem,
@@ -106,7 +133,9 @@ def Fintype.divisionRingOfIsDomain (R : Type _) [Ring R] [IsDomain R] [Decidable
     DivisionRing R :=
   { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with }
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
+-/
 
+#print Fintype.fieldOfDomain /-
 /-- Every finite commutative domain is a field.
 
 TODO: Prove Wedderburn's little theorem, which shows a finite domain is automatically commutative,
@@ -114,17 +143,26 @@ dropping one assumption from this theorem. -/
 def Fintype.fieldOfDomain (R) [CommRing R] [IsDomain R] [DecidableEq R] [Fintype R] : Field R :=
   { Fintype.groupWithZeroOfCancel R, ‹CommRing R› with }
 #align fintype.field_of_domain Fintype.fieldOfDomain
+-/
 
+#print Finite.isField_of_domain /-
 theorem Finite.isField_of_domain (R) [CommRing R] [IsDomain R] [Finite R] : IsField R :=
   by
   cases nonempty_fintype R
   exact @Field.toIsField R (@Fintype.fieldOfDomain R _ _ (Classical.decEq R) _)
 #align finite.is_field_of_domain Finite.isField_of_domain
+-/
 
 end Ring
 
 variable [CommRing R] [IsDomain R] [Group G]
 
+/- warning: card_nth_roots_subgroup_units -> card_nthRoots_subgroup_units is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align card_nth_roots_subgroup_units card_nthRoots_subgroup_unitsₓ'. -/
 theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective f) {n : ℕ}
     (hn : 0 < n) (g₀ : G) :
     ({ g ∈ univ | g ^ n = g₀ } : Finset G).card ≤ (nthRoots n (f g₀)).card :=
@@ -140,6 +178,12 @@ theorem card_nthRoots_subgroup_units [Fintype G] (f : G →* R) (hf : Injective
     assumption
 #align card_nth_roots_subgroup_units card_nthRoots_subgroup_units
 
+/- warning: is_cyclic_of_subgroup_is_domain -> isCyclic_of_subgroup_isDomain is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_cyclic_of_subgroup_is_domain isCyclic_of_subgroup_isDomainₓ'. -/
 /-- A finite subgroup of the unit group of an integral domain is cyclic. -/
 theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective f) : IsCyclic G := by
   classical
@@ -160,6 +204,12 @@ section
 
 variable (S : Subgroup Rˣ) [Finite S]
 
+/- warning: subgroup_units_cyclic -> subgroup_units_cyclic is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (S : Subgroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) [_inst_4 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Subgroup.setLike.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S)], IsCyclic.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Subgroup.setLike.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))))) S) (Subgroup.toGroup.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) S)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (S : Subgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) [_inst_4 : Finite.{succ u1} (Subtype.{succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Membership.mem.{u1, u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Subgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Subgroup.instSetLikeSubgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S))], IsCyclic.{u1} (Subtype.{succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Membership.mem.{u1, u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Subgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Subgroup.instSetLikeSubgroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) x S)) (Subgroup.toGroup.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Units.instGroupUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) S)
+Case conversion may be inaccurate. Consider using '#align subgroup_units_cyclic subgroup_units_cyclicₓ'. -/
 /-- A finite subgroup of the units of an integral domain is cyclic. -/
 instance subgroup_units_cyclic : IsCyclic S :=
   by
@@ -179,6 +229,12 @@ open Polynomial
 
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
 
+/- warning: polynomial.div_eq_quo_add_rem_div -> Polynomial.div_eq_quo_add_rem_div is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (K : Type) [_inst_4 : Field.{0} K] [_inst_5 : Algebra.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4)))] [_inst_6 : IsFractionRing.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) K (EuclideanDomain.toCommRing.{0} K (Field.toEuclideanDomain.{0} K _inst_4)) _inst_5] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) {g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) g) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (r : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) r) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) g)) (Eq.{1} K (HDiv.hDiv.{0, 0, 0} K K K (instHDiv.{0} K (DivInvMonoid.toHasDiv.{0} K (DivisionRing.toDivInvMonoid.{0} K (Field.toDivisionRing.{0} K _inst_4)))) ((fun (a : Type.{u1}) (b : Type) [self : HasLiftT.{succ u1, 1} a b] => self.0) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (algebraMap.coeHTCT.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))) _inst_5) f) ((fun (a : Type.{u1}) (b : Type) [self : HasLiftT.{succ u1, 1} a b] => self.0) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (algebraMap.coeHTCT.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))) _inst_5) g)) (HAdd.hAdd.{0, 0, 0} K K K (instHAdd.{0} K (Distrib.toHasAdd.{0} K (Ring.toDistrib.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))))) ((fun (a : Type.{u1}) (b : Type) [self : HasLiftT.{succ u1, 1} a b] => self.0) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (algebraMap.coeHTCT.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))) _inst_5) q) (HDiv.hDiv.{0, 0, 0} K K K (instHDiv.{0} K (DivInvMonoid.toHasDiv.{0} K (DivisionRing.toDivInvMonoid.{0} K (Field.toDivisionRing.{0} K _inst_4)))) ((fun (a : Type.{u1}) (b : Type) [self : HasLiftT.{succ u1, 1} a b] => self.0) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (algebraMap.coeHTCT.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))) _inst_5) r) ((fun (a : Type.{u1}) (b : Type) [self : HasLiftT.{succ u1, 1} a b] => self.0) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (algebraMap.coeHTCT.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{0} K (DivisionRing.toRing.{0} K (Field.toDivisionRing.{0} K _inst_4))) _inst_5) g)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (K : Type) [_inst_4 : Field.{0} K] [_inst_5 : Algebra.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (DivisionSemiring.toSemiring.{0} K (Semifield.toDivisionSemiring.{0} K (Field.toSemifield.{0} K _inst_4)))] [_inst_6 : IsFractionRing.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1) K (EuclideanDomain.toCommRing.{0} K (Field.toEuclideanDomain.{0} K _inst_4)) _inst_5] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) {g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) g) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (r : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) g)) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) f) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) f) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) f) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) f) (Field.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) f) _inst_4)) (FunLike.coe.{succ u1, succ u1, 1} (RingHom.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) K (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{0} K (DivisionSemiring.toSemiring.{0} K (Semifield.toDivisionSemiring.{0} K (Field.toSemifield.{0} K _inst_4))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => K) a) (MulHomClass.toFunLike.{u1, u1, 0} (RingHom.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} 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(CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{0} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} K (Semiring.toNonAssocSemiring.{0} K (DivisionSemiring.toSemiring.{0} K (Semifield.toDivisionSemiring.{0} K (Field.toSemifield.{0} K _inst_4)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, 0} (RingHom.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) K (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{0} K (DivisionSemiring.toSemiring.{0} K 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(CommRing.toCommSemiring.{u1} R _inst_1))) K (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (DivisionSemiring.toSemiring.{0} K (Semifield.toDivisionSemiring.{0} K (Field.toSemifield.{0} K _inst_4))) _inst_5) g)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.div_eq_quo_add_rem_div Polynomial.div_eq_quo_add_rem_divₓ'. -/
 theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     ∃ q r : R[X], r.degree < g.degree ∧ (↑f : K) / ↑g = ↑q + ↑r / ↑g :=
   by
@@ -196,6 +252,12 @@ end EuclideanDivision
 
 variable [Fintype G]
 
+/- warning: card_fiber_eq_of_mem_range -> card_fiber_eq_of_mem_range is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_3 : Group.{u1} G] [_inst_4 : Fintype.{u1} G] {H : Type.{u2}} [_inst_5 : Group.{u2} H] [_inst_6 : DecidableEq.{succ u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_3))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_5)))) {x : H} {y : H}, (Membership.Mem.{u2, u2} H (Set.{u2} H) (Set.hasMem.{u2} H) x (Set.range.{u2, succ u1} H G (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_3))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_5)))) (fun (_x : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_3))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_rangeₓ'. -/
 theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
     (univ.filterₓ fun g => f g = x).card = (univ.filterₓ fun g => f g = y).card :=
@@ -213,6 +275,12 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
       mul_inv_cancel_right, inv_mul_cancel_right]
 #align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_range
 
+/- warning: sum_hom_units_eq_zero -> sum_hom_units_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align sum_hom_units_eq_zero sum_hom_units_eq_zeroₓ'. -/
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
 theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) = 0 := by
@@ -279,6 +347,12 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
     simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero
 
+/- warning: sum_hom_units -> sum_hom_units is a dubious translation:
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(DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) _inst_5 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Fintype.card.{u2} G _inst_4)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {G : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Group.{u2} G] [_inst_4 : Fintype.{u2} G] (f : MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) [_inst_5 : Decidable (Eq.{max (succ u1) (succ u2)} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) f (OfNat.ofNat.{max u1 u2} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) 1 (One.toOfNat1.{max u1 u2} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (instOneMonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))], Eq.{succ u1} R (Finset.sum.{u1, u2} R G (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finset.univ.{u2} G _inst_4) (fun (g : G) => FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) G R (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3)))) (MulOneClass.toMul.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidHom.monoidHomClass.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) f g)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (ite.{1} Nat (Eq.{max (succ u1) (succ u2)} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) f (OfNat.ofNat.{max u1 u2} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) 1 (One.toOfNat1.{max u1 u2} (MonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (instOneMonoidHom.{u2, u1} G R (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_3))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) _inst_5 (Fintype.card.{u2} G _inst_4) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+Case conversion may be inaccurate. Consider using '#align sum_hom_units sum_hom_unitsₓ'. -/
 /-- In an integral domain, a sum indexed by a homomorphism from a finite group is zero,
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/

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

@@ -274,7 +274,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
               rw [← pow_eq_mod_orderOf, hn]⟩
       _ = 0 := _
       
-    rw [← mul_left_inj' hx1, zero_mul, geom_sum_mul, coe_coe]
+    rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul, coe_coe]
     norm_cast
     simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero

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

@@ -75,7 +75,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
     dvd_add (dvd_mul_of_dvd_right (gcd_dvd_left _ _) _) (dvd_mul_of_dvd_right (gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
@@ -237,15 +237,15 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
       _ =
           ∑ u : Rˣ in univ.image f.to_hom_units,
             (univ.filter fun g => f.to_hom_units g = u).card • u :=
-        sum_comp (coe : Rˣ → R) f.to_hom_units
+        (sum_comp (coe : Rˣ → R) f.to_hom_units)
       _ = ∑ u : Rˣ in univ.image f.to_hom_units, c • u :=
-        sum_congr rfl fun u hu => congr_arg₂ _ _ rfl
+        (sum_congr rfl fun u hu => congr_arg₂ _ _ rfl)
       -- remaining goal 1, proven below
           _ =
           ∑ b : MonoidHom.range f.to_hom_units, c • ↑b :=
-        Finset.sum_subtype _ (by simp) _
+        (Finset.sum_subtype _ (by simp) _)
       _ = c • ∑ b : MonoidHom.range f.to_hom_units, (b : R) := smul_sum.symm
-      _ = c • 0 := congr_arg₂ _ rfl _
+      _ = c • 0 := (congr_arg₂ _ rfl _)
       -- remaining goal 2, proven below
           _ =
           0 :=

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

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

@@ -98,6 +98,7 @@ def Fintype.divisionRingOfIsDomain (R : Type*) [Ring R] [IsDomain R] [DecidableE
     DivisionRing R where
   __ := Fintype.groupWithZeroOfCancel R
   __ := ‹Ring R›
+  nnqsmul := _
   qsmul := _
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
 

This is the parts of the diff of #11203 which don't mention NNRat.cast.

• Use more where notation.
• Write qsmul := _ instead of qsmul := qsmulRec _ to make the instances more robust to definition changes.
• Delete qsmulRec.
• Move qsmul before ratCast_def in instance declarations.
• Name more instances.
• Rename rat_smul to qsmul.

@@ -95,9 +95,10 @@ variable [Ring R] [IsDomain R] [Fintype R]
 /-- Every finite domain is a division ring. More generally, they are fields; this can be found in
 `Mathlib.RingTheory.LittleWedderburn`. -/
 def Fintype.divisionRingOfIsDomain (R : Type*) [Ring R] [IsDomain R] [DecidableEq R] [Fintype R] :
-    DivisionRing R :=
-  { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with
-    qsmul := qsmulRec _}
+    DivisionRing R where
+  __ := Fintype.groupWithZeroOfCancel R
+  __ := ‹Ring R›
+  qsmul := _
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
 
 /-- Every finite commutative domain is a field. More generally, commutativity is not required: this

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

@@ -241,7 +241,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
       _ = ∑ b : MonoidHom.range f.toHomUnits, c • ((b : Rˣ) : R) :=
         (Finset.sum_subtype _ (by simp) _)
       _ = c • ∑ b : MonoidHom.range f.toHomUnits, ((b : Rˣ) : R) := smul_sum.symm
-      _ = c • (0 : R) := (congr_arg₂ _ rfl ?_)
+      _ = c • (0 : R) := congr_arg₂ _ rfl ?_
       -- remaining goal 2, proven below
       _ = (0 : R) := smul_zero _
     · -- remaining goal 1

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
 -/
-import Mathlib.Data.Polynomial.RingDivision
-import Mathlib.GroupTheory.SpecificGroups.Cyclic
 import Mathlib.Algebra.GeomSum
+import Mathlib.Algebra.Polynomial.RingDivision
+import Mathlib.GroupTheory.SpecificGroups.Cyclic
 
 #align_import ring_theory.integral_domain from "leanprover-community/mathlib"@"6e70e0d419bf686784937d64ed4bfde866ff229e"
 

Follows on from #6262. Again, this does not attempt to fix any diamonds; it only identifies where they may be.

@@ -96,13 +96,14 @@ variable [Ring R] [IsDomain R] [Fintype R]
 `Mathlib.RingTheory.LittleWedderburn`. -/
 def Fintype.divisionRingOfIsDomain (R : Type*) [Ring R] [IsDomain R] [DecidableEq R] [Fintype R] :
     DivisionRing R :=
-  { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with }
+  { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with
+    qsmul := qsmulRec _}
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
 
 /-- Every finite commutative domain is a field. More generally, commutativity is not required: this
 can be found in `Mathlib.RingTheory.LittleWedderburn`. -/
 def Fintype.fieldOfDomain (R) [CommRing R] [IsDomain R] [DecidableEq R] [Fintype R] : Field R :=
-  { Fintype.groupWithZeroOfCancel R, ‹CommRing R› with }
+  { Fintype.divisionRingOfIsDomain R, ‹CommRing R› with }
 #align fintype.field_of_domain Fintype.fieldOfDomain
 
 theorem Finite.isField_of_domain (R) [CommRing R] [IsDomain R] [Finite R] : IsField R := by

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -64,7 +64,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type*} [CommSemiring R] [IsD
   refine' exists_eq_pow_of_mul_eq_pow (isUnit_of_dvd_one _) h
   obtain ⟨x, y, hxy⟩ := cp
   rw [← hxy]
-  exact  -- porting note: added `GCDMonoid.` twice
+  exact  -- Porting note: added `GCDMonoid.` twice
     dvd_add (dvd_mul_of_dvd_right (GCDMonoid.gcd_dvd_left _ _) _)
       (dvd_mul_of_dvd_right (GCDMonoid.gcd_dvd_right _ _) _)
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
@@ -114,7 +114,7 @@ end Ring
 
 variable [CommRing R] [IsDomain R] [Group G]
 
--- porting note: Finset doesn't seem to have `{g ∈ univ | g^n = g₀}` notation anymore,
+-- Porting note: Finset doesn't seem to have `{g ∈ univ | g^n = g₀}` notation anymore,
 -- so we have to use `Finset.filter` instead
 theorem card_nthRoots_subgroup_units [Fintype G] [DecidableEq G] (f : G →* R) (hf : Injective f)
     {n : ℕ} (hn : 0 < n) (g₀ : G) :
@@ -152,7 +152,7 @@ variable (S : Subgroup Rˣ) [Finite S]
 
 /-- A finite subgroup of the units of an integral domain is cyclic. -/
 instance subgroup_units_cyclic : IsCyclic S := by
-  -- porting note: the original proof used a `coe`, but I was not able to get it to work.
+  -- Porting note: the original proof used a `coe`, but I was not able to get it to work.
   apply isCyclic_of_subgroup_isDomain (R := R) (G := S) _ _
   · exact MonoidHom.mk (OneHom.mk (fun s => ↑s.val) rfl) (by simp)
   · exact Units.ext.comp Subtype.val_injective
@@ -175,10 +175,10 @@ theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
   refine' ⟨f /ₘ g, f %ₘ g, _, _⟩
   · exact degree_modByMonic_lt _ hg
   · have hg' : algebraMap R[X] K g ≠ 0 :=
-      -- porting note: the proof was `by exact_mod_cast Monic.ne_zero hg`
+      -- Porting note: the proof was `by exact_mod_cast Monic.ne_zero hg`
       (map_ne_zero_iff _ (IsFractionRing.injective R[X] K)).mpr (Monic.ne_zero hg)
     field_simp [hg']
-    -- porting note: `norm_cast` was here, but does nothing.
+    -- Porting note: `norm_cast` was here, but does nothing.
     rw [add_comm, mul_comm, ← map_mul, ← map_add, modByMonic_add_div f hg]
 
 #align polynomial.div_eq_quo_add_rem_div Polynomial.div_eq_quo_add_rem_div
@@ -191,7 +191,7 @@ variable [Fintype G]
 
 theorem card_fiber_eq_of_mem_range {H : Type*} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
-    -- porting note: the `filter` had an index `ₓ` that I removed.
+    -- Porting note: the `filter` had an index `ₓ` that I removed.
     (univ.filter fun g => f g = x).card = (univ.filter fun g => f g = y).card := by
   rcases hx with ⟨x, rfl⟩
   rcases hy with ⟨y, rfl⟩
@@ -199,14 +199,14 @@ theorem card_fiber_eq_of_mem_range {H : Type*} [Group H] [DecidableEq H] (f : G
   · simp (config := { contextual := true }) only [*, mem_filter, one_mul, MonoidHom.map_mul,
       mem_univ, mul_right_inv, eq_self_iff_true, MonoidHom.map_mul_inv, and_self_iff,
       forall_true_iff]
-    -- porting note: added the following `simp`
+    -- Porting note: added the following `simp`
     simp only [true_and, map_inv, mul_right_inv, one_mul, and_self, implies_true, forall_const]
   · simp only [mul_left_inj, imp_self, forall₂_true_iff]
   · simp only [true_and_iff, mem_filter, mem_univ] at hg
     simp only [hg, mem_filter, one_mul, MonoidHom.map_mul, mem_univ, mul_right_inv,
       eq_self_iff_true, exists_prop_of_true, MonoidHom.map_mul_inv, and_self_iff,
       mul_inv_cancel_right, inv_mul_cancel_right]
-    -- porting note: added the next line.  It is weird!
+    -- Porting note: added the next line.  It is weird!
     simp only [map_inv, mul_right_inv, one_mul, and_self, exists_prop]
 #align card_fiber_eq_of_mem_range card_fiber_eq_of_mem_range
 
@@ -225,7 +225,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
       cases' hx ⟨f.toHomUnits g, g, rfl⟩ with n hn
       rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
         eq_comm] at hn
-    replace hx1 : (x.val : R) - 1 ≠ 0 := -- porting note: was `(x : R)`
+    replace hx1 : (x.val : R) - 1 ≠ 0 := -- Porting note: was `(x : R)`
       fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
     let c := (univ.filter fun g => f.toHomUnits g = 1).card
     calc
@@ -276,7 +276,7 @@ theorem sum_hom_units (f : G →* R) [Decidable (f = 1)] :
     ∑ g : G, f g = if f = 1 then Fintype.card G else 0 := by
   split_ifs with h
   · simp [h, card_univ]
-  · rw [cast_zero] -- porting note: added
+  · rw [cast_zero] -- Porting note: added
     exact sum_hom_units_eq_zero f h
 #align sum_hom_units sum_hom_units
 

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -214,10 +214,9 @@ theorem card_fiber_eq_of_mem_range {H : Type*} [Group H] [DecidableEq H] (f : G
 -/
 theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
   classical
-    obtain ⟨x, hx⟩ :
-      ∃ x : MonoidHom.range f.toHomUnits,
-        ∀ y : MonoidHom.range f.toHomUnits, y ∈ Submonoid.powers x
-    exact IsCyclic.exists_monoid_generator
+    obtain ⟨x, hx⟩ : ∃ x : MonoidHom.range f.toHomUnits,
+        ∀ y : MonoidHom.range f.toHomUnits, y ∈ Submonoid.powers x :=
+      IsCyclic.exists_monoid_generator
     have hx1 : x ≠ 1 := by
       rintro rfl
       apply hf

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

This follows on from #6964.

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

@@ -226,8 +226,8 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
       cases' hx ⟨f.toHomUnits g, g, rfl⟩ with n hn
       rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
         eq_comm] at hn
-    replace hx1 : (x.val : R) - 1 ≠ 0  -- porting note: was `(x : R)`
-    exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
+    replace hx1 : (x.val : R) - 1 ≠ 0 := -- porting note: was `(x : R)`
+      fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
     let c := (univ.filter fun g => f.toHomUnits g = 1).card
     calc
       ∑ g : G, f g = ∑ g : G, (f.toHomUnits g : R) := rfl

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

@@ -255,15 +255,14 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
       (∑ b : MonoidHom.range f.toHomUnits, ((b : Rˣ) : R))
         = ∑ n in range (orderOf x), ((x : Rˣ) : R) ^ n :=
         Eq.symm <|
-          sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
-            (by simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow,
-                Units.val_pow_eq_pow_val])
-            (fun m n hm hn => pow_injOn_Iio_orderOf (by simpa only [mem_range] using hm)
-                (by simpa only [mem_range] using hn))
+          sum_nbij (x ^ ·) (by simp only [mem_univ, forall_true_iff])
+            (by simpa using pow_injOn_Iio_orderOf)
             (fun b _ => let ⟨n, hn⟩ := hx b
               ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)),
                -- Porting note: have to use `dsimp` to apply the function
                by dsimp at hn ⊢; rw [pow_mod_orderOf, hn]⟩)
+            (by simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow,
+                Units.val_pow_eq_pow_val])
       _ = 0 := ?_
 
     rw [← mul_left_inj' hx1, zero_mul, geom_sum_mul]

Follow-up #9184

@@ -72,7 +72,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type*} [CommSemiring R] [IsD
 nonrec
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type*} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
-    (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
+    (h : ∀ i ∈ s, ∀ j ∈ s, i ≠ j → IsCoprime (f i) (f j))
     (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
     intro i hi

Co-authored-by: Eric Rodriguez <37984851+ericrbg@users.noreply.github.com>

@@ -19,9 +19,10 @@ Assorted theorems about integral domains.
 * `isCyclic_of_subgroup_isDomain`: A finite subgroup of the units of an integral domain is cyclic.
 * `Fintype.fieldOfDomain`: A finite integral domain is a field.
 
-## TODO
+## Notes
 
-Prove Wedderburn's little theorem, which shows that all finite division rings are actually fields.
+Wedderburn's little theorem, which shows that all finite division rings are actually fields,
+is in `Mathlib.RingTheory.LittleWedderburn`.
 
 ## Tags
 
@@ -91,19 +92,15 @@ section Ring
 
 variable [Ring R] [IsDomain R] [Fintype R]
 
-/-- Every finite domain is a division ring.
-
-TODO: Prove Wedderburn's little theorem,
-which shows a finite domain is in fact commutative, hence a field. -/
+/-- Every finite domain is a division ring. More generally, they are fields; this can be found in
+`Mathlib.RingTheory.LittleWedderburn`. -/
 def Fintype.divisionRingOfIsDomain (R : Type*) [Ring R] [IsDomain R] [DecidableEq R] [Fintype R] :
     DivisionRing R :=
   { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with }
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
 
-/-- Every finite commutative domain is a field.
-
-TODO: Prove Wedderburn's little theorem, which shows a finite domain is automatically commutative,
-dropping one assumption from this theorem. -/
+/-- Every finite commutative domain is a field. More generally, commutativity is not required: this
+can be found in `Mathlib.RingTheory.LittleWedderburn`. -/
 def Fintype.fieldOfDomain (R) [CommRing R] [IsDomain R] [DecidableEq R] [Fintype R] : Field R :=
   { Fintype.groupWithZeroOfCancel R, ‹CommRing R› with }
 #align fintype.field_of_domain Fintype.fieldOfDomain

Many lemmas in GroupTheory.OrderOfElement were stated for elements of finite groups even though they work more generally for torsion elements of possibly infinite groups. This PR generalises those lemmas (and leaves convenience lemmas stated for finite groups), and fixes a bunch of names to use dot notation.

Renames

• Function.eq_of_lt_minimalPeriod_of_iterate_eq → Function.iterate_injOn_Iio_minimalPeriod
• Function.eq_iff_lt_minimalPeriod_of_iterate_eq → Function.iterate_eq_iterate_iff_of_lt_minimalPeriod
• isOfFinOrder_iff_coe → Submonoid.isOfFinOrder_coe
• orderOf_pos' → IsOfFinOrder.orderOf_pos
• pow_eq_mod_orderOf → pow_mod_orderOf (and turned around)
• pow_injective_of_lt_orderOf → pow_injOn_Iio_orderOf
• mem_powers_iff_mem_range_order_of' → IsOfFinOrder.mem_powers_iff_mem_range_orderOf
• orderOf_pow'' → IsOfFinOrder.orderOf_pow
• orderOf_pow_coprime → Nat.Coprime.orderOf_pow
• zpow_eq_mod_orderOf → zpow_mod_orderOf (and turned around)
• exists_pow_eq_one → isOfFinOrder_of_finite
• pow_apply_eq_pow_mod_orderOf_cycleOf_apply → pow_mod_orderOf_cycleOf_apply

New lemmas

• IsOfFinOrder.powers_eq_image_range_orderOf
• IsOfFinOrder.natCard_powers_le_orderOf
• IsOfFinOrder.finite_powers
• finite_powers
• infinite_powers
• Nat.card_submonoidPowers
• IsOfFinOrder.mem_powers_iff_mem_zpowers
• IsOfFinOrder.powers_eq_zpowers
• IsOfFinOrder.mem_zpowers_iff_mem_range_orderOf
• IsOfFinOrder.exists_pow_eq_one

Other changes

• Move decidableMemPowers/fintypePowers to GroupTheory.Submonoid.Membership and decidableMemZpowers/fintypeZpowers to GroupTheory.Subgroup.ZPowers.
• finEquivPowers, finEquivZpowers, powersEquivPowers and zpowersEquivZpowers now assume IsOfFinTorsion x instead of Finite G.
• isOfFinOrder_iff_pow_eq_one now takes one less explicit argument.
• Delete Equiv.Perm.IsCycle.exists_pow_eq_one since it was saying that a permutation over a finite type is torsion, but this is trivial since the group of permutation is itself finite, so we can use isOfFinOrder_of_finite instead.

@@ -261,13 +261,12 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
           sum_bij (fun n _ => x ^ n) (by simp only [mem_univ, forall_true_iff])
             (by simp only [imp_true_iff, eq_self_iff_true, Subgroup.coe_pow,
                 Units.val_pow_eq_pow_val])
-            (fun m n hm hn =>
-              pow_injective_of_lt_orderOf _ (by simpa only [mem_range] using hm)
+            (fun m n hm hn => pow_injOn_Iio_orderOf (by simpa only [mem_range] using hm)
                 (by simpa only [mem_range] using hn))
             (fun b _ => let ⟨n, hn⟩ := hx b
               ⟨n % orderOf x, mem_range.2 (Nat.mod_lt _ (orderOf_pos _)),
                -- Porting note: have to use `dsimp` to apply the function
-               by dsimp at hn ⊢; rw [← pow_eq_mod_orderOf, hn]⟩)
+               by dsimp at hn ⊢; rw [pow_mod_orderOf, hn]⟩)
       _ = 0 := ?_
 
     rw [← mul_left_inj' hx1, zero_mul, geom_sum_mul]

Removes nonterminal simps on lines looking like simp [...]

@@ -52,7 +52,7 @@ def Fintype.groupWithZeroOfCancel (M : Type*) [CancelMonoidWithZero M] [Decidabl
     ‹CancelMonoidWithZero M› with
     inv := fun a => if h : a = 0 then 0 else Fintype.bijInv (mul_right_bijective_of_finite₀ h) 1
     mul_inv_cancel := fun a ha => by
-      simp [Inv.inv, dif_neg ha]
+      simp only [Inv.inv, dif_neg ha]
       exact Fintype.rightInverse_bijInv _ _
     inv_zero := by simp [Inv.inv, dif_pos rfl] }
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel

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

@@ -120,7 +120,7 @@ variable [CommRing R] [IsDomain R] [Group G]
 -- porting note: Finset doesn't seem to have `{g ∈ univ | g^n = g₀}` notation anymore,
 -- so we have to use `Finset.filter` instead
 theorem card_nthRoots_subgroup_units [Fintype G] [DecidableEq G] (f : G →* R) (hf : Injective f)
-  {n : ℕ} (hn : 0 < n) (g₀ : G) :
+    {n : ℕ} (hn : 0 < n) (g₀ : G) :
     Finset.card (Finset.univ.filter (fun g ↦ g^n = g₀)) ≤ Multiset.card (nthRoots n (f g₀)) := by
   haveI : DecidableEq R := Classical.decEq _
   refine' le_trans _ (nthRoots n (f g₀)).toFinset_card_le

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

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

@@ -270,7 +270,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0
                by dsimp at hn ⊢; rw [← pow_eq_mod_orderOf, hn]⟩)
       _ = 0 := ?_
 
-    rw [← mul_left_inj' hx1, MulZeroClass.zero_mul, geom_sum_mul]
+    rw [← mul_left_inj' hx1, zero_mul, geom_sum_mul]
     norm_cast
     simp [pow_orderOf_eq_one]
 #align sum_hom_units_eq_zero sum_hom_units_eq_zero

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

This has nice performance benefits.

@@ -35,7 +35,7 @@ open Finset Polynomial Function BigOperators Nat
 section CancelMonoidWithZero
 
 -- There doesn't seem to be a better home for these right now
-variable {M : Type _} [CancelMonoidWithZero M] [Finite M]
+variable {M : Type*} [CancelMonoidWithZero M] [Finite M]
 
 theorem mul_right_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b => a * b :=
   Finite.injective_iff_bijective.1 <| mul_right_injective₀ ha
@@ -46,7 +46,7 @@ theorem mul_left_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b
 #align mul_left_bijective_of_finite₀ mul_left_bijective_of_finite₀
 
 /-- Every finite nontrivial cancel_monoid_with_zero is a group_with_zero. -/
-def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [DecidableEq M] [Fintype M]
+def Fintype.groupWithZeroOfCancel (M : Type*) [CancelMonoidWithZero M] [DecidableEq M] [Fintype M]
     [Nontrivial M] : GroupWithZero M :=
   { ‹Nontrivial M›,
     ‹CancelMonoidWithZero M› with
@@ -57,7 +57,7 @@ def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [Decidab
     inv_zero := by simp [Inv.inv, dif_pos rfl] }
 #align fintype.group_with_zero_of_cancel Fintype.groupWithZeroOfCancel
 
-theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [IsDomain R]
+theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type*} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {a b c : R} {n : ℕ} (cp : IsCoprime a b) (h : a * b = c ^ n) :
     ∃ d : R, a = d ^ n := by
   refine' exists_eq_pow_of_mul_eq_pow (isUnit_of_dvd_one _) h
@@ -69,7 +69,7 @@ theorem exists_eq_pow_of_mul_eq_pow_of_coprime {R : Type _} [CommSemiring R] [Is
 #align exists_eq_pow_of_mul_eq_pow_of_coprime exists_eq_pow_of_mul_eq_pow_of_coprime
 
 nonrec
-theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
+theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type*} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
     (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
@@ -85,7 +85,7 @@ theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemir
 
 end CancelMonoidWithZero
 
-variable {R : Type _} {G : Type _}
+variable {R : Type*} {G : Type*}
 
 section Ring
 
@@ -95,7 +95,7 @@ variable [Ring R] [IsDomain R] [Fintype R]
 
 TODO: Prove Wedderburn's little theorem,
 which shows a finite domain is in fact commutative, hence a field. -/
-def Fintype.divisionRingOfIsDomain (R : Type _) [Ring R] [IsDomain R] [DecidableEq R] [Fintype R] :
+def Fintype.divisionRingOfIsDomain (R : Type*) [Ring R] [IsDomain R] [DecidableEq R] [Fintype R] :
     DivisionRing R :=
   { show GroupWithZero R from Fintype.groupWithZeroOfCancel R, ‹Ring R› with }
 #align fintype.division_ring_of_is_domain Fintype.divisionRingOfIsDomain
@@ -192,7 +192,7 @@ end EuclideanDivision
 
 variable [Fintype G]
 
-theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
+theorem card_fiber_eq_of_mem_range {H : Type*} [Group H] [DecidableEq H] (f : G →* H) {x y : H}
     (hx : x ∈ Set.range f) (hy : y ∈ Set.range f) :
     -- porting note: the `filter` had an index `ₓ` that I removed.
     (univ.filter fun g => f g = x).card = (univ.filter fun g => f g = y).card := by

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.integral_domain
-! leanprover-community/mathlib commit 6e70e0d419bf686784937d64ed4bfde866ff229e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.RingDivision
 import Mathlib.GroupTheory.SpecificGroups.Cyclic
 import Mathlib.Algebra.GeomSum
 
+#align_import ring_theory.integral_domain from "leanprover-community/mathlib"@"6e70e0d419bf686784937d64ed4bfde866ff229e"
+
 /-!
 # Integral domains
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -160,8 +160,8 @@ variable (S : Subgroup Rˣ) [Finite S]
 instance subgroup_units_cyclic : IsCyclic S := by
   -- porting note: the original proof used a `coe`, but I was not able to get it to work.
   apply isCyclic_of_subgroup_isDomain (R := R) (G := S) _ _
-  . exact MonoidHom.mk (OneHom.mk (fun s => ↑s.val) rfl) (by simp)
-  . exact Units.ext.comp Subtype.val_injective
+  · exact MonoidHom.mk (OneHom.mk (fun s => ↑s.val) rfl) (by simp)
+  · exact Units.ext.comp Subtype.val_injective
 #align subgroup_units_cyclic subgroup_units_cyclic
 
 end

• 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

@@ -75,7 +75,7 @@ nonrec
 theorem Finset.exists_eq_pow_of_mul_eq_pow_of_coprime {ι R : Type _} [CommSemiring R] [IsDomain R]
     [GCDMonoid R] [Unique Rˣ] {n : ℕ} {c : R} {s : Finset ι} {f : ι → R}
     (h : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), i ≠ j → IsCoprime (f i) (f j))
-    (hprod : (∏ i in s, f i) = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
+    (hprod : ∏ i in s, f i = c ^ n) : ∀ i ∈ s, ∃ d : R, f i = d ^ n := by
   classical
     intro i hi
     rw [← insert_erase hi, prod_insert (not_mem_erase i s)] at hprod
@@ -218,7 +218,7 @@ theorem card_fiber_eq_of_mem_range {H : Type _} [Group H] [DecidableEq H] (f : G
 
 /-- In an integral domain, a sum indexed by a nontrivial homomorphism from a finite group is zero.
 -/
-theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) = 0 := by
+theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : ∑ g : G, f g = 0 := by
   classical
     obtain ⟨x, hx⟩ :
       ∃ x : MonoidHom.range f.toHomUnits,
@@ -236,7 +236,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
     exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
     let c := (univ.filter fun g => f.toHomUnits g = 1).card
     calc
-      (∑ g : G, f g) = ∑ g : G, (f.toHomUnits g : R) := rfl
+      ∑ g : G, f g = ∑ g : G, (f.toHomUnits g : R) := rfl
       _ = ∑ u : Rˣ in univ.image f.toHomUnits,
             (univ.filter fun g => f.toHomUnits g = u).card • (u : R) :=
         (sum_comp ((↑) : Rˣ → R) f.toHomUnits)
@@ -282,7 +282,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
 unless the homomorphism is trivial, in which case the sum is equal to the cardinality of the group.
 -/
 theorem sum_hom_units (f : G →* R) [Decidable (f = 1)] :
-    (∑ g : G, f g) = if f = 1 then Fintype.card G else 0 := by
+    ∑ g : G, f g = if f = 1 then Fintype.card G else 0 := by
   split_ifs with h
   · simp [h, card_univ]
   · rw [cast_zero] -- porting note: added

I wrote a script to find lines that contain an odd number of backticks

@@ -232,7 +232,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
       cases' hx ⟨f.toHomUnits g, g, rfl⟩ with n hn
       rwa [Subtype.ext_iff, Units.ext_iff, Subtype.coe_mk, MonoidHom.coe_toHomUnits, one_pow,
         eq_comm] at hn
-    replace hx1 : (x.val : R) - 1 ≠ 0  -- porting note: was `(x : R)
+    replace hx1 : (x.val : R) - 1 ≠ 0  -- porting note: was `(x : R)`
     exact fun h => hx1 (Subtype.eq (Units.ext (sub_eq_zero.1 h)))
     let c := (univ.filter fun g => f.toHomUnits g = 1).card
     calc

@@ -11,7 +11,6 @@ Authors: Johan Commelin, Chris Hughes
 import Mathlib.Data.Polynomial.RingDivision
 import Mathlib.GroupTheory.SpecificGroups.Cyclic
 import Mathlib.Algebra.GeomSum
-import Mathlib.Tactic.LibrarySearch
 
 /-!
 # Integral domains
@@ -20,8 +19,8 @@ Assorted theorems about integral domains.
 
 ## Main theorems
 
-* `is_cyclic_of_subgroup_is_domain`: A finite subgroup of the units of an integral domain is cyclic.
-* `fintype.field_of_domain`: A finite integral domain is a field.
+* `isCyclic_of_subgroup_isDomain`: A finite subgroup of the units of an integral domain is cyclic.
+* `Fintype.fieldOfDomain`: A finite integral domain is a field.
 
 ## TODO
 
@@ -31,14 +30,10 @@ Prove Wedderburn's little theorem, which shows that all finite division rings ar
 
 integral domain, finite integral domain, finite field
 -/
-set_option autoImplicit false
-
 
 section
 
-open Finset Polynomial Function
-
-open BigOperators Nat
+open Finset Polynomial Function BigOperators Nat
 
 section CancelMonoidWithZero
 
@@ -57,8 +52,7 @@ theorem mul_left_bijective_of_finite₀ {a : M} (ha : a ≠ 0) : Bijective fun b
 def Fintype.groupWithZeroOfCancel (M : Type _) [CancelMonoidWithZero M] [DecidableEq M] [Fintype M]
     [Nontrivial M] : GroupWithZero M :=
   { ‹Nontrivial M›,
-    ‹CancelMonoidWithZero
-        M› with
+    ‹CancelMonoidWithZero M› with
     inv := fun a => if h : a = 0 then 0 else Fintype.bijInv (mul_right_bijective_of_finite₀ h) 1
     mul_inv_cancel := fun a ha => by
       simp [Inv.inv, dif_neg ha]
@@ -154,7 +148,7 @@ theorem isCyclic_of_subgroup_isDomain [Finite G] (f : G →* R) (hf : Injective
 /-- The unit group of a finite integral domain is cyclic.
 
 To support `ℤˣ` and other infinite monoids with finite groups of units, this requires only
-`finite Rˣ` rather than deducing it from `finite R`. -/
+`Finite Rˣ` rather than deducing it from `Finite R`. -/
 instance [Finite Rˣ] : IsCyclic Rˣ :=
   isCyclic_of_subgroup_isDomain (Units.coeHom R) <| Units.ext
 
@@ -179,7 +173,7 @@ namespace Polynomial
 open Polynomial
 
 variable (K : Type) [Field K] [Algebra R[X] K] [IsFractionRing R[X] K]
-set_option maxHeartbeats 0
+
 theorem div_eq_quo_add_rem_div (f : R[X]) {g : R[X]} (hg : g.Monic) :
     ∃ q r : R[X], r.degree < g.degree ∧
       (algebraMap R[X] K f) / (algebraMap R[X] K g) =
@@ -243,8 +237,7 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
     let c := (univ.filter fun g => f.toHomUnits g = 1).card
     calc
       (∑ g : G, f g) = ∑ g : G, (f.toHomUnits g : R) := rfl
-      _ =
-          ∑ u : Rˣ in univ.image f.toHomUnits,
+      _ = ∑ u : Rˣ in univ.image f.toHomUnits,
             (univ.filter fun g => f.toHomUnits g = u).card • (u : R) :=
         (sum_comp ((↑) : Rˣ → R) f.toHomUnits)
       _ = ∑ u : Rˣ in univ.image f.toHomUnits, c • (u : R) :=
@@ -257,7 +250,6 @@ theorem sum_hom_units_eq_zero (f : G →* R) (hf : f ≠ 1) : (∑ g : G, f g) =
       _ = c • (0 : R) := (congr_arg₂ _ rfl ?_)
       -- remaining goal 2, proven below
       _ = (0 : R) := smul_zero _
-
     · -- remaining goal 1
       show (univ.filter fun g : G => f.toHomUnits g = u).card = c
       apply card_fiber_eq_of_mem_range f.toHomUnits

Co-authored-by: Vierkantor <vierkantor@vierkantor.com>