algebra.gcd_monoid.basic | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

550b5853

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

baba818b

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -835,7 +835,7 @@ theorem lcm_dvd_iff [GCDMonoid α] {a b c : α} : lcm a b ∣ c ↔ a ∣ c ∧
     have h : gcd a b ≠ 0 := fun H => h1 ((gcd_eq_zero_iff _ _).1 H).1
     rw [← mul_dvd_mul_iff_left h, (gcd_mul_lcm a b).dvd_iff_dvd_left, ←
       (gcd_mul_right' c a b).dvd_iff_dvd_right, dvd_gcd_iff, mul_comm b c, mul_dvd_mul_iff_left h1,
-      mul_dvd_mul_iff_right h2, and_comm']
+      mul_dvd_mul_iff_right h2, and_comm]
 #align lcm_dvd_iff lcm_dvd_iff
 -/

baba818b

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -694,7 +694,7 @@ theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd a (b
   · induction' k with k hk
     · simp only [pow_zero]
       exact (gcd_one_right' a).Dvd
-    rw [pow_succ, pow_succ]
+    rw [pow_succ', pow_succ']
     trans gcd a b * gcd a (b ^ k)
     apply gcd_mul_dvd_mul_gcd a b (b ^ k)
     exact (mul_dvd_mul_iff_left hg).mpr hk
@@ -1186,7 +1186,7 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
     rcases gcd_dvd_right a c with ⟨e, he⟩
     rcases gcd_dvd_left a c with ⟨f, hf⟩
     use e + f * d
-    rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel]
+    rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel_right]
 #align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_right
 -/

baba818b

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -467,7 +467,7 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     (fun h => by
       let ⟨ca, ha⟩ := gcd_dvd_left a b
       let ⟨cb, hb⟩ := gcd_dvd_right a b
-      rw [h, MulZeroClass.zero_mul] at ha hb  <;> exact ⟨ha, hb⟩)
+      rw [h, MulZeroClass.zero_mul] at ha hb <;> exact ⟨ha, hb⟩)
     fun ⟨ha, hb⟩ => by
     rw [ha, hb, ← zero_dvd_iff]
     apply dvd_gcd <;> rfl
@@ -642,7 +642,7 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ :=
   by
   by_cases h0 : gcd k m = 0
-  · rw [gcd_eq_zero_iff] at h0 
+  · rw [gcd_eq_zero_iff] at h0
     rcases h0 with ⟨rfl, rfl⟩
     refine' ⟨0, n, dvd_refl 0, dvd_refl n, _⟩
     simp
@@ -651,7 +651,7 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     suffices h : gcd k m * a ∣ gcd k m * n
     · cases' h with b hb
       use b
-      rw [mul_assoc] at hb 
+      rw [mul_assoc] at hb
       apply mul_left_cancel₀ h0 hb
     rw [← ha]
     exact dvd_gcd_mul_of_dvd_mul H
@@ -686,7 +686,7 @@ theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd
 theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd a (b ^ k) ∣ gcd a b ^ k :=
   by
   by_cases hg : gcd a b = 0
-  · rw [gcd_eq_zero_iff] at hg 
+  · rw [gcd_eq_zero_iff] at hg
     rcases hg with ⟨rfl, rfl⟩
     exact
       (gcd_zero_left' (0 ^ k : α)).Dvd.trans
@@ -722,11 +722,11 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
       apply dvd_trans _ hab.dvd
       apply gcd_dvd_gcd hd₁ (dvd_refl b)
   have h2 : d₁ ^ k ∣ a * b := by use d₂ ^ k; rw [h, hc]; exact mul_pow d₁ d₂ k
-  rw [mul_comm] at h2 
+  rw [mul_comm] at h2
   have h3 : d₁ ^ k ∣ a := by
     apply (dvd_gcd_mul_of_dvd_mul h2).trans
     rw [IsUnit.mul_left_dvd _ _ _ h1]
-  have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3 ; apply absurd (zero_dvd_iff.mp h3) ha
+  have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3; apply absurd (zero_dvd_iff.mp h3) ha
   exact ⟨h4, h3⟩
 #align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_pow
 -/
@@ -754,10 +754,10 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
   obtain ⟨d₁, d₂, hd₁, hd₂, hc⟩ := exists_dvd_and_dvd_of_dvd_mul hc
   use d₁
   obtain ⟨h0₁, ⟨a', ha'⟩⟩ := pow_dvd_of_mul_eq_pow ha hab h hc hd₁
-  rw [mul_comm] at h hc 
-  rw [(gcd_comm' a b).isUnit_iff] at hab 
+  rw [mul_comm] at h hc
+  rw [(gcd_comm' a b).isUnit_iff] at hab
   obtain ⟨h0₂, ⟨b', hb'⟩⟩ := pow_dvd_of_mul_eq_pow hb hab h hc hd₂
-  rw [ha', hb', hc, mul_pow] at h 
+  rw [ha', hb', hc, mul_pow] at h
   have h' : a' * b' = 1 := by
     apply (mul_right_inj' h0₁).mp; rw [mul_one]
     apply (mul_right_inj' h0₂).mp; rw [← h]
@@ -1120,7 +1120,7 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _) <;>
         apply lcm_dvd_iff.2 ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩
     cases g₁; cases g₂
-    dsimp only at hgcd hlcm 
+    dsimp only at hgcd hlcm
     simp only [hgcd, hlcm]⟩
 #align subsingleton_gcd_monoid_of_unique_units subsingleton_gcdMonoid_of_unique_units
 -/
@@ -1294,7 +1294,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
               (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))).symm
         set l := Classical.choose (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))
         obtain rfl | hb := eq_or_ne b 0
-        · simp only [normalize_zero, MulZeroClass.mul_zero, mul_eq_zero] at this 
+        · simp only [normalize_zero, MulZeroClass.mul_zero, mul_eq_zero] at this
           obtain ha | hl := this
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
@@ -1305,8 +1305,8 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
           contrapose! hab
           rw [← normalize_eq_zero, ← this, hab, MulZeroClass.zero_mul]
         have h2 : normalize (gcd a b * l) = gcd a b * l := by rw [this, normalize_idem]
-        rw [← normalize_gcd] at this 
-        rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2 
+        rw [← normalize_gcd] at this
+        rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2
     gcd_hMul_lcm := fun a b => by
       split_ifs with a0
       · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
@@ -1316,7 +1316,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
       split_ifs with a0; · rfl
-      rw [← normalize_eq_zero] at a0 
+      rw [← normalize_eq_zero] at a0
       have h :=
         (Classical.choose_spec
             (dvd_normalize_iff.2 ((gcd_dvd_left a 0).trans (Dvd.intro 0 rfl)))).symm
@@ -1324,7 +1324,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         by
         rw [← normalize_gcd]
         exact normalize_eq_normalize (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) (dvd_zero a))
-      rw [← gcd0] at a0 
+      rw [← gcd0] at a0
       apply Or.resolve_left (mul_eq_zero.1 _) a0
       rw [h, MulZeroClass.mul_zero, normalize_zero] }
 #align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCD
@@ -1352,7 +1352,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), mul_comm,
         mul_dvd_mul_iff_right h]
@@ -1364,7 +1364,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b),
         mul_dvd_mul_iff_right h_1]
@@ -1376,12 +1376,12 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm c b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd c b)]
       rcases ab with ⟨d, rfl⟩
-      rw [mul_eq_zero] at h_1 
-      push_neg at h_1 
+      rw [mul_eq_zero] at h_1
+      push_neg at h_1
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]
@@ -1418,7 +1418,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       apply mul_left_cancel₀ h0
       refine' trans _ (Classical.choose_spec (exists_gcd a b))
@@ -1435,7 +1435,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), normalize_dvd_iff,
         mul_comm, mul_dvd_mul_iff_right h]
@@ -1447,7 +1447,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), normalize_dvd_iff,
         mul_dvd_mul_iff_right h_1]
@@ -1459,15 +1459,15 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm c b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ←
         Classical.choose_spec
           (dvd_normalize_iff.2 (lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl))),
         dvd_normalize_iff]
       rcases ab with ⟨d, rfl⟩
-      rw [mul_eq_zero] at h_1 
-      push_neg at h_1 
+      rw [mul_eq_zero] at h_1
+      push_neg at h_1
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]

baba818b

bump to nightly-2024-02-23-08

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

ac9421d6

Diff

@@ -421,10 +421,10 @@ theorem gcd_assoc' [GCDMonoid α] (m n k : α) : Associated (gcd (gcd m n) k) (g
 #align gcd_assoc' gcd_assoc'
 -/
 
-instance [NormalizedGCDMonoid α] : IsCommutative α gcd :=
+instance [NormalizedGCDMonoid α] : Std.Commutative α gcd :=
   ⟨gcd_comm⟩
 
-instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
+instance [NormalizedGCDMonoid α] : Std.Associative α gcd :=
   ⟨gcd_assoc⟩
 
 #print gcd_eq_normalize /-
@@ -912,10 +912,10 @@ theorem lcm_assoc' [GCDMonoid α] (m n k : α) : Associated (lcm (lcm m n) k) (l
 #align lcm_assoc' lcm_assoc'
 -/
 
-instance [NormalizedGCDMonoid α] : IsCommutative α lcm :=
+instance [NormalizedGCDMonoid α] : Std.Commutative α lcm :=
   ⟨lcm_comm⟩
 
-instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
+instance [NormalizedGCDMonoid α] : Std.Associative α lcm :=
   ⟨lcm_assoc⟩
 
 #print lcm_eq_normalize /-

baba818b

bump to nightly-2024-02-14-08

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

b742255f

Diff

@@ -1059,8 +1059,8 @@ end Lcm
 
 namespace GCDMonoid
 
-#print GCDMonoid.prime_of_irreducible /-
-theorem prime_of_irreducible [GCDMonoid α] {x : α} (hi : Irreducible x) : Prime x :=
+#print Irreducible.prime /-
+theorem prime [GCDMonoid α] {x : α} (hi : Irreducible x) : Prime x :=
   ⟨hi.NeZero,
     ⟨hi.1, fun a b h => by
       cases' gcd_dvd_left x a with y hy
@@ -1071,13 +1071,13 @@ theorem prime_of_irreducible [GCDMonoid α] {x : α} (hi : Irreducible x) : Prim
       · left
         rw [hy]
         exact dvd_trans (associated_mul_unit_left _ _ hu).Dvd (gcd_dvd_right x a)⟩⟩
-#align gcd_monoid.prime_of_irreducible GCDMonoid.prime_of_irreducible
+#align gcd_monoid.prime_of_irreducible Irreducible.prime
 -/
 
-#print GCDMonoid.irreducible_iff_prime /-
+#print irreducible_iff_prime /-
 theorem irreducible_iff_prime [GCDMonoid α] {p : α} : Irreducible p ↔ Prime p :=
-  ⟨prime_of_irreducible, Prime.irreducible⟩
-#align gcd_monoid.irreducible_iff_prime GCDMonoid.irreducible_iff_prime
+  ⟨prime, Prime.irreducible⟩
+#align gcd_monoid.irreducible_iff_prime irreducible_iff_prime
 -/
 
 end GCDMonoid

baba818b

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker
 -/
-import Mathbin.Algebra.Associated
-import Mathbin.Algebra.GroupPower.Lemmas
-import Mathbin.Algebra.Ring.Regular
+import Algebra.Associated
+import Algebra.GroupPower.Lemmas
+import Algebra.Ring.Regular
 
 #align_import algebra.gcd_monoid.basic from "leanprover-community/mathlib"@"baba818b9acea366489e8ba32d2cc0fcaf50a1f7"

baba818b

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -76,12 +76,12 @@ elements. -/
 class NormalizationMonoid (α : Type _) [CancelCommMonoidWithZero α] where
   normUnit : α → αˣ
   normUnit_zero : norm_unit 0 = 1
-  normUnit_mul : ∀ {a b}, a ≠ 0 → b ≠ 0 → norm_unit (a * b) = norm_unit a * norm_unit b
+  normUnit_hMul : ∀ {a b}, a ≠ 0 → b ≠ 0 → norm_unit (a * b) = norm_unit a * norm_unit b
   normUnit_coe_units : ∀ u : αˣ, norm_unit u = u⁻¹
 #align normalization_monoid NormalizationMonoid
 -/
 
-export NormalizationMonoid (normUnit normUnit_zero normUnit_mul normUnit_coe_units)
+export NormalizationMonoid (normUnit normUnit_zero normUnit_hMul normUnit_coe_units)
 
 attribute [simp] norm_unit_coe_units norm_unit_zero norm_unit_mul
 
@@ -334,7 +334,7 @@ class GCDMonoid (α : Type _) [CancelCommMonoidWithZero α] where
   gcd_dvd_left : ∀ a b, gcd a b ∣ a
   gcd_dvd_right : ∀ a b, gcd a b ∣ b
   dvd_gcd : ∀ {a b c}, a ∣ c → a ∣ b → a ∣ gcd c b
-  gcd_mul_lcm : ∀ a b, Associated (gcd a b * lcm a b) (a * b)
+  gcd_hMul_lcm : ∀ a b, Associated (gcd a b * lcm a b) (a * b)
   lcm_zero_left : ∀ a, lcm 0 a = 0
   lcm_zero_right : ∀ a, lcm a 0 = 0
 #align gcd_monoid GCDMonoid
@@ -371,7 +371,7 @@ theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a
 
 #print gcd_mul_lcm /-
 theorem gcd_mul_lcm [GCDMonoid α] : ∀ a b : α, Associated (gcd a b * lcm a b) (a * b) :=
-  GCDMonoid.gcd_mul_lcm
+  GCDMonoid.gcd_hMul_lcm
 #align gcd_mul_lcm gcd_mul_lcm
 -/
 
@@ -1094,7 +1094,7 @@ instance (priority := 100) normalizationMonoidOfUniqueUnits : NormalizationMonoi
     where
   normUnit x := 1
   normUnit_zero := rfl
-  normUnit_mul x y hx hy := (mul_one 1).symm
+  normUnit_hMul x y hx hy := (mul_one 1).symm
   normUnit_coe_units u := Subsingleton.elim _ _
 #align normalization_monoid_of_unique_units normalizationMonoidOfUniqueUnits
 -/
@@ -1220,7 +1220,7 @@ def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates
     if a = 0 then 1
     else Classical.choose (Associates.mk_eq_mk_iff_associated.1 (hinv (Associates.mk a)).symm)
   normUnit_zero := if_pos rfl
-  normUnit_mul a b ha hb :=
+  normUnit_hMul a b ha hb :=
     by
     rw [if_neg (mul_ne_zero ha hb), if_neg ha, if_neg hb, Units.ext_iff, Units.val_mul]
     suffices
@@ -1253,7 +1253,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
     dvd_gcd := fun a b c => dvd_gcd
     lcm := fun a b =>
       if a = 0 then 0 else Classical.choose ((gcd_dvd_left a b).trans (Dvd.intro b rfl))
-    gcd_mul_lcm := fun a b => by
+    gcd_hMul_lcm := fun a b => by
       split_ifs with a0
       · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
       · rw [← Classical.choose_spec ((gcd_dvd_left a b).trans (Dvd.intro b rfl))]
@@ -1307,7 +1307,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         have h2 : normalize (gcd a b * l) = gcd a b * l := by rw [this, normalize_idem]
         rw [← normalize_gcd] at this 
         rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2 
-    gcd_mul_lcm := fun a b => by
+    gcd_hMul_lcm := fun a b => by
       split_ifs with a0
       · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
       · rw [←
@@ -1338,7 +1338,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
   let exists_gcd a b := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
   { lcm
     gcd := fun a b => if a = 0 then b else if b = 0 then a else Classical.choose (exists_gcd a b)
-    gcd_mul_lcm := fun a b => by
+    gcd_hMul_lcm := fun a b => by
       split_ifs
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), MulZeroClass.mul_zero, MulZeroClass.zero_mul]
       · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), MulZeroClass.mul_zero]
@@ -1401,7 +1401,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
     gcd := fun a b =>
       if a = 0 then normalize b
       else if b = 0 then normalize a else Classical.choose (exists_gcd a b)
-    gcd_mul_lcm := fun a b => by
+    gcd_hMul_lcm := fun a b => by
       split_ifs with h h_1
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), MulZeroClass.mul_zero, MulZeroClass.zero_mul]
       ·
@@ -1536,7 +1536,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
     where
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹
   normUnit_zero := dif_pos rfl
-  normUnit_mul x y x0 y0 := Units.eq_iff.1 (by simp [x0, y0, mul_comm])
+  normUnit_hMul x y x0 y0 := Units.eq_iff.1 (by simp [x0, y0, mul_comm])
   normUnit_coe_units u := by rw [dif_neg (Units.ne_zero _), Units.mk0_val]; infer_instance
   gcd a b := if a = 0 ∧ b = 0 then 0 else 1
   lcm a b := if a = 0 ∨ b = 0 then 0 else 1
@@ -1547,7 +1547,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
     cases' not_and_distrib.mp h with h h <;>
         refine' is_unit_iff_dvd_one.mp (isUnit_of_dvd_unit _ (IsUnit.mk0 _ h)) <;>
       assumption
-  gcd_mul_lcm a b := by
+  gcd_hMul_lcm a b := by
     by_cases ha : a = 0; · simp [ha]
     by_cases hb : b = 0; · simp [hb]
     rw [if_neg (not_and_of_not_left _ ha), one_mul, if_neg (not_or_of_not ha hb)]

baba818b

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker
-
-! This file was ported from Lean 3 source module algebra.gcd_monoid.basic
-! leanprover-community/mathlib commit baba818b9acea366489e8ba32d2cc0fcaf50a1f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Associated
 import Mathbin.Algebra.GroupPower.Lemmas
 import Mathbin.Algebra.Ring.Regular
 
+#align_import algebra.gcd_monoid.basic from "leanprover-community/mathlib"@"baba818b9acea366489e8ba32d2cc0fcaf50a1f7"
+
 /-!
 # Monoids with normalization functions, `gcd`, and `lcm`

baba818b

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -1115,11 +1115,11 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
   ⟨fun g₁ g₂ =>
     by
     have hgcd : g₁.gcd = g₂.gcd := by
-      ext (a b)
+      ext a b
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _) <;>
         apply dvd_gcd (gcd_dvd_left _ _) (gcd_dvd_right _ _)
     have hlcm : g₁.lcm = g₂.lcm := by
-      ext (a b)
+      ext a b
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _) <;>
         apply lcm_dvd_iff.2 ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩
     cases g₁; cases g₂

baba818b

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -92,10 +92,12 @@ section NormalizationMonoid
 
 variable [CancelCommMonoidWithZero α] [NormalizationMonoid α]
 
+#print normUnit_one /-
 @[simp]
 theorem normUnit_one : normUnit (1 : α) = 1 :=
   normUnit_coe_units 1
 #align norm_unit_one normUnit_one
+-/
 
 #print normalize /-
 /-- Chooses an element of each associate class, by multiplying by `norm_unit` -/
@@ -116,53 +118,76 @@ def normalize : α →*₀ α where
 #align normalize normalize
 -/
 
+#print associated_normalize /-
 theorem associated_normalize (x : α) : Associated x (normalize x) :=
   ⟨_, rfl⟩
 #align associated_normalize associated_normalize
+-/
 
+#print normalize_associated /-
 theorem normalize_associated (x : α) : Associated (normalize x) x :=
   (associated_normalize _).symm
 #align normalize_associated normalize_associated
+-/
 
+#print associated_normalize_iff /-
 theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Associated x y :=
   ⟨fun h => h.trans (normalize_associated y), fun h => h.trans (associated_normalize y)⟩
 #align associated_normalize_iff associated_normalize_iff
+-/
 
+#print normalize_associated_iff /-
 theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Associated x y :=
   ⟨fun h => (associated_normalize _).trans h, fun h => (normalize_associated _).trans h⟩
 #align normalize_associated_iff normalize_associated_iff
+-/
 
+#print Associates.mk_normalize /-
 theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associates.mk x :=
   Associates.mk_eq_mk_iff_associated.2 (normalize_associated _)
 #align associates.mk_normalize Associates.mk_normalize
+-/
 
+#print normalize_apply /-
 @[simp]
 theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
   rfl
 #align normalize_apply normalize_apply
+-/
 
+#print normalize_zero /-
 @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
   normalize.map_zero
 #align normalize_zero normalize_zero
+-/
 
+#print normalize_one /-
 @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
   normalize.map_one
 #align normalize_one normalize_one
+-/
 
+#print normalize_coe_units /-
 theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 #align normalize_coe_units normalize_coe_units
+-/
 
+#print normalize_eq_zero /-
 theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
   ⟨fun hx => (associated_zero_iff_eq_zero x).1 <| hx ▸ associated_normalize _, by
     rintro rfl <;> exact normalize_zero⟩
 #align normalize_eq_zero normalize_eq_zero
+-/
 
+#print normalize_eq_one /-
 theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
 #align normalize_eq_one normalize_eq_one
+-/
 
+#print normUnit_mul_normUnit /-
 @[simp]
 theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
   by
@@ -171,10 +196,14 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
   · rw [norm_unit_zero, MulZeroClass.zero_mul, norm_unit_zero]
   · rw [norm_unit_mul h (Units.ne_zero _), norm_unit_coe_units, mul_inv_eq_one]
 #align norm_unit_mul_norm_unit normUnit_mul_normUnit
+-/
 
+#print normalize_idem /-
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
+-/
 
+#print normalize_eq_normalize /-
 theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
   by
   nontriviality α
@@ -186,26 +215,35 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
     a * ↑(norm_unit a) = a * ↑(norm_unit a) * ↑u * ↑u⁻¹ := (Units.mul_inv_cancel_right _ _).symm
     _ = a * ↑u * ↑(norm_unit a) * ↑u⁻¹ := by rw [mul_right_comm a]
 #align normalize_eq_normalize normalize_eq_normalize
+-/
 
+#print normalize_eq_normalize_iff /-
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
   ⟨fun h => ⟨Units.dvd_mul_right.1 ⟨_, h.symm⟩, Units.dvd_mul_right.1 ⟨_, h⟩⟩, fun ⟨hxy, hyx⟩ =>
     normalize_eq_normalize hxy hyx⟩
 #align normalize_eq_normalize_iff normalize_eq_normalize_iff
+-/
 
+#print dvd_antisymm_of_normalize_eq /-
 theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : normalize b = b)
     (hab : a ∣ b) (hba : b ∣ a) : a = b :=
   ha ▸ hb ▸ normalize_eq_normalize hab hba
 #align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eq
+-/
 
+#print dvd_normalize_iff /-
 --can be proven by simp
 theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
   Units.dvd_mul_right
 #align dvd_normalize_iff dvd_normalize_iff
+-/
 
+#print normalize_dvd_iff /-
 --can be proven by simp
 theorem normalize_dvd_iff {a b : α} : normalize a ∣ b ↔ a ∣ b :=
   Units.mul_right_dvd
 #align normalize_dvd_iff normalize_dvd_iff
+-/
 
 end NormalizationMonoid
 
@@ -223,40 +261,54 @@ protected def out : Associates α → α :=
 #align associates.out Associates.out
 -/
 
+#print Associates.out_mk /-
 @[simp]
 theorem out_mk (a : α) : (Associates.mk a).out = normalize a :=
   rfl
 #align associates.out_mk Associates.out_mk
+-/
 
+#print Associates.out_one /-
 @[simp]
 theorem out_one : (1 : Associates α).out = 1 :=
   normalize_one
 #align associates.out_one Associates.out_one
+-/
 
+#print Associates.out_mul /-
 theorem out_mul (a b : Associates α) : (a * b).out = a.out * b.out :=
   Quotient.induction_on₂ a b fun a b => by
     simp only [Associates.quotient_mk_eq_mk, out_mk, mk_mul_mk, normalize.map_mul]
 #align associates.out_mul Associates.out_mul
+-/
 
+#print Associates.dvd_out_iff /-
 theorem dvd_out_iff (a : α) (b : Associates α) : a ∣ b.out ↔ Associates.mk a ≤ b :=
   Quotient.inductionOn b <| by
     simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
 #align associates.dvd_out_iff Associates.dvd_out_iff
+-/
 
+#print Associates.out_dvd_iff /-
 theorem out_dvd_iff (a : α) (b : Associates α) : b.out ∣ a ↔ b ≤ Associates.mk a :=
   Quotient.inductionOn b <| by
     simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
 #align associates.out_dvd_iff Associates.out_dvd_iff
+-/
 
+#print Associates.out_top /-
 @[simp]
 theorem out_top : (⊤ : Associates α).out = 0 :=
   normalize_zero
 #align associates.out_top Associates.out_top
+-/
 
+#print Associates.normalize_out /-
 @[simp]
 theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
   Quotient.inductionOn a normalize_idem
 #align associates.normalize_out Associates.normalize_out
+-/
 
 #print Associates.mk_out /-
 @[simp]
@@ -313,14 +365,18 @@ section GCDMonoid
 
 variable [CancelCommMonoidWithZero α]
 
+#print normalize_gcd /-
 @[simp]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
   NormalizedGCDMonoid.normalize_gcd
 #align normalize_gcd normalize_gcd
+-/
 
+#print gcd_mul_lcm /-
 theorem gcd_mul_lcm [GCDMonoid α] : ∀ a b : α, Associated (gcd a b * lcm a b) (a * b) :=
   GCDMonoid.gcd_mul_lcm
 #align gcd_mul_lcm gcd_mul_lcm
+-/
 
 section Gcd
 
@@ -374,29 +430,40 @@ instance [NormalizedGCDMonoid α] : IsCommutative α gcd :=
 instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
   ⟨gcd_assoc⟩
 
+#print gcd_eq_normalize /-
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
   normalize_gcd a b ▸ normalize_eq_normalize habc hcab
 #align gcd_eq_normalize gcd_eq_normalize
+-/
 
+#print gcd_zero_left /-
 @[simp]
 theorem gcd_zero_left [NormalizedGCDMonoid α] (a : α) : gcd 0 a = normalize a :=
   gcd_eq_normalize (gcd_dvd_right 0 a) (dvd_gcd (dvd_zero _) (dvd_refl a))
 #align gcd_zero_left gcd_zero_left
+-/
 
+#print gcd_zero_left' /-
 theorem gcd_zero_left' [GCDMonoid α] (a : α) : Associated (gcd 0 a) a :=
   associated_of_dvd_dvd (gcd_dvd_right 0 a) (dvd_gcd (dvd_zero _) (dvd_refl a))
 #align gcd_zero_left' gcd_zero_left'
+-/
 
+#print gcd_zero_right /-
 @[simp]
 theorem gcd_zero_right [NormalizedGCDMonoid α] (a : α) : gcd a 0 = normalize a :=
   gcd_eq_normalize (gcd_dvd_left a 0) (dvd_gcd (dvd_refl a) (dvd_zero _))
 #align gcd_zero_right gcd_zero_right
+-/
 
+#print gcd_zero_right' /-
 theorem gcd_zero_right' [GCDMonoid α] (a : α) : Associated (gcd a 0) a :=
   associated_of_dvd_dvd (gcd_dvd_left a 0) (dvd_gcd (dvd_refl a) (dvd_zero _))
 #align gcd_zero_right' gcd_zero_right'
+-/
 
+#print gcd_eq_zero_iff /-
 @[simp]
 theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b = 0 :=
   Iff.intro
@@ -408,26 +475,35 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     rw [ha, hb, ← zero_dvd_iff]
     apply dvd_gcd <;> rfl
 #align gcd_eq_zero_iff gcd_eq_zero_iff
+-/
 
+#print gcd_one_left /-
 @[simp]
 theorem gcd_one_left [NormalizedGCDMonoid α] (a : α) : gcd 1 a = 1 :=
   dvd_antisymm_of_normalize_eq (normalize_gcd _ _) normalize_one (gcd_dvd_left _ _) (one_dvd _)
 #align gcd_one_left gcd_one_left
+-/
 
+#print gcd_one_left' /-
 @[simp]
 theorem gcd_one_left' [GCDMonoid α] (a : α) : Associated (gcd 1 a) 1 :=
   associated_of_dvd_dvd (gcd_dvd_left _ _) (one_dvd _)
 #align gcd_one_left' gcd_one_left'
+-/
 
+#print gcd_one_right /-
 @[simp]
 theorem gcd_one_right [NormalizedGCDMonoid α] (a : α) : gcd a 1 = 1 :=
   dvd_antisymm_of_normalize_eq (normalize_gcd _ _) normalize_one (gcd_dvd_right _ _) (one_dvd _)
 #align gcd_one_right gcd_one_right
+-/
 
+#print gcd_one_right' /-
 @[simp]
 theorem gcd_one_right' [GCDMonoid α] (a : α) : Associated (gcd a 1) 1 :=
   associated_of_dvd_dvd (gcd_dvd_right _ _) (one_dvd _)
 #align gcd_one_right' gcd_one_right'
+-/
 
 #print gcd_dvd_gcd /-
 theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d) : gcd a c ∣ gcd b d :=
@@ -435,11 +511,14 @@ theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 #align gcd_dvd_gcd gcd_dvd_gcd
 -/
 
+#print gcd_same /-
 @[simp]
 theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
   gcd_eq_normalize (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) (dvd_refl a))
 #align gcd_same gcd_same
+-/
 
+#print gcd_mul_left /-
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     gcd (a * b) (a * c) = normalize a * gcd b c :=
@@ -455,7 +534,9 @@ theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
             ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ gcd_dvd_right _ _))
       (dvd_gcd (mul_dvd_mul_left a <| gcd_dvd_left _ _) (mul_dvd_mul_left a <| gcd_dvd_right _ _))
 #align gcd_mul_left gcd_mul_left
+-/
 
+#print gcd_mul_left' /-
 theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a * c)) (a * gcd b c) :=
   by
   obtain rfl | ha := eq_or_ne a 0
@@ -469,42 +550,59 @@ theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a *
         ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ gcd_dvd_right _ _)
   · exact dvd_gcd (mul_dvd_mul_left a <| gcd_dvd_left _ _) (mul_dvd_mul_left a <| gcd_dvd_right _ _)
 #align gcd_mul_left' gcd_mul_left'
+-/
 
+#print gcd_mul_right /-
 @[simp]
 theorem gcd_mul_right [NormalizedGCDMonoid α] (a b c : α) :
     gcd (b * a) (c * a) = gcd b c * normalize a := by simp only [mul_comm, gcd_mul_left]
 #align gcd_mul_right gcd_mul_right
+-/
 
+#print gcd_mul_right' /-
 @[simp]
 theorem gcd_mul_right' [GCDMonoid α] (a b c : α) : Associated (gcd (b * a) (c * a)) (gcd b c * a) :=
   by simp only [mul_comm, gcd_mul_left']
 #align gcd_mul_right' gcd_mul_right'
+-/
 
+#print gcd_eq_left_iff /-
 theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     gcd a b = a ↔ a ∣ b :=
   Iff.intro (fun eq => Eq ▸ gcd_dvd_right _ _) fun hab =>
     dvd_antisymm_of_normalize_eq (normalize_gcd _ _) h (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) hab)
 #align gcd_eq_left_iff gcd_eq_left_iff
+-/
 
+#print gcd_eq_right_iff /-
 theorem gcd_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     gcd a b = b ↔ b ∣ a := by simpa only [gcd_comm a b] using gcd_eq_left_iff b a h
 #align gcd_eq_right_iff gcd_eq_right_iff
+-/
 
+#print gcd_dvd_gcd_mul_left /-
 theorem gcd_dvd_gcd_mul_left [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd (k * m) n :=
   gcd_dvd_gcd (dvd_mul_left _ _) dvd_rfl
 #align gcd_dvd_gcd_mul_left gcd_dvd_gcd_mul_left
+-/
 
+#print gcd_dvd_gcd_mul_right /-
 theorem gcd_dvd_gcd_mul_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd (m * k) n :=
   gcd_dvd_gcd (dvd_mul_right _ _) dvd_rfl
 #align gcd_dvd_gcd_mul_right gcd_dvd_gcd_mul_right
+-/
 
+#print gcd_dvd_gcd_mul_left_right /-
 theorem gcd_dvd_gcd_mul_left_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd m (k * n) :=
   gcd_dvd_gcd dvd_rfl (dvd_mul_left _ _)
 #align gcd_dvd_gcd_mul_left_right gcd_dvd_gcd_mul_left_right
+-/
 
+#print gcd_dvd_gcd_mul_right_right /-
 theorem gcd_dvd_gcd_mul_right_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd m (n * k) :=
   gcd_dvd_gcd dvd_rfl (dvd_mul_right _ _)
 #align gcd_dvd_gcd_mul_right_right gcd_dvd_gcd_mul_right_right
+-/
 
 #print Associated.gcd_eq_left /-
 theorem Associated.gcd_eq_left [NormalizedGCDMonoid α] {m n : α} (h : Associated m n) (k : α) :
@@ -522,14 +620,19 @@ theorem Associated.gcd_eq_right [NormalizedGCDMonoid α] {m n : α} (h : Associa
 #align associated.gcd_eq_right Associated.gcd_eq_right
 -/
 
+#print dvd_gcd_mul_of_dvd_mul /-
 theorem dvd_gcd_mul_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ gcd k m * n :=
   (dvd_gcd (dvd_mul_right _ n) H).trans (gcd_mul_right' n k m).Dvd
 #align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mul
+-/
 
+#print dvd_mul_gcd_of_dvd_mul /-
 theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
   rw [mul_comm] at H ⊢; exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
+-/
 
+#print exists_dvd_and_dvd_of_dvd_mul /-
 /-- Represent a divisor of `m * n` as a product of a divisor of `m` and a divisor of `n`.
 
 In other words, the nonzero elements of a `gcd_monoid` form a decomposition monoid
@@ -556,14 +659,18 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     rw [← ha]
     exact dvd_gcd_mul_of_dvd_mul H
 #align exists_dvd_and_dvd_of_dvd_mul exists_dvd_and_dvd_of_dvd_mul
+-/
 
+#print dvd_mul /-
 theorem dvd_mul [GCDMonoid α] {k m n : α} : k ∣ m * n ↔ ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ :=
   by
   refine' ⟨exists_dvd_and_dvd_of_dvd_mul, _⟩
   rintro ⟨d₁, d₂, hy, hz, rfl⟩
   exact mul_dvd_mul hy hz
 #align dvd_mul dvd_mul
+-/
 
+#print gcd_mul_dvd_mul_gcd /-
 theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd k m * gcd k n :=
   by
   obtain ⟨m', n', hm', hn', h⟩ := exists_dvd_and_dvd_of_dvd_mul (gcd_dvd_right k (m * n))
@@ -576,6 +683,7 @@ theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd
   · have hn'k : n' ∣ k := (dvd_mul_left n' m').trans hm'n'
     exact dvd_gcd hn'k hn'
 #align gcd_mul_dvd_mul_gcd gcd_mul_dvd_mul_gcd
+-/
 
 #print gcd_pow_right_dvd_pow_gcd /-
 theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd a (b ^ k) ∣ gcd a b ^ k :=
@@ -605,6 +713,7 @@ theorem gcd_pow_left_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd (a ^
 #align gcd_pow_left_dvd_pow_gcd gcd_pow_left_dvd_pow_gcd
 -/
 
+#print pow_dvd_of_mul_eq_pow /-
 theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠ 0) (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) (hc : c = d₁ * d₂) (hd₁ : d₁ ∣ a) : d₁ ^ k ≠ 0 ∧ d₁ ^ k ∣ a :=
   by
@@ -623,7 +732,9 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
   have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3 ; apply absurd (zero_dvd_iff.mp h3) ha
   exact ⟨h4, h3⟩
 #align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_pow
+-/
 
+#print exists_associated_pow_of_mul_eq_pow /-
 theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) : ∃ d : α, Associated (d ^ k) a :=
   by
@@ -657,19 +768,24 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
   use Units.mkOfMulEqOne _ _ h'
   rw [Units.val_mkOfMulEqOne, ha']
 #align exists_associated_pow_of_mul_eq_pow exists_associated_pow_of_mul_eq_pow
+-/
 
+#print exists_eq_pow_of_mul_eq_pow /-
 theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) : ∃ d : α, a = d ^ k :=
   let ⟨d, hd⟩ := exists_associated_pow_of_mul_eq_pow hab h
   ⟨d, (associated_iff_eq.mp hd).symm⟩
 #align exists_eq_pow_of_mul_eq_pow exists_eq_pow_of_mul_eq_pow
+-/
 
+#print gcd_greatest /-
 theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
     GCDMonoid.gcd a b = normalize d :=
   haveI h := hd _ (GCDMonoid.gcd_dvd_left a b) (GCDMonoid.gcd_dvd_right a b)
   gcd_eq_normalize h (GCDMonoid.dvd_gcd hda hdb)
 #align gcd_greatest gcd_greatest
+-/
 
 #print gcd_greatest_associated /-
 theorem gcd_greatest_associated {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] {a b d : α}
@@ -680,6 +796,7 @@ theorem gcd_greatest_associated {α : Type _} [CancelCommMonoidWithZero α] [GCD
 #align gcd_greatest_associated gcd_greatest_associated
 -/
 
+#print isUnit_gcd_of_eq_mul_gcd /-
 theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α]
     {x y x' y' : α} (ex : x = gcd x y * x') (ey : y = gcd x y * y') (h : gcd x y ≠ 0) :
     IsUnit (gcd x' y') := by
@@ -688,7 +805,9 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GC
   convert (gcd_mul_left' _ _ _).symm using 1
   rw [← ex, ← ey, mul_one]
 #align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcd
+-/
 
+#print extract_gcd /-
 theorem extract_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] (x y : α) :
     ∃ x' y', x = gcd x y * x' ∧ y = gcd x y * y' ∧ IsUnit (gcd x' y') :=
   by
@@ -701,6 +820,7 @@ theorem extract_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] (
   obtain ⟨y', ey⟩ := gcd_dvd_right x y
   exact ⟨x', y', ex, ey, isUnit_gcd_of_eq_mul_gcd ex ey h⟩
 #align extract_gcd extract_gcd
+-/
 
 end Gcd
 
@@ -740,6 +860,7 @@ theorem lcm_dvd [GCDMonoid α] {a b c : α} (hab : a ∣ b) (hcb : c ∣ b) : lc
 #align lcm_dvd lcm_dvd
 -/
 
+#print lcm_eq_zero_iff /-
 @[simp]
 theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b = 0 :=
   Iff.intro
@@ -750,11 +871,14 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
       simpa only [associated_zero_iff_eq_zero, mul_eq_zero])
     (by rintro (rfl | rfl) <;> [apply lcm_zero_left; apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
+-/
 
+#print normalize_lcm /-
 @[simp]
 theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
   NormalizedGCDMonoid.normalize_lcm a b
 #align normalize_lcm normalize_lcm
+-/
 
 #print lcm_comm /-
 theorem lcm_comm [NormalizedGCDMonoid α] (a b : α) : lcm a b = lcm b a :=
@@ -797,10 +921,12 @@ instance [NormalizedGCDMonoid α] : IsCommutative α lcm :=
 instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
   ⟨lcm_assoc⟩
 
+#print lcm_eq_normalize /-
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=
   normalize_lcm a b ▸ normalize_eq_normalize habc hcab
 #align lcm_eq_normalize lcm_eq_normalize
+-/
 
 #print lcm_dvd_lcm /-
 theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d) : lcm a c ∣ lcm b d :=
@@ -808,38 +934,51 @@ theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 #align lcm_dvd_lcm lcm_dvd_lcm
 -/
 
+#print lcm_units_coe_left /-
 @[simp]
 theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (↑u) a = normalize a :=
   lcm_eq_normalize (lcm_dvd Units.coe_dvd dvd_rfl) (dvd_lcm_right _ _)
 #align lcm_units_coe_left lcm_units_coe_left
+-/
 
+#print lcm_units_coe_right /-
 @[simp]
 theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a ↑u = normalize a :=
   (lcm_comm a u).trans <| lcm_units_coe_left _ _
 #align lcm_units_coe_right lcm_units_coe_right
+-/
 
+#print lcm_one_left /-
 @[simp]
 theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :=
   lcm_units_coe_left 1 a
 #align lcm_one_left lcm_one_left
+-/
 
+#print lcm_one_right /-
 @[simp]
 theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a :=
   lcm_units_coe_right a 1
 #align lcm_one_right lcm_one_right
+-/
 
+#print lcm_same /-
 @[simp]
 theorem lcm_same [NormalizedGCDMonoid α] (a : α) : lcm a a = normalize a :=
   lcm_eq_normalize (lcm_dvd dvd_rfl dvd_rfl) (dvd_lcm_left _ _)
 #align lcm_same lcm_same
+-/
 
+#print lcm_eq_one_iff /-
 @[simp]
 theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a ∣ 1 ∧ b ∣ 1 :=
   Iff.intro (fun eq => Eq ▸ ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩) fun ⟨⟨c, hc⟩, ⟨d, hd⟩⟩ =>
     show lcm (Units.mkOfMulEqOne a c hc.symm : α) (Units.mkOfMulEqOne b d hd.symm) = 1 by
       rw [lcm_units_coe_left, normalize_coe_units]
 #align lcm_eq_one_iff lcm_eq_one_iff
+-/
 
+#print lcm_mul_left /-
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     lcm (a * b) (a * c) = normalize a * lcm b c :=
@@ -856,37 +995,52 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
           lcm_dvd ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ dvd_lcm_left _ _)
             ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ dvd_lcm_right _ _)))
 #align lcm_mul_left lcm_mul_left
+-/
 
+#print lcm_mul_right /-
 @[simp]
 theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
     lcm (b * a) (c * a) = lcm b c * normalize a := by simp only [mul_comm, lcm_mul_left]
 #align lcm_mul_right lcm_mul_right
+-/
 
+#print lcm_eq_left_iff /-
 theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     lcm a b = a ↔ b ∣ a :=
   Iff.intro (fun eq => Eq ▸ dvd_lcm_right _ _) fun hab =>
     dvd_antisymm_of_normalize_eq (normalize_lcm _ _) h (lcm_dvd (dvd_refl a) hab) (dvd_lcm_left _ _)
 #align lcm_eq_left_iff lcm_eq_left_iff
+-/
 
+#print lcm_eq_right_iff /-
 theorem lcm_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     lcm a b = b ↔ a ∣ b := by simpa only [lcm_comm b a] using lcm_eq_left_iff b a h
 #align lcm_eq_right_iff lcm_eq_right_iff
+-/
 
+#print lcm_dvd_lcm_mul_left /-
 theorem lcm_dvd_lcm_mul_left [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm (k * m) n :=
   lcm_dvd_lcm (dvd_mul_left _ _) dvd_rfl
 #align lcm_dvd_lcm_mul_left lcm_dvd_lcm_mul_left
+-/
 
+#print lcm_dvd_lcm_mul_right /-
 theorem lcm_dvd_lcm_mul_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm (m * k) n :=
   lcm_dvd_lcm (dvd_mul_right _ _) dvd_rfl
 #align lcm_dvd_lcm_mul_right lcm_dvd_lcm_mul_right
+-/
 
+#print lcm_dvd_lcm_mul_left_right /-
 theorem lcm_dvd_lcm_mul_left_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm m (k * n) :=
   lcm_dvd_lcm dvd_rfl (dvd_mul_left _ _)
 #align lcm_dvd_lcm_mul_left_right lcm_dvd_lcm_mul_left_right
+-/
 
+#print lcm_dvd_lcm_mul_right_right /-
 theorem lcm_dvd_lcm_mul_right_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm m (n * k) :=
   lcm_dvd_lcm dvd_rfl (dvd_mul_right _ _)
 #align lcm_dvd_lcm_mul_right_right lcm_dvd_lcm_mul_right_right
+-/
 
 #print lcm_eq_of_associated_left /-
 theorem lcm_eq_of_associated_left [NormalizedGCDMonoid α] {m n : α} (h : Associated m n) (k : α) :
@@ -987,16 +1141,21 @@ instance subsingleton_normalizedGCDMonoid_of_unique_units : Subsingleton (Normal
 #align subsingleton_normalized_gcd_monoid_of_unique_units subsingleton_normalizedGCDMonoid_of_unique_units
 -/
 
+#print normUnit_eq_one /-
 @[simp]
 theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
   rfl
 #align norm_unit_eq_one normUnit_eq_one
+-/
 
+#print normalize_eq /-
 @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
   mul_one x
 #align normalize_eq normalize_eq
+-/
 
+#print associatesEquivOfUniqueUnits /-
 /-- If a monoid's only unit is `1`, then it is isomorphic to its associates. -/
 @[simps]
 def associatesEquivOfUniqueUnits : Associates α ≃* α
@@ -1007,6 +1166,7 @@ def associatesEquivOfUniqueUnits : Associates α ≃* α
   right_inv t := (Associates.out_mk _).trans <| normalize_eq _
   map_mul' := Associates.out_mul
 #align associates_equiv_of_unique_units associatesEquivOfUniqueUnits
+-/
 
 end UniqueUnit
 
@@ -1014,6 +1174,7 @@ section IsDomain
 
 variable [CommRing α] [IsDomain α] [NormalizedGCDMonoid α]
 
+#print gcd_eq_of_dvd_sub_right /-
 theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a c :=
   by
   apply dvd_antisymm_of_normalize_eq (normalize_gcd _ _) (normalize_gcd _ _) <;>
@@ -1030,10 +1191,13 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
     use e + f * d
     rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel]
 #align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_right
+-/
 
+#print gcd_eq_of_dvd_sub_left /-
 theorem gcd_eq_of_dvd_sub_left {a b c : α} (h : a ∣ b - c) : gcd b a = gcd c a := by
   rw [gcd_comm _ a, gcd_comm _ a, gcd_eq_of_dvd_sub_right h]
 #align gcd_eq_of_dvd_sub_left gcd_eq_of_dvd_sub_left
+-/
 
 end IsDomain
 
@@ -1050,6 +1214,7 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
     a * ↑(Classical.choose (associated_map_mk hinv a)) = f (Associates.mk a) :=
   Classical.choose_spec (associated_map_mk hinv a)
 
+#print normalizationMonoidOfMonoidHomRightInverse /-
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)
     (hinv : Function.RightInverse f Associates.mk) : NormalizationMonoid α
@@ -1078,6 +1243,7 @@ def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates
       Associates.mk_eq_mk_iff_associated.2 (associated_one_iff_isUnit.2 ⟨u, rfl⟩),
       Associates.mk_one, MonoidHom.map_one]
 #align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverse
+-/
 
 #print gcdMonoidOfGCD /-
 /-- Define `gcd_monoid` on a structure just from the `gcd` and its properties. -/
@@ -1107,6 +1273,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
 #align gcd_monoid_of_gcd gcdMonoidOfGCD
 -/
 
+#print normalizedGCDMonoidOfGCD /-
 /-- Define `normalized_gcd_monoid` on a structure just from the `gcd` and its properties. -/
 noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq α] (gcd : α → α → α)
     (gcd_dvd_left : ∀ a b, gcd a b ∣ a) (gcd_dvd_right : ∀ a b, gcd a b ∣ b)
@@ -1164,6 +1331,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
       apply Or.resolve_left (mul_eq_zero.1 _) a0
       rw [h, MulZeroClass.mul_zero, normalize_zero] }
 #align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCD
+-/
 
 #print gcdMonoidOfLCM /-
 /-- Define `gcd_monoid` on a structure just from the `lcm` and its properties. -/
@@ -1224,6 +1392,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
 #align gcd_monoid_of_lcm gcdMonoidOfLCM
 -/
 
+#print normalizedGCDMonoidOfLCM /-
 /-- Define `normalized_gcd_monoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
     (dvd_lcm_left : ∀ a b, a ∣ lcm a b) (dvd_lcm_right : ∀ a b, b ∣ lcm a b)
@@ -1307,6 +1476,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]
       apply ac }
 #align normalized_gcd_monoid_of_lcm normalizedGCDMonoidOfLCM
+-/
 
 #print gcdMonoidOfExistsGCD /-
 /-- Define a `gcd_monoid` structure on a monoid just from the existence of a `gcd`. -/
@@ -1391,12 +1561,16 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
   normalize_gcd a b := if h : a = 0 ∧ b = 0 then by simp [if_pos h] else by simp [if_neg h]
   normalize_lcm a b := if h : a = 0 ∨ b = 0 then by simp [if_pos h] else by simp [if_neg h]
 
+#print CommGroupWithZero.coe_normUnit /-
 @[simp]
 theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻¹ := by simp [norm_unit, h0]
 #align comm_group_with_zero.coe_norm_unit CommGroupWithZero.coe_normUnit
+-/
 
+#print CommGroupWithZero.normalize_eq_one /-
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one
+-/
 
 end CommGroupWithZero

baba818b

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -185,7 +185,6 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
   calc
     a * ↑(norm_unit a) = a * ↑(norm_unit a) * ↑u * ↑u⁻¹ := (Units.mul_inv_cancel_right _ _).symm
     _ = a * ↑u * ↑(norm_unit a) * ↑u⁻¹ := by rw [mul_right_comm a]
-    
 #align normalize_eq_normalize normalize_eq_normalize
 
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
@@ -603,7 +602,6 @@ theorem gcd_pow_left_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd (a ^
     gcd (a ^ k) b ∣ gcd b (a ^ k) := (gcd_comm' _ _).Dvd
     _ ∣ gcd b a ^ k := gcd_pow_right_dvd_pow_gcd
     _ ∣ gcd a b ^ k := pow_dvd_pow_of_dvd (gcd_comm' _ _).Dvd _
-    
 #align gcd_pow_left_dvd_pow_gcd gcd_pow_left_dvd_pow_gcd
 -/

baba818b

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -687,7 +687,7 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GC
     IsUnit (gcd x' y') := by
   rw [← associated_one_iff_isUnit]
   refine' Associated.of_mul_left _ (Associated.refl <| gcd x y) h
-  convert(gcd_mul_left' _ _ _).symm using 1
+  convert (gcd_mul_left' _ _ _).symm using 1
   rw [← ex, ← ey, mul_one]
 #align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcd
 
@@ -1137,7 +1137,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
             exact gcd_dvd_left _ _
-          · convert@normalize_zero α _ _
+          · convert @normalize_zero α _ _
         have h1 : gcd a b ≠ 0 := by
           have hab : a * b ≠ 0 := mul_ne_zero a0 hb
           contrapose! hab
@@ -1218,7 +1218,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd c b)]
       rcases ab with ⟨d, rfl⟩
       rw [mul_eq_zero] at h_1 
-      push_neg  at h_1 
+      push_neg at h_1 
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]
@@ -1303,7 +1303,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
         dvd_normalize_iff]
       rcases ab with ⟨d, rfl⟩
       rw [mul_eq_zero] at h_1 
-      push_neg  at h_1 
+      push_neg at h_1 
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]

baba818b

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -300,7 +300,7 @@ supremum, `1` is bottom, and `0` is top. The type class focuses on `gcd` and we
 corresponding `lcm` facts from `gcd`.
 -/
 class NormalizedGCDMonoid (α : Type _) [CancelCommMonoidWithZero α] extends NormalizationMonoid α,
-  GCDMonoid α where
+    GCDMonoid α where
   normalize_gcd : ∀ a b, normalize (gcd a b) = gcd a b
   normalize_lcm : ∀ a b, normalize (lcm a b) = lcm a b
 #align normalized_gcd_monoid NormalizedGCDMonoid
@@ -404,7 +404,7 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     (fun h => by
       let ⟨ca, ha⟩ := gcd_dvd_left a b
       let ⟨cb, hb⟩ := gcd_dvd_right a b
-      rw [h, MulZeroClass.zero_mul] at ha hb <;> exact ⟨ha, hb⟩)
+      rw [h, MulZeroClass.zero_mul] at ha hb  <;> exact ⟨ha, hb⟩)
     fun ⟨ha, hb⟩ => by
     rw [ha, hb, ← zero_dvd_iff]
     apply dvd_gcd <;> rfl
@@ -528,7 +528,7 @@ theorem dvd_gcd_mul_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k
 #align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mul
 
 theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
-  rw [mul_comm] at H⊢; exact dvd_gcd_mul_of_dvd_mul H
+  rw [mul_comm] at H ⊢; exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
 
 /-- Represent a divisor of `m * n` as a product of a divisor of `m` and a divisor of `n`.
@@ -543,7 +543,7 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ :=
   by
   by_cases h0 : gcd k m = 0
-  · rw [gcd_eq_zero_iff] at h0
+  · rw [gcd_eq_zero_iff] at h0 
     rcases h0 with ⟨rfl, rfl⟩
     refine' ⟨0, n, dvd_refl 0, dvd_refl n, _⟩
     simp
@@ -552,7 +552,7 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     suffices h : gcd k m * a ∣ gcd k m * n
     · cases' h with b hb
       use b
-      rw [mul_assoc] at hb
+      rw [mul_assoc] at hb 
       apply mul_left_cancel₀ h0 hb
     rw [← ha]
     exact dvd_gcd_mul_of_dvd_mul H
@@ -582,7 +582,7 @@ theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd
 theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd a (b ^ k) ∣ gcd a b ^ k :=
   by
   by_cases hg : gcd a b = 0
-  · rw [gcd_eq_zero_iff] at hg
+  · rw [gcd_eq_zero_iff] at hg 
     rcases hg with ⟨rfl, rfl⟩
     exact
       (gcd_zero_left' (0 ^ k : α)).Dvd.trans
@@ -618,11 +618,11 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
       apply dvd_trans _ hab.dvd
       apply gcd_dvd_gcd hd₁ (dvd_refl b)
   have h2 : d₁ ^ k ∣ a * b := by use d₂ ^ k; rw [h, hc]; exact mul_pow d₁ d₂ k
-  rw [mul_comm] at h2
+  rw [mul_comm] at h2 
   have h3 : d₁ ^ k ∣ a := by
     apply (dvd_gcd_mul_of_dvd_mul h2).trans
     rw [IsUnit.mul_left_dvd _ _ _ h1]
-  have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3; apply absurd (zero_dvd_iff.mp h3) ha
+  have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3 ; apply absurd (zero_dvd_iff.mp h3) ha
   exact ⟨h4, h3⟩
 #align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_pow
 
@@ -642,16 +642,16 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
     rw [hb]
     exact gcd_zero_right' a
   obtain rfl | hk := k.eq_zero_or_pos
-  · use 1; rw [pow_zero] at h⊢; use Units.mkOfMulEqOne _ _ h
+  · use 1; rw [pow_zero] at h ⊢; use Units.mkOfMulEqOne _ _ h
     rw [Units.val_mkOfMulEqOne, one_mul]
   have hc : c ∣ a * b := by rw [h]; exact dvd_pow_self _ hk.ne'
   obtain ⟨d₁, d₂, hd₁, hd₂, hc⟩ := exists_dvd_and_dvd_of_dvd_mul hc
   use d₁
   obtain ⟨h0₁, ⟨a', ha'⟩⟩ := pow_dvd_of_mul_eq_pow ha hab h hc hd₁
-  rw [mul_comm] at h hc
-  rw [(gcd_comm' a b).isUnit_iff] at hab
+  rw [mul_comm] at h hc 
+  rw [(gcd_comm' a b).isUnit_iff] at hab 
   obtain ⟨h0₂, ⟨b', hb'⟩⟩ := pow_dvd_of_mul_eq_pow hb hab h hc hd₂
-  rw [ha', hb', hc, mul_pow] at h
+  rw [ha', hb', hc, mul_pow] at h 
   have h' : a' * b' = 1 := by
     apply (mul_right_inj' h0₁).mp; rw [mul_one]
     apply (mul_right_inj' h0₂).mp; rw [← h]
@@ -749,8 +749,8 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
       by
       have : Associated (a * b) 0 :=
         (gcd_mul_lcm a b).symm.trans <| by rw [h, MulZeroClass.mul_zero]
-      simpa only [associated_zero_iff_eq_zero, mul_eq_zero] )
-    (by rintro (rfl | rfl) <;> [apply lcm_zero_left;apply lcm_zero_right])
+      simpa only [associated_zero_iff_eq_zero, mul_eq_zero])
+    (by rintro (rfl | rfl) <;> [apply lcm_zero_left; apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
 
 @[simp]
@@ -971,7 +971,7 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _) <;>
         apply lcm_dvd_iff.2 ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩
     cases g₁; cases g₂
-    dsimp only at hgcd hlcm
+    dsimp only at hgcd hlcm 
     simp only [hgcd, hlcm]⟩
 #align subsingleton_gcd_monoid_of_unique_units subsingleton_gcdMonoid_of_unique_units
 -/
@@ -1132,7 +1132,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
               (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))).symm
         set l := Classical.choose (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))
         obtain rfl | hb := eq_or_ne b 0
-        · simp only [normalize_zero, MulZeroClass.mul_zero, mul_eq_zero] at this
+        · simp only [normalize_zero, MulZeroClass.mul_zero, mul_eq_zero] at this 
           obtain ha | hl := this
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
@@ -1143,8 +1143,8 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
           contrapose! hab
           rw [← normalize_eq_zero, ← this, hab, MulZeroClass.zero_mul]
         have h2 : normalize (gcd a b * l) = gcd a b * l := by rw [this, normalize_idem]
-        rw [← normalize_gcd] at this
-        rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2
+        rw [← normalize_gcd] at this 
+        rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2 
     gcd_mul_lcm := fun a b => by
       split_ifs with a0
       · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
@@ -1154,7 +1154,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
       split_ifs with a0; · rfl
-      rw [← normalize_eq_zero] at a0
+      rw [← normalize_eq_zero] at a0 
       have h :=
         (Classical.choose_spec
             (dvd_normalize_iff.2 ((gcd_dvd_left a 0).trans (Dvd.intro 0 rfl)))).symm
@@ -1162,7 +1162,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         by
         rw [← normalize_gcd]
         exact normalize_eq_normalize (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) (dvd_zero a))
-      rw [← gcd0] at a0
+      rw [← gcd0] at a0 
       apply Or.resolve_left (mul_eq_zero.1 _) a0
       rw [h, MulZeroClass.mul_zero, normalize_zero] }
 #align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCD
@@ -1189,7 +1189,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), mul_comm,
         mul_dvd_mul_iff_right h]
@@ -1201,7 +1201,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b),
         mul_dvd_mul_iff_right h_1]
@@ -1213,12 +1213,12 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       have h0 : lcm c b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd c b)]
       rcases ab with ⟨d, rfl⟩
-      rw [mul_eq_zero] at h_1
-      push_neg  at h_1
+      rw [mul_eq_zero] at h_1 
+      push_neg  at h_1 
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]
@@ -1254,7 +1254,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       apply mul_left_cancel₀ h0
       refine' trans _ (Classical.choose_spec (exists_gcd a b))
@@ -1271,7 +1271,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), normalize_dvd_iff,
         mul_comm, mul_dvd_mul_iff_right h]
@@ -1283,7 +1283,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ← Classical.choose_spec (exists_gcd a b), normalize_dvd_iff,
         mul_dvd_mul_iff_right h_1]
@@ -1295,15 +1295,15 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       have h0 : lcm c b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl)
-        rw [Con, zero_dvd_iff, mul_eq_zero] at h
+        rw [Con, zero_dvd_iff, mul_eq_zero] at h 
         cases h <;> tauto
       rw [← mul_dvd_mul_iff_left h0, ←
         Classical.choose_spec
           (dvd_normalize_iff.2 (lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left c rfl))),
         dvd_normalize_iff]
       rcases ab with ⟨d, rfl⟩
-      rw [mul_eq_zero] at h_1
-      push_neg  at h_1
+      rw [mul_eq_zero] at h_1 
+      push_neg  at h_1 
       rw [mul_comm a, ← mul_assoc, mul_dvd_mul_iff_right h_1.1]
       apply lcm_dvd (Dvd.intro d rfl)
       rw [mul_comm, mul_dvd_mul_iff_right h_1.2]

baba818b

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -92,12 +92,6 @@ section NormalizationMonoid
 
 variable [CancelCommMonoidWithZero α] [NormalizationMonoid α]
 
-/- warning: norm_unit_one -> normUnit_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (OfNat.mk.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.one.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.mulOneClass.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.toOfNat1.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (InvOneClass.toOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivInvOneMonoid.toInvOneClass.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionMonoid.toDivInvOneMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionCommMonoid.toDivisionMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommGroup.toDivisionCommMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.instCommGroupUnitsToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-Case conversion may be inaccurate. Consider using '#align norm_unit_one normUnit_oneₓ'. -/
 @[simp]
 theorem normUnit_one : normUnit (1 : α) = 1 :=
   normUnit_coe_units 1
@@ -122,125 +116,53 @@ def normalize : α →*₀ α where
 #align normalize normalize
 -/
 
-/- warning: associated_normalize -> associated_normalize is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
-Case conversion may be inaccurate. Consider using '#align associated_normalize associated_normalizeₓ'. -/
 theorem associated_normalize (x : α) : Associated x (normalize x) :=
   ⟨_, rfl⟩
 #align associated_normalize associated_normalize
 
-/- warning: normalize_associated -> normalize_associated is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) x
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
-Case conversion may be inaccurate. Consider using '#align normalize_associated normalize_associatedₓ'. -/
 theorem normalize_associated (x : α) : Associated (normalize x) x :=
   (associated_normalize _).symm
 #align normalize_associated normalize_associated
 
-/- warning: associated_normalize_iff -> associated_normalize_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
-Case conversion may be inaccurate. Consider using '#align associated_normalize_iff associated_normalize_iffₓ'. -/
 theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Associated x y :=
   ⟨fun h => h.trans (normalize_associated y), fun h => h.trans (associated_normalize y)⟩
 #align associated_normalize_iff associated_normalize_iff
 
-/- warning: normalize_associated_iff -> normalize_associated_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
-Case conversion may be inaccurate. Consider using '#align normalize_associated_iff normalize_associated_iffₓ'. -/
 theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Associated x y :=
   ⟨fun h => (associated_normalize _).trans h, fun h => (normalize_associated _).trans h⟩
 #align normalize_associated_iff normalize_associated_iff
 
-/- warning: associates.mk_normalize -> Associates.mk_normalize is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
-Case conversion may be inaccurate. Consider using '#align associates.mk_normalize Associates.mk_normalizeₓ'. -/
 theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associates.mk x :=
   Associates.mk_eq_mk_iff_associated.2 (normalize_associated _)
 #align associates.mk_normalize Associates.mk_normalize
 
-/- warning: normalize_apply -> normalize_apply is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
-Case conversion may be inaccurate. Consider using '#align normalize_apply normalize_applyₓ'. -/
 @[simp]
 theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
   rfl
 #align normalize_apply normalize_apply
 
-/- warning: normalize_zero -> normalize_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
-Case conversion may be inaccurate. Consider using '#align normalize_zero normalize_zeroₓ'. -/
 @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
   normalize.map_zero
 #align normalize_zero normalize_zero
 
-/- warning: normalize_one -> normalize_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align normalize_one normalize_oneₓ'. -/
 @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
   normalize.map_one
 #align normalize_one normalize_one
 
-/- warning: normalize_coe_units -> normalize_coe_units is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align normalize_coe_units normalize_coe_unitsₓ'. -/
 theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 #align normalize_coe_units normalize_coe_units
 
-/- warning: normalize_eq_zero -> normalize_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align normalize_eq_zero normalize_eq_zeroₓ'. -/
 theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
   ⟨fun hx => (associated_zero_iff_eq_zero x).1 <| hx ▸ associated_normalize _, by
     rintro rfl <;> exact normalize_zero⟩
 #align normalize_eq_zero normalize_eq_zero
 
-/- warning: normalize_eq_one -> normalize_eq_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
-Case conversion may be inaccurate. Consider using '#align normalize_eq_one normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
 #align normalize_eq_one normalize_eq_one
 
-/- warning: norm_unit_mul_norm_unit -> normUnit_mul_normUnit is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 a)))) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (OfNat.mk.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.one.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.mulOneClass.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 a)))) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.toOfNat1.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (InvOneClass.toOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivInvOneMonoid.toInvOneClass.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionMonoid.toDivInvOneMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionCommMonoid.toDivisionMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommGroup.toDivisionCommMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.instCommGroupUnitsToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-Case conversion may be inaccurate. Consider using '#align norm_unit_mul_norm_unit normUnit_mul_normUnitₓ'. -/
 @[simp]
 theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
   by
@@ -250,18 +172,9 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
   · rw [norm_unit_mul h (Units.ne_zero _), norm_unit_coe_units, mul_inv_eq_one]
 #align norm_unit_mul_norm_unit normUnit_mul_normUnit
 
-/- warning: normalize_idem -> normalize_idem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normalize_idem normalize_idemₓ'. -/
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
 
-/- warning: normalize_eq_normalize -> normalize_eq_normalize is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
-Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize normalize_eq_normalizeₓ'. -/
 theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
   by
   nontriviality α
@@ -275,45 +188,21 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
     
 #align normalize_eq_normalize normalize_eq_normalize
 
-/- warning: normalize_eq_normalize_iff -> normalize_eq_normalize_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
-Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize_iff normalize_eq_normalize_iffₓ'. -/
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
   ⟨fun h => ⟨Units.dvd_mul_right.1 ⟨_, h.symm⟩, Units.dvd_mul_right.1 ⟨_, h⟩⟩, fun ⟨hxy, hyx⟩ =>
     normalize_eq_normalize hxy hyx⟩
 #align normalize_eq_normalize_iff normalize_eq_normalize_iff
 
-/- warning: dvd_antisymm_of_normalize_eq -> dvd_antisymm_of_normalize_eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
-Case conversion may be inaccurate. Consider using '#align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eqₓ'. -/
 theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : normalize b = b)
     (hab : a ∣ b) (hba : b ∣ a) : a = b :=
   ha ▸ hb ▸ normalize_eq_normalize hab hba
 #align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eq
 
-/- warning: dvd_normalize_iff -> dvd_normalize_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align dvd_normalize_iff dvd_normalize_iffₓ'. -/
 --can be proven by simp
 theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
   Units.dvd_mul_right
 #align dvd_normalize_iff dvd_normalize_iff
 
-/- warning: normalize_dvd_iff -> normalize_dvd_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align normalize_dvd_iff normalize_dvd_iffₓ'. -/
 --can be proven by simp
 theorem normalize_dvd_iff {a b : α} : normalize a ∣ b ↔ a ∣ b :=
   Units.mul_right_dvd
@@ -335,78 +224,36 @@ protected def out : Associates α → α :=
 #align associates.out Associates.out
 -/
 
-/- warning: associates.out_mk -> Associates.out_mk is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
-Case conversion may be inaccurate. Consider using '#align associates.out_mk Associates.out_mkₓ'. -/
 @[simp]
 theorem out_mk (a : α) : (Associates.mk a).out = normalize a :=
   rfl
 #align associates.out_mk Associates.out_mk
 
-/- warning: associates.out_one -> Associates.out_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (OfNat.mk.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.one.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.hasOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.toOfNat1.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instOneAssociates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align associates.out_one Associates.out_oneₓ'. -/
 @[simp]
 theorem out_one : (1 : Associates α).out = 1 :=
   normalize_one
 #align associates.out_one Associates.out_one
 
-/- warning: associates.out_mul -> Associates.out_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (instHMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.hasMul.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a b)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (Associates.out.{u1} α _inst_1 _inst_2 a) (Associates.out.{u1} α _inst_1 _inst_2 b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (instHMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instMulAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a b)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (Associates.out.{u1} α _inst_1 _inst_2 a) (Associates.out.{u1} α _inst_1 _inst_2 b))
-Case conversion may be inaccurate. Consider using '#align associates.out_mul Associates.out_mulₓ'. -/
 theorem out_mul (a b : Associates α) : (a * b).out = a.out * b.out :=
   Quotient.induction_on₂ a b fun a b => by
     simp only [Associates.quotient_mk_eq_mk, out_mk, mk_mul_mk, normalize.map_mul]
 #align associates.out_mul Associates.out_mul
 
-/- warning: associates.dvd_out_iff -> Associates.dvd_out_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (Associates.out.{u1} α _inst_1 _inst_2 b)) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a) b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (Associates.out.{u1} α _inst_1 _inst_2 b)) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a) b)
-Case conversion may be inaccurate. Consider using '#align associates.dvd_out_iff Associates.dvd_out_iffₓ'. -/
 theorem dvd_out_iff (a : α) (b : Associates α) : a ∣ b.out ↔ Associates.mk a ≤ b :=
   Quotient.inductionOn b <| by
     simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
 #align associates.dvd_out_iff Associates.dvd_out_iff
 
-/- warning: associates.out_dvd_iff -> Associates.out_dvd_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.out.{u1} α _inst_1 _inst_2 b) a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) b (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.out.{u1} α _inst_1 _inst_2 b) a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) b (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a))
-Case conversion may be inaccurate. Consider using '#align associates.out_dvd_iff Associates.out_dvd_iffₓ'. -/
 theorem out_dvd_iff (a : α) (b : Associates α) : b.out ∣ a ↔ b ≤ Associates.mk a :=
   Quotient.inductionOn b <| by
     simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
 #align associates.out_dvd_iff Associates.out_dvd_iff
 
-/- warning: associates.out_top -> Associates.out_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Top.top.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.hasTop.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Top.top.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instTopAssociates.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align associates.out_top Associates.out_topₓ'. -/
 @[simp]
 theorem out_top : (⊤ : Associates α).out = 0 :=
   normalize_zero
 #align associates.out_top Associates.out_top
 
-/- warning: associates.normalize_out -> Associates.normalize_out is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
-Case conversion may be inaccurate. Consider using '#align associates.normalize_out Associates.normalize_outₓ'. -/
 @[simp]
 theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
   Quotient.inductionOn a normalize_idem
@@ -467,23 +314,11 @@ section GCDMonoid
 
 variable [CancelCommMonoidWithZero α]
 
-/- warning: normalize_gcd -> normalize_gcd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
-Case conversion may be inaccurate. Consider using '#align normalize_gcd normalize_gcdₓ'. -/
 @[simp]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
   NormalizedGCDMonoid.normalize_gcd
 #align normalize_gcd normalize_gcd
 
-/- warning: gcd_mul_lcm -> gcd_mul_lcm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 a b)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 a b)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b)
-Case conversion may be inaccurate. Consider using '#align gcd_mul_lcm gcd_mul_lcmₓ'. -/
 theorem gcd_mul_lcm [GCDMonoid α] : ∀ a b : α, Associated (gcd a b * lcm a b) (a * b) :=
   GCDMonoid.gcd_mul_lcm
 #align gcd_mul_lcm gcd_mul_lcm
@@ -540,65 +375,29 @@ instance [NormalizedGCDMonoid α] : IsCommutative α gcd :=
 instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
   ⟨gcd_assoc⟩
 
-/- warning: gcd_eq_normalize -> gcd_eq_normalize is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_normalize gcd_eq_normalizeₓ'. -/
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
   normalize_gcd a b ▸ normalize_eq_normalize habc hcab
 #align gcd_eq_normalize gcd_eq_normalize
 
-/- warning: gcd_zero_left -> gcd_zero_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align gcd_zero_left gcd_zero_leftₓ'. -/
 @[simp]
 theorem gcd_zero_left [NormalizedGCDMonoid α] (a : α) : gcd 0 a = normalize a :=
   gcd_eq_normalize (gcd_dvd_right 0 a) (dvd_gcd (dvd_zero _) (dvd_refl a))
 #align gcd_zero_left gcd_zero_left
 
-/- warning: gcd_zero_left' -> gcd_zero_left' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) a
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) a
-Case conversion may be inaccurate. Consider using '#align gcd_zero_left' gcd_zero_left'ₓ'. -/
 theorem gcd_zero_left' [GCDMonoid α] (a : α) : Associated (gcd 0 a) a :=
   associated_of_dvd_dvd (gcd_dvd_right 0 a) (dvd_gcd (dvd_zero _) (dvd_refl a))
 #align gcd_zero_left' gcd_zero_left'
 
-/- warning: gcd_zero_right -> gcd_zero_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align gcd_zero_right gcd_zero_rightₓ'. -/
 @[simp]
 theorem gcd_zero_right [NormalizedGCDMonoid α] (a : α) : gcd a 0 = normalize a :=
   gcd_eq_normalize (gcd_dvd_left a 0) (dvd_gcd (dvd_refl a) (dvd_zero _))
 #align gcd_zero_right gcd_zero_right
 
-/- warning: gcd_zero_right' -> gcd_zero_right' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) a
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a
-Case conversion may be inaccurate. Consider using '#align gcd_zero_right' gcd_zero_right'ₓ'. -/
 theorem gcd_zero_right' [GCDMonoid α] (a : α) : Associated (gcd a 0) a :=
   associated_of_dvd_dvd (gcd_dvd_left a 0) (dvd_gcd (dvd_refl a) (dvd_zero _))
 #align gcd_zero_right' gcd_zero_right'
 
-/- warning: gcd_eq_zero_iff -> gcd_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_zero_iff gcd_eq_zero_iffₓ'. -/
 @[simp]
 theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b = 0 :=
   Iff.intro
@@ -611,45 +410,21 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     apply dvd_gcd <;> rfl
 #align gcd_eq_zero_iff gcd_eq_zero_iff
 
-/- warning: gcd_one_left -> gcd_one_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align gcd_one_left gcd_one_leftₓ'. -/
 @[simp]
 theorem gcd_one_left [NormalizedGCDMonoid α] (a : α) : gcd 1 a = 1 :=
   dvd_antisymm_of_normalize_eq (normalize_gcd _ _) normalize_one (gcd_dvd_left _ _) (one_dvd _)
 #align gcd_one_left gcd_one_left
 
-/- warning: gcd_one_left' -> gcd_one_left' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align gcd_one_left' gcd_one_left'ₓ'. -/
 @[simp]
 theorem gcd_one_left' [GCDMonoid α] (a : α) : Associated (gcd 1 a) 1 :=
   associated_of_dvd_dvd (gcd_dvd_left _ _) (one_dvd _)
 #align gcd_one_left' gcd_one_left'
 
-/- warning: gcd_one_right -> gcd_one_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align gcd_one_right gcd_one_rightₓ'. -/
 @[simp]
 theorem gcd_one_right [NormalizedGCDMonoid α] (a : α) : gcd a 1 = 1 :=
   dvd_antisymm_of_normalize_eq (normalize_gcd _ _) normalize_one (gcd_dvd_right _ _) (one_dvd _)
 #align gcd_one_right gcd_one_right
 
-/- warning: gcd_one_right' -> gcd_one_right' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align gcd_one_right' gcd_one_right'ₓ'. -/
 @[simp]
 theorem gcd_one_right' [GCDMonoid α] (a : α) : Associated (gcd a 1) 1 :=
   associated_of_dvd_dvd (gcd_dvd_right _ _) (one_dvd _)
@@ -661,23 +436,11 @@ theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 #align gcd_dvd_gcd gcd_dvd_gcd
 -/
 
-/- warning: gcd_same -> gcd_same is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align gcd_same gcd_sameₓ'. -/
 @[simp]
 theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
   gcd_eq_normalize (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) (dvd_refl a))
 #align gcd_same gcd_same
 
-/- warning: gcd_mul_left -> gcd_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
-Case conversion may be inaccurate. Consider using '#align gcd_mul_left gcd_mul_leftₓ'. -/
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     gcd (a * b) (a * c) = normalize a * gcd b c :=
@@ -694,12 +457,6 @@ theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
       (dvd_gcd (mul_dvd_mul_left a <| gcd_dvd_left _ _) (mul_dvd_mul_left a <| gcd_dvd_right _ _))
 #align gcd_mul_left gcd_mul_left
 
-/- warning: gcd_mul_left' -> gcd_mul_left' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 b c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 b c))
-Case conversion may be inaccurate. Consider using '#align gcd_mul_left' gcd_mul_left'ₓ'. -/
 theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a * c)) (a * gcd b c) :=
   by
   obtain rfl | ha := eq_or_ne a 0
@@ -714,86 +471,38 @@ theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a *
   · exact dvd_gcd (mul_dvd_mul_left a <| gcd_dvd_left _ _) (mul_dvd_mul_left a <| gcd_dvd_right _ _)
 #align gcd_mul_left' gcd_mul_left'
 
-/- warning: gcd_mul_right -> gcd_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
-Case conversion may be inaccurate. Consider using '#align gcd_mul_right gcd_mul_rightₓ'. -/
 @[simp]
 theorem gcd_mul_right [NormalizedGCDMonoid α] (a b c : α) :
     gcd (b * a) (c * a) = gcd b c * normalize a := by simp only [mul_comm, gcd_mul_left]
 #align gcd_mul_right gcd_mul_right
 
-/- warning: gcd_mul_right' -> gcd_mul_right' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 b c) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 b c) a)
-Case conversion may be inaccurate. Consider using '#align gcd_mul_right' gcd_mul_right'ₓ'. -/
 @[simp]
 theorem gcd_mul_right' [GCDMonoid α] (a b c : α) : Associated (gcd (b * a) (c * a)) (gcd b c * a) :=
   by simp only [mul_comm, gcd_mul_left']
 #align gcd_mul_right' gcd_mul_right'
 
-/- warning: gcd_eq_left_iff -> gcd_eq_left_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_left_iff gcd_eq_left_iffₓ'. -/
 theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     gcd a b = a ↔ a ∣ b :=
   Iff.intro (fun eq => Eq ▸ gcd_dvd_right _ _) fun hab =>
     dvd_antisymm_of_normalize_eq (normalize_gcd _ _) h (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) hab)
 #align gcd_eq_left_iff gcd_eq_left_iff
 
-/- warning: gcd_eq_right_iff -> gcd_eq_right_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_right_iff gcd_eq_right_iffₓ'. -/
 theorem gcd_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     gcd a b = b ↔ b ∣ a := by simpa only [gcd_comm a b] using gcd_eq_left_iff b a h
 #align gcd_eq_right_iff gcd_eq_right_iff
 
-/- warning: gcd_dvd_gcd_mul_left -> gcd_dvd_gcd_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k m) n)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k m) n)
-Case conversion may be inaccurate. Consider using '#align gcd_dvd_gcd_mul_left gcd_dvd_gcd_mul_leftₓ'. -/
 theorem gcd_dvd_gcd_mul_left [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd (k * m) n :=
   gcd_dvd_gcd (dvd_mul_left _ _) dvd_rfl
 #align gcd_dvd_gcd_mul_left gcd_dvd_gcd_mul_left
 
-/- warning: gcd_dvd_gcd_mul_right -> gcd_dvd_gcd_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m k) n)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m k) n)
-Case conversion may be inaccurate. Consider using '#align gcd_dvd_gcd_mul_right gcd_dvd_gcd_mul_rightₓ'. -/
 theorem gcd_dvd_gcd_mul_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd (m * k) n :=
   gcd_dvd_gcd (dvd_mul_right _ _) dvd_rfl
 #align gcd_dvd_gcd_mul_right gcd_dvd_gcd_mul_right
 
-/- warning: gcd_dvd_gcd_mul_left_right -> gcd_dvd_gcd_mul_left_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k n))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k n))
-Case conversion may be inaccurate. Consider using '#align gcd_dvd_gcd_mul_left_right gcd_dvd_gcd_mul_left_rightₓ'. -/
 theorem gcd_dvd_gcd_mul_left_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd m (k * n) :=
   gcd_dvd_gcd dvd_rfl (dvd_mul_left _ _)
 #align gcd_dvd_gcd_mul_left_right gcd_dvd_gcd_mul_left_right
 
-/- warning: gcd_dvd_gcd_mul_right_right -> gcd_dvd_gcd_mul_right_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) n k))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) n k))
-Case conversion may be inaccurate. Consider using '#align gcd_dvd_gcd_mul_right_right gcd_dvd_gcd_mul_right_rightₓ'. -/
 theorem gcd_dvd_gcd_mul_right_right [GCDMonoid α] (m n k : α) : gcd m n ∣ gcd m (n * k) :=
   gcd_dvd_gcd dvd_rfl (dvd_mul_right _ _)
 #align gcd_dvd_gcd_mul_right_right gcd_dvd_gcd_mul_right_right
@@ -814,32 +523,14 @@ theorem Associated.gcd_eq_right [NormalizedGCDMonoid α] {m n : α} (h : Associa
 #align associated.gcd_eq_right Associated.gcd_eq_right
 -/
 
-/- warning: dvd_gcd_mul_of_dvd_mul -> dvd_gcd_mul_of_dvd_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k m) n))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k m) n))
-Case conversion may be inaccurate. Consider using '#align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mulₓ'. -/
 theorem dvd_gcd_mul_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ gcd k m * n :=
   (dvd_gcd (dvd_mul_right _ n) H).trans (gcd_mul_right' n k m).Dvd
 #align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mul
 
-/- warning: dvd_mul_gcd_of_dvd_mul -> dvd_mul_gcd_of_dvd_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k n)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k n)))
-Case conversion may be inaccurate. Consider using '#align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mulₓ'. -/
 theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
   rw [mul_comm] at H⊢; exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
 
-/- warning: exists_dvd_and_dvd_of_dvd_mul -> exists_dvd_and_dvd_of_dvd_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Exists.{succ u1} α (fun (d₁ : α) => Exists.{succ u1} α (fun (d₂ : α) => And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ m) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₂ n) (Eq.{succ u1} α k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Exists.{succ u1} α (fun (d₁ : α) => Exists.{succ u1} α (fun (d₂ : α) => And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ m) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₂ n) (Eq.{succ u1} α k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂))))))
-Case conversion may be inaccurate. Consider using '#align exists_dvd_and_dvd_of_dvd_mul exists_dvd_and_dvd_of_dvd_mulₓ'. -/
 /-- Represent a divisor of `m * n` as a product of a divisor of `m` and a divisor of `n`.
 
 In other words, the nonzero elements of a `gcd_monoid` form a decomposition monoid
@@ -867,12 +558,6 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     exact dvd_gcd_mul_of_dvd_mul H
 #align exists_dvd_and_dvd_of_dvd_mul exists_dvd_and_dvd_of_dvd_mul
 
-/- warning: dvd_mul -> dvd_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {k : α} {m : α} {n : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) (Exists.{succ u1} α (fun (d₁ : α) => Exists.{succ u1} α (fun (d₂ : α) => And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ m) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₂ n) (Eq.{succ u1} α k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {k : α} {m : α} {n : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) (Exists.{succ u1} α (fun (d₁ : α) => Exists.{succ u1} α (fun (d₂ : α) => And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ m) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₂ n) (Eq.{succ u1} α k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂))))))
-Case conversion may be inaccurate. Consider using '#align dvd_mul dvd_mulₓ'. -/
 theorem dvd_mul [GCDMonoid α] {k m n : α} : k ∣ m * n ↔ ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ :=
   by
   refine' ⟨exists_dvd_and_dvd_of_dvd_mul, _⟩
@@ -880,12 +565,6 @@ theorem dvd_mul [GCDMonoid α] {k m n : α} : k ∣ m * n ↔ ∃ d₁ d₂, d
   exact mul_dvd_mul hy hz
 #align dvd_mul dvd_mul
 
-/- warning: gcd_mul_dvd_mul_gcd -> gcd_mul_dvd_mul_gcd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (k : α) (m : α) (n : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k m) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k n))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (k : α) (m : α) (n : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k m) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k n))
-Case conversion may be inaccurate. Consider using '#align gcd_mul_dvd_mul_gcd gcd_mul_dvd_mul_gcdₓ'. -/
 theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd k m * gcd k n :=
   by
   obtain ⟨m', n', hm', hn', h⟩ := exists_dvd_and_dvd_of_dvd_mul (gcd_dvd_right k (m * n))
@@ -928,12 +607,6 @@ theorem gcd_pow_left_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd (a ^
 #align gcd_pow_left_dvd_pow_gcd gcd_pow_left_dvd_pow_gcd
 -/
 
-/- warning: pow_dvd_of_mul_eq_pow -> pow_dvd_of_mul_eq_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α} {d₁ : α} {d₂ : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) -> (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Eq.{succ u1} α c (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂)) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ a) -> (And (Ne.{succ u1} α (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ k) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ k) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α} {d₁ : α} {d₂ : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Eq.{succ u1} α c (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) d₁ d₂)) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ a) -> (And (Ne.{succ u1} α (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ k) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d₁ k) a)))
-Case conversion may be inaccurate. Consider using '#align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_powₓ'. -/
 theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠ 0) (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) (hc : c = d₁ * d₂) (hd₁ : d₁ ∣ a) : d₁ ^ k ≠ 0 ∧ d₁ ^ k ∣ a :=
   by
@@ -953,12 +626,6 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
   exact ⟨h4, h3⟩
 #align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_pow
 
-/- warning: exists_associated_pow_of_mul_eq_pow -> exists_associated_pow_of_mul_eq_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Exists.{succ u1} α (fun (d : α) => Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d k) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Exists.{succ u1} α (fun (d : α) => Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d k) a)))
-Case conversion may be inaccurate. Consider using '#align exists_associated_pow_of_mul_eq_pow exists_associated_pow_of_mul_eq_powₓ'. -/
 theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) : ∃ d : α, Associated (d ^ k) a :=
   by
@@ -993,24 +660,12 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
   rw [Units.val_mkOfMulEqOne, ha']
 #align exists_associated_pow_of_mul_eq_pow exists_associated_pow_of_mul_eq_pow
 
-/- warning: exists_eq_pow_of_mul_eq_pow -> exists_eq_pow_of_mul_eq_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] [_inst_3 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] {a : α} {b : α} {c : α}, (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Exists.{succ u1} α (fun (d : α) => Eq.{succ u1} α a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d k))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] [_inst_3 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] {a : α} {b : α} {c : α}, (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 a b)) -> (forall {k : Nat}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c k)) -> (Exists.{succ u1} α (fun (d : α) => Eq.{succ u1} α a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) d k))))
-Case conversion may be inaccurate. Consider using '#align exists_eq_pow_of_mul_eq_pow exists_eq_pow_of_mul_eq_powₓ'. -/
 theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (hab : IsUnit (gcd a b))
     {k : ℕ} (h : a * b = c ^ k) : ∃ d : α, a = d ^ k :=
   let ⟨d, hd⟩ := exists_associated_pow_of_mul_eq_pow hab h
   ⟨d, (associated_iff_eq.mp hd).symm⟩
 #align exists_eq_pow_of_mul_eq_pow exists_eq_pow_of_mul_eq_pow
 
-/- warning: gcd_greatest -> gcd_greatest is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_2 _inst_3) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
-Case conversion may be inaccurate. Consider using '#align gcd_greatest gcd_greatestₓ'. -/
 theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
     GCDMonoid.gcd a b = normalize d :=
@@ -1027,12 +682,6 @@ theorem gcd_greatest_associated {α : Type _} [CancelCommMonoidWithZero α] [GCD
 #align gcd_greatest_associated gcd_greatest_associated
 -/
 
-/- warning: is_unit_gcd_of_eq_mul_gcd -> isUnit_gcd_of_eq_mul_gcd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : GCDMonoid.{u1} α _inst_2] {x : α} {y : α} {x' : α} {y' : α}, (Eq.{succ u1} α x (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) x')) -> (Eq.{succ u1} α y (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) y')) -> (Ne.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))))) -> (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x' y'))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : GCDMonoid.{u1} α _inst_2] {x : α} {y : α} {x' : α} {y' : α}, (Eq.{succ u1} α x (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) x')) -> (Eq.{succ u1} α y (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) y')) -> (Ne.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) -> (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x' y'))
-Case conversion may be inaccurate. Consider using '#align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcdₓ'. -/
 theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α]
     {x y x' y' : α} (ex : x = gcd x y * x') (ey : y = gcd x y * y') (h : gcd x y ≠ 0) :
     IsUnit (gcd x' y') := by
@@ -1042,12 +691,6 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GC
   rw [← ex, ← ey, mul_one]
 #align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcd
 
-/- warning: extract_gcd -> extract_gcd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : GCDMonoid.{u1} α _inst_2] (x : α) (y : α), Exists.{succ u1} α (fun (x' : α) => Exists.{succ u1} α (fun (y' : α) => And (Eq.{succ u1} α x (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) x')) (And (Eq.{succ u1} α y (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) y')) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x' y')))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : GCDMonoid.{u1} α _inst_2] (x : α) (y : α), Exists.{succ u1} α (fun (x' : α) => Exists.{succ u1} α (fun (y' : α) => And (Eq.{succ u1} α x (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) x')) (And (Eq.{succ u1} α y (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x y) y')) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (GCDMonoid.gcd.{u1} α _inst_2 _inst_3 x' y')))))
-Case conversion may be inaccurate. Consider using '#align extract_gcd extract_gcdₓ'. -/
 theorem extract_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] (x y : α) :
     ∃ x' y', x = gcd x y * x' ∧ y = gcd x y * y' ∧ IsUnit (gcd x' y') :=
   by
@@ -1099,12 +742,6 @@ theorem lcm_dvd [GCDMonoid α] {a b c : α} (hab : a ∣ b) (hcb : c ∣ b) : lc
 #align lcm_dvd lcm_dvd
 -/
 
-/- warning: lcm_eq_zero_iff -> lcm_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 a b) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Or (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 a b) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Or (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align lcm_eq_zero_iff lcm_eq_zero_iffₓ'. -/
 @[simp]
 theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b = 0 :=
   Iff.intro
@@ -1116,12 +753,6 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
     (by rintro (rfl | rfl) <;> [apply lcm_zero_left;apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
 
-/- warning: normalize_lcm -> normalize_lcm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
-Case conversion may be inaccurate. Consider using '#align normalize_lcm normalize_lcmₓ'. -/
 @[simp]
 theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
   NormalizedGCDMonoid.normalize_lcm a b
@@ -1168,12 +799,6 @@ instance [NormalizedGCDMonoid α] : IsCommutative α lcm :=
 instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
   ⟨lcm_assoc⟩
 
-/- warning: lcm_eq_normalize -> lcm_eq_normalize is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
-Case conversion may be inaccurate. Consider using '#align lcm_eq_normalize lcm_eq_normalizeₓ'. -/
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=
   normalize_lcm a b ▸ normalize_eq_normalize habc hcab
@@ -1185,67 +810,31 @@ theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 #align lcm_dvd_lcm lcm_dvd_lcm
 -/
 
-/- warning: lcm_units_coe_left -> lcm_units_coe_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align lcm_units_coe_left lcm_units_coe_leftₓ'. -/
 @[simp]
 theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (↑u) a = normalize a :=
   lcm_eq_normalize (lcm_dvd Units.coe_dvd dvd_rfl) (dvd_lcm_right _ _)
 #align lcm_units_coe_left lcm_units_coe_left
 
-/- warning: lcm_units_coe_right -> lcm_units_coe_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align lcm_units_coe_right lcm_units_coe_rightₓ'. -/
 @[simp]
 theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a ↑u = normalize a :=
   (lcm_comm a u).trans <| lcm_units_coe_left _ _
 #align lcm_units_coe_right lcm_units_coe_right
 
-/- warning: lcm_one_left -> lcm_one_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align lcm_one_left lcm_one_leftₓ'. -/
 @[simp]
 theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :=
   lcm_units_coe_left 1 a
 #align lcm_one_left lcm_one_left
 
-/- warning: lcm_one_right -> lcm_one_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align lcm_one_right lcm_one_rightₓ'. -/
 @[simp]
 theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a :=
   lcm_units_coe_right a 1
 #align lcm_one_right lcm_one_right
 
-/- warning: lcm_same -> lcm_same is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
-Case conversion may be inaccurate. Consider using '#align lcm_same lcm_sameₓ'. -/
 @[simp]
 theorem lcm_same [NormalizedGCDMonoid α] (a : α) : lcm a a = normalize a :=
   lcm_eq_normalize (lcm_dvd dvd_rfl dvd_rfl) (dvd_lcm_left _ _)
 #align lcm_same lcm_same
 
-/- warning: lcm_eq_one_iff -> lcm_eq_one_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align lcm_eq_one_iff lcm_eq_one_iffₓ'. -/
 @[simp]
 theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a ∣ 1 ∧ b ∣ 1 :=
   Iff.intro (fun eq => Eq ▸ ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩) fun ⟨⟨c, hc⟩, ⟨d, hd⟩⟩ =>
@@ -1253,12 +842,6 @@ theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a 
       rw [lcm_units_coe_left, normalize_coe_units]
 #align lcm_eq_one_iff lcm_eq_one_iff
 
-/- warning: lcm_mul_left -> lcm_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
-Case conversion may be inaccurate. Consider using '#align lcm_mul_left lcm_mul_leftₓ'. -/
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     lcm (a * b) (a * c) = normalize a * lcm b c :=
@@ -1276,75 +859,33 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
             ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ dvd_lcm_right _ _)))
 #align lcm_mul_left lcm_mul_left
 
-/- warning: lcm_mul_right -> lcm_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
-Case conversion may be inaccurate. Consider using '#align lcm_mul_right lcm_mul_rightₓ'. -/
 @[simp]
 theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
     lcm (b * a) (c * a) = lcm b c * normalize a := by simp only [mul_comm, lcm_mul_left]
 #align lcm_mul_right lcm_mul_right
 
-/- warning: lcm_eq_left_iff -> lcm_eq_left_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
-Case conversion may be inaccurate. Consider using '#align lcm_eq_left_iff lcm_eq_left_iffₓ'. -/
 theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     lcm a b = a ↔ b ∣ a :=
   Iff.intro (fun eq => Eq ▸ dvd_lcm_right _ _) fun hab =>
     dvd_antisymm_of_normalize_eq (normalize_lcm _ _) h (lcm_dvd (dvd_refl a) hab) (dvd_lcm_left _ _)
 #align lcm_eq_left_iff lcm_eq_left_iff
 
-/- warning: lcm_eq_right_iff -> lcm_eq_right_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align lcm_eq_right_iff lcm_eq_right_iffₓ'. -/
 theorem lcm_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     lcm a b = b ↔ a ∣ b := by simpa only [lcm_comm b a] using lcm_eq_left_iff b a h
 #align lcm_eq_right_iff lcm_eq_right_iff
 
-/- warning: lcm_dvd_lcm_mul_left -> lcm_dvd_lcm_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k m) n)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k m) n)
-Case conversion may be inaccurate. Consider using '#align lcm_dvd_lcm_mul_left lcm_dvd_lcm_mul_leftₓ'. -/
 theorem lcm_dvd_lcm_mul_left [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm (k * m) n :=
   lcm_dvd_lcm (dvd_mul_left _ _) dvd_rfl
 #align lcm_dvd_lcm_mul_left lcm_dvd_lcm_mul_left
 
-/- warning: lcm_dvd_lcm_mul_right -> lcm_dvd_lcm_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m k) n)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m k) n)
-Case conversion may be inaccurate. Consider using '#align lcm_dvd_lcm_mul_right lcm_dvd_lcm_mul_rightₓ'. -/
 theorem lcm_dvd_lcm_mul_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm (m * k) n :=
   lcm_dvd_lcm (dvd_mul_right _ _) dvd_rfl
 #align lcm_dvd_lcm_mul_right lcm_dvd_lcm_mul_right
 
-/- warning: lcm_dvd_lcm_mul_left_right -> lcm_dvd_lcm_mul_left_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k n))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) k n))
-Case conversion may be inaccurate. Consider using '#align lcm_dvd_lcm_mul_left_right lcm_dvd_lcm_mul_left_rightₓ'. -/
 theorem lcm_dvd_lcm_mul_left_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm m (k * n) :=
   lcm_dvd_lcm dvd_rfl (dvd_mul_left _ _)
 #align lcm_dvd_lcm_mul_left_right lcm_dvd_lcm_mul_left_right
 
-/- warning: lcm_dvd_lcm_mul_right_right -> lcm_dvd_lcm_mul_right_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) n k))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] (m : α) (n : α) (k : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m n) (GCDMonoid.lcm.{u1} α _inst_1 _inst_2 m (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) n k))
-Case conversion may be inaccurate. Consider using '#align lcm_dvd_lcm_mul_right_right lcm_dvd_lcm_mul_right_rightₓ'. -/
 theorem lcm_dvd_lcm_mul_right_right [GCDMonoid α] (m n k : α) : lcm m n ∣ lcm m (n * k) :=
   lcm_dvd_lcm dvd_rfl (dvd_mul_right _ _)
 #align lcm_dvd_lcm_mul_right_right lcm_dvd_lcm_mul_right_right
@@ -1448,34 +989,16 @@ instance subsingleton_normalizedGCDMonoid_of_unique_units : Subsingleton (Normal
 #align subsingleton_normalized_gcd_monoid_of_unique_units subsingleton_normalizedGCDMonoid_of_unique_units
 -/
 
-/- warning: norm_unit_eq_one -> normUnit_eq_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (OfNat.mk.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.one.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.mulOneClass.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (NormalizationMonoid.normUnit.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 1 (One.toOfNat1.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (InvOneClass.toOne.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivInvOneMonoid.toInvOneClass.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionMonoid.toDivInvOneMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (DivisionCommMonoid.toDivisionMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommGroup.toDivisionCommMonoid.{u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Units.instCommGroupUnitsToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))))
-Case conversion may be inaccurate. Consider using '#align norm_unit_eq_one normUnit_eq_oneₓ'. -/
 @[simp]
 theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
   rfl
 #align norm_unit_eq_one normUnit_eq_one
 
-/- warning: normalize_eq -> normalize_eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
-Case conversion may be inaccurate. Consider using '#align normalize_eq normalize_eqₓ'. -/
 @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
   mul_one x
 #align normalize_eq normalize_eq
 
-/- warning: associates_equiv_of_unique_units -> associatesEquivOfUniqueUnits is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))], MulEquiv.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Associates.hasMul.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))], MulEquiv.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Associates.instMulAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align associates_equiv_of_unique_units associatesEquivOfUniqueUnitsₓ'. -/
 /-- If a monoid's only unit is `1`, then it is isomorphic to its associates. -/
 @[simps]
 def associatesEquivOfUniqueUnits : Associates α ≃* α
@@ -1493,12 +1016,6 @@ section IsDomain
 
 variable [CommRing α] [IsDomain α] [NormalizedGCDMonoid α]
 
-/- warning: gcd_eq_of_dvd_sub_right -> gcd_eq_of_dvd_sub_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (CommSemiring.toSemiring.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_rightₓ'. -/
 theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a c :=
   by
   apply dvd_antisymm_of_normalize_eq (normalize_gcd _ _) (normalize_gcd _ _) <;>
@@ -1516,12 +1033,6 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
     rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel]
 #align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_right
 
-/- warning: gcd_eq_of_dvd_sub_left -> gcd_eq_of_dvd_sub_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (CommSemiring.toSemiring.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
-Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_left gcd_eq_of_dvd_sub_leftₓ'. -/
 theorem gcd_eq_of_dvd_sub_left {a b c : α} (h : a ∣ b - c) : gcd b a = gcd c a := by
   rw [gcd_comm _ a, gcd_comm _ a, gcd_eq_of_dvd_sub_right h]
 #align gcd_eq_of_dvd_sub_left gcd_eq_of_dvd_sub_left
@@ -1541,9 +1052,6 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
     a * ↑(Classical.choose (associated_map_mk hinv a)) = f (Associates.mk a) :=
   Classical.choose_spec (associated_map_mk hinv a)
 
-/- warning: normalization_monoid_of_monoid_hom_right_inverse -> normalizationMonoidOfMonoidHomRightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverseₓ'. -/
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)
     (hinv : Function.RightInverse f Associates.mk) : NormalizationMonoid α
@@ -1601,12 +1109,6 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
 #align gcd_monoid_of_gcd gcdMonoidOfGCD
 -/
 
-/- warning: normalized_gcd_monoid_of_gcd -> normalizedGCDMonoidOfGCD is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCDₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `gcd` and its properties. -/
 noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq α] (gcd : α → α → α)
     (gcd_dvd_left : ∀ a b, gcd a b ∣ a) (gcd_dvd_right : ∀ a b, gcd a b ∣ b)
@@ -1724,12 +1226,6 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
 #align gcd_monoid_of_lcm gcdMonoidOfLCM
 -/
 
-/- warning: normalized_gcd_monoid_of_lcm -> normalizedGCDMonoidOfLCM is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_lcm normalizedGCDMonoidOfLCMₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
     (dvd_lcm_left : ∀ a b, a ∣ lcm a b) (dvd_lcm_right : ∀ a b, b ∣ lcm a b)
@@ -1897,22 +1393,10 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
   normalize_gcd a b := if h : a = 0 ∧ b = 0 then by simp [if_pos h] else by simp [if_neg h]
   normalize_lcm a b := if h : a = 0 ∨ b = 0 then by simp [if_pos h] else by simp [if_neg h]
 
-/- warning: comm_group_with_zero.coe_norm_unit -> CommGroupWithZero.coe_normUnit is a dubious translation:
-lean 3 declaration is
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (coeBase.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (Units.hasCoe.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (DivInvMonoid.toHasInv.{u1} G₀ (GroupWithZero.toDivInvMonoid.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))) a))
-but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} G₀ (Units.val.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (CommGroupWithZero.toInv.{u1} G₀ _inst_1) a))
-Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.coe_norm_unit CommGroupWithZero.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻¹ := by simp [norm_unit, h0]
 #align comm_group_with_zero.coe_norm_unit CommGroupWithZero.coe_normUnit
 
-/- warning: comm_group_with_zero.normalize_eq_one -> CommGroupWithZero.normalize_eq_one is a dubious translation:
-lean 3 declaration is
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
-but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one

baba818b

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -830,10 +830,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : GCDMonoid.{u1} α _inst_1] {m : α} {n : α} {k : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m n)) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) k (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) m (GCDMonoid.gcd.{u1} α _inst_1 _inst_2 k n)))
 Case conversion may be inaccurate. Consider using '#align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mulₓ'. -/
-theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n :=
-  by
-  rw [mul_comm] at H⊢
-  exact dvd_gcd_mul_of_dvd_mul H
+theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
+  rw [mul_comm] at H⊢; exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
 
 /- warning: exists_dvd_and_dvd_of_dvd_mul -> exists_dvd_and_dvd_of_dvd_mul is a dubious translation:
@@ -943,23 +941,15 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
     apply isUnit_of_dvd_one
     trans gcd d₁ b ^ k
     · exact gcd_pow_left_dvd_pow_gcd
-    · apply IsUnit.dvd
-      apply IsUnit.pow
-      apply isUnit_of_dvd_one
+    · apply IsUnit.dvd; apply IsUnit.pow; apply isUnit_of_dvd_one
       apply dvd_trans _ hab.dvd
       apply gcd_dvd_gcd hd₁ (dvd_refl b)
-  have h2 : d₁ ^ k ∣ a * b := by
-    use d₂ ^ k
-    rw [h, hc]
-    exact mul_pow d₁ d₂ k
+  have h2 : d₁ ^ k ∣ a * b := by use d₂ ^ k; rw [h, hc]; exact mul_pow d₁ d₂ k
   rw [mul_comm] at h2
   have h3 : d₁ ^ k ∣ a := by
     apply (dvd_gcd_mul_of_dvd_mul h2).trans
     rw [IsUnit.mul_left_dvd _ _ _ h1]
-  have h4 : d₁ ^ k ≠ 0 := by
-    intro hdk
-    rw [hdk] at h3
-    apply absurd (zero_dvd_iff.mp h3) ha
+  have h4 : d₁ ^ k ≠ 0 := by intro hdk; rw [hdk] at h3; apply absurd (zero_dvd_iff.mp h3) ha
   exact ⟨h4, h3⟩
 #align pow_dvd_of_mul_eq_pow pow_dvd_of_mul_eq_pow
 
@@ -973,31 +963,21 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
     {k : ℕ} (h : a * b = c ^ k) : ∃ d : α, Associated (d ^ k) a :=
   by
   cases subsingleton_or_nontrivial α
-  · use 0
-    rw [Subsingleton.elim a (0 ^ k)]
+  · use 0; rw [Subsingleton.elim a (0 ^ k)]
   by_cases ha : a = 0
-  · use 0
-    rw [ha]
+  · use 0; rw [ha]
     obtain rfl | hk := k.eq_zero_or_pos
-    · exfalso
-      revert h
-      rw [ha, MulZeroClass.zero_mul, pow_zero]
-      apply zero_ne_one
+    · exfalso; revert h; rw [ha, MulZeroClass.zero_mul, pow_zero]; apply zero_ne_one
     · rw [zero_pow hk]
   by_cases hb : b = 0
-  · use 1
-    rw [one_pow]
+  · use 1; rw [one_pow]
     apply (associated_one_iff_is_unit.mpr hab).symm.trans
     rw [hb]
     exact gcd_zero_right' a
   obtain rfl | hk := k.eq_zero_or_pos
-  · use 1
-    rw [pow_zero] at h⊢
-    use Units.mkOfMulEqOne _ _ h
+  · use 1; rw [pow_zero] at h⊢; use Units.mkOfMulEqOne _ _ h
     rw [Units.val_mkOfMulEqOne, one_mul]
-  have hc : c ∣ a * b := by
-    rw [h]
-    exact dvd_pow_self _ hk.ne'
+  have hc : c ∣ a * b := by rw [h]; exact dvd_pow_self _ hk.ne'
   obtain ⟨d₁, d₂, hd₁, hd₂, hc⟩ := exists_dvd_and_dvd_of_dvd_mul hc
   use d₁
   obtain ⟨h0₁, ⟨a', ha'⟩⟩ := pow_dvd_of_mul_eq_pow ha hab h hc hd₁
@@ -1006,10 +986,8 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
   obtain ⟨h0₂, ⟨b', hb'⟩⟩ := pow_dvd_of_mul_eq_pow hb hab h hc hd₂
   rw [ha', hb', hc, mul_pow] at h
   have h' : a' * b' = 1 := by
-    apply (mul_right_inj' h0₁).mp
-    rw [mul_one]
-    apply (mul_right_inj' h0₂).mp
-    rw [← h]
+    apply (mul_right_inj' h0₁).mp; rw [mul_one]
+    apply (mul_right_inj' h0₂).mp; rw [← h]
     rw [mul_assoc, mul_comm a', ← mul_assoc _ b', ← mul_assoc b', mul_comm b']
   use Units.mkOfMulEqOne _ _ h'
   rw [Units.val_mkOfMulEqOne, ha']
@@ -1397,9 +1375,7 @@ theorem prime_of_irreducible [GCDMonoid α] {x : α} (hi : Irreducible x) : Prim
     ⟨hi.1, fun a b h => by
       cases' gcd_dvd_left x a with y hy
       cases' hi.is_unit_or_is_unit hy with hu hu
-      · right
-        trans gcd (x * b) (a * b)
-        apply dvd_gcd (dvd_mul_right x b) h
+      · right; trans gcd (x * b) (a * b); apply dvd_gcd (dvd_mul_right x b) h
         rw [(gcd_mul_right' b x a).dvd_iff_dvd_left]
         exact (associated_unit_mul_left _ _ hu).Dvd
       · left
@@ -1453,8 +1429,7 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
       ext (a b)
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _) <;>
         apply lcm_dvd_iff.2 ⟨dvd_lcm_left _ _, dvd_lcm_right _ _⟩
-    cases g₁
-    cases g₂
+    cases g₁; cases g₂
     dsimp only at hgcd hlcm
     simp only [hgcd, hlcm]⟩
 #align subsingleton_gcd_monoid_of_unique_units subsingleton_gcdMonoid_of_unique_units
@@ -1615,8 +1590,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
       · rw [← Classical.choose_spec ((gcd_dvd_left a b).trans (Dvd.intro b rfl))]
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      split_ifs with a0
-      · rfl
+      split_ifs with a0; · rfl
       have h := (Classical.choose_spec ((gcd_dvd_left a 0).trans (Dvd.intro 0 rfl))).symm
       have a0' : gcd a 0 ≠ 0 := by
         contrapose! a0
@@ -1677,8 +1651,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         exact normalize_associated (a * b)
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      split_ifs with a0
-      · rfl
+      split_ifs with a0; · rfl
       rw [← normalize_eq_zero] at a0
       have h :=
         (Classical.choose_spec
@@ -1709,8 +1682,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
     gcd_dvd_left := fun a b => by
       split_ifs with h h_1
-      · rw [h]
-        apply dvd_zero
+      · rw [h]; apply dvd_zero
       · exact dvd_rfl
       have h0 : lcm a b ≠ 0 := by
         intro con
@@ -1723,8 +1695,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
     gcd_dvd_right := fun a b => by
       split_ifs with h h_1
       · exact dvd_rfl
-      · rw [h_1]
-        apply dvd_zero
+      · rw [h_1]; apply dvd_zero
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
@@ -1799,8 +1770,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
     gcd_dvd_left := fun a b => by
       split_ifs
-      · rw [h]
-        apply dvd_zero
+      · rw [h]; apply dvd_zero
       · exact (normalize_associated _).Dvd
       have h0 : lcm a b ≠ 0 := by
         intro con
@@ -1813,8 +1783,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
     gcd_dvd_right := fun a b => by
       split_ifs
       · exact (normalize_associated _).Dvd
-      · rw [h_1]
-        apply dvd_zero
+      · rw [h_1]; apply dvd_zero
       have h0 : lcm a b ≠ 0 := by
         intro con
         have h := lcm_dvd (Dvd.intro b rfl) (Dvd.intro_left a rfl)
@@ -1907,19 +1876,11 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹
   normUnit_zero := dif_pos rfl
   normUnit_mul x y x0 y0 := Units.eq_iff.1 (by simp [x0, y0, mul_comm])
-  normUnit_coe_units u := by
-    rw [dif_neg (Units.ne_zero _), Units.mk0_val]
-    infer_instance
+  normUnit_coe_units u := by rw [dif_neg (Units.ne_zero _), Units.mk0_val]; infer_instance
   gcd a b := if a = 0 ∧ b = 0 then 0 else 1
   lcm a b := if a = 0 ∨ b = 0 then 0 else 1
-  gcd_dvd_left a b := by
-    split_ifs with h
-    · rw [h.1]
-    · exact one_dvd _
-  gcd_dvd_right a b := by
-    split_ifs with h
-    · rw [h.2]
-    · exact one_dvd _
+  gcd_dvd_left a b := by split_ifs with h; · rw [h.1]; · exact one_dvd _
+  gcd_dvd_right a b := by split_ifs with h; · rw [h.2]; · exact one_dvd _
   dvd_gcd a b c hac hab := by
     split_ifs with h; · apply dvd_zero
     cases' not_and_distrib.mp h with h h <;>

baba818b

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -251,10 +251,7 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
 #align norm_unit_mul_norm_unit normUnit_mul_normUnit
 
 /- warning: normalize_idem -> normalize_idem is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align normalize_idem normalize_idemₓ'. -/
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
@@ -1568,13 +1565,9 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
     (hinv : Function.RightInverse f Associates.mk) (a : α) :
     a * ↑(Classical.choose (associated_map_mk hinv a)) = f (Associates.mk a) :=
   Classical.choose_spec (associated_map_mk hinv a)
-#align map_mk_unit_aux map_mk_unit_aux
 
 /- warning: normalization_monoid_of_monoid_hom_right_inverse -> normalizationMonoidOfMonoidHomRightInverse is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) => (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
+<too large>
 Case conversion may be inaccurate. Consider using '#align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverseₓ'. -/
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)

baba818b

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -1138,7 +1138,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
       have : Associated (a * b) 0 :=
         (gcd_mul_lcm a b).symm.trans <| by rw [h, MulZeroClass.mul_zero]
       simpa only [associated_zero_iff_eq_zero, mul_eq_zero] )
-    (by rintro (rfl | rfl) <;> [apply lcm_zero_left, apply lcm_zero_right])
+    (by rintro (rfl | rfl) <;> [apply lcm_zero_left;apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
 
 /- warning: normalize_lcm -> normalize_lcm is a dubious translation:

baba818b

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -126,7 +126,7 @@ def normalize : α →*₀ α where
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align associated_normalize associated_normalizeₓ'. -/
 theorem associated_normalize (x : α) : Associated x (normalize x) :=
   ⟨_, rfl⟩
@@ -136,7 +136,7 @@ theorem associated_normalize (x : α) : Associated x (normalize x) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_associated normalize_associatedₓ'. -/
 theorem normalize_associated (x : α) : Associated (normalize x) x :=
   (associated_normalize _).symm
@@ -146,7 +146,7 @@ theorem normalize_associated (x : α) : Associated (normalize x) x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align associated_normalize_iff associated_normalize_iffₓ'. -/
 theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Associated x y :=
   ⟨fun h => h.trans (normalize_associated y), fun h => h.trans (associated_normalize y)⟩
@@ -156,7 +156,7 @@ theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align normalize_associated_iff normalize_associated_iffₓ'. -/
 theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Associated x y :=
   ⟨fun h => (associated_normalize _).trans h, fun h => (normalize_associated _).trans h⟩
@@ -166,7 +166,7 @@ theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align associates.mk_normalize Associates.mk_normalizeₓ'. -/
 theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associates.mk x :=
   Associates.mk_eq_mk_iff_associated.2 (normalize_associated _)
@@ -176,7 +176,7 @@ theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associa
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 Case conversion may be inaccurate. Consider using '#align normalize_apply normalize_applyₓ'. -/
 @[simp]
 theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
@@ -187,7 +187,7 @@ theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align normalize_zero normalize_zeroₓ'. -/
 @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
@@ -198,7 +198,7 @@ theorem normalize_zero : normalize (0 : α) = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_one normalize_oneₓ'. -/
 @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
@@ -209,7 +209,7 @@ theorem normalize_one : normalize (1 : α) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_coe_units normalize_coe_unitsₓ'. -/
 theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 #align normalize_coe_units normalize_coe_units
@@ -218,7 +218,7 @@ theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_zero normalize_eq_zeroₓ'. -/
 theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
   ⟨fun hx => (associated_zero_iff_eq_zero x).1 <| hx ▸ associated_normalize _, by
@@ -229,7 +229,7 @@ theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align normalize_eq_one normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
@@ -254,7 +254,7 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align normalize_idem normalize_idemₓ'. -/
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
@@ -263,7 +263,7 @@ theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by si
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize normalize_eq_normalizeₓ'. -/
 theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
   by
@@ -282,7 +282,7 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize_iff normalize_eq_normalize_iffₓ'. -/
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
   ⟨fun h => ⟨Units.dvd_mul_right.1 ⟨_, h.symm⟩, Units.dvd_mul_right.1 ⟨_, h⟩⟩, fun ⟨hxy, hyx⟩ =>
@@ -293,7 +293,7 @@ theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 Case conversion may be inaccurate. Consider using '#align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eqₓ'. -/
 theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : normalize b = b)
     (hab : a ∣ b) (hba : b ∣ a) : a = b :=
@@ -304,7 +304,7 @@ theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : nor
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align dvd_normalize_iff dvd_normalize_iffₓ'. -/
 --can be proven by simp
 theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
@@ -315,7 +315,7 @@ theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_dvd_iff normalize_dvd_iffₓ'. -/
 --can be proven by simp
 theorem normalize_dvd_iff {a b : α} : normalize a ∣ b ↔ a ∣ b :=
@@ -342,7 +342,7 @@ protected def out : Associates α → α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
 Case conversion may be inaccurate. Consider using '#align associates.out_mk Associates.out_mkₓ'. -/
 @[simp]
 theorem out_mk (a : α) : (Associates.mk a).out = normalize a :=
@@ -408,7 +408,7 @@ theorem out_top : (⊤ : Associates α).out = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align associates.normalize_out Associates.normalize_outₓ'. -/
 @[simp]
 theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
@@ -474,7 +474,7 @@ variable [CancelCommMonoidWithZero α]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_gcd normalize_gcdₓ'. -/
 @[simp]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
@@ -547,7 +547,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_normalize gcd_eq_normalizeₓ'. -/
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
@@ -558,7 +558,7 @@ theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_left gcd_zero_leftₓ'. -/
 @[simp]
 theorem gcd_zero_left [NormalizedGCDMonoid α] (a : α) : gcd 0 a = normalize a :=
@@ -579,7 +579,7 @@ theorem gcd_zero_left' [GCDMonoid α] (a : α) : Associated (gcd 0 a) a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_right gcd_zero_rightₓ'. -/
 @[simp]
 theorem gcd_zero_right [NormalizedGCDMonoid α] (a : α) : gcd a 0 = normalize a :=
@@ -668,7 +668,7 @@ theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_same gcd_sameₓ'. -/
 @[simp]
 theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
@@ -679,7 +679,7 @@ theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_left gcd_mul_leftₓ'. -/
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -721,7 +721,7 @@ theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a *
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_right gcd_mul_rightₓ'. -/
 @[simp]
 theorem gcd_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -743,7 +743,7 @@ theorem gcd_mul_right' [GCDMonoid α] (a b c : α) : Associated (gcd (b * a) (c
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_left_iff gcd_eq_left_iffₓ'. -/
 theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     gcd a b = a ↔ a ∣ b :=
@@ -755,7 +755,7 @@ theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_right_iff gcd_eq_right_iffₓ'. -/
 theorem gcd_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     gcd a b = b ↔ b ∣ a := by simpa only [gcd_comm a b] using gcd_eq_left_iff b a h
@@ -1034,7 +1034,7 @@ theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (h
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_2 _inst_3) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
+  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 Case conversion may be inaccurate. Consider using '#align gcd_greatest gcd_greatestₓ'. -/
 theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
@@ -1145,7 +1145,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_lcm normalize_lcmₓ'. -/
 @[simp]
 theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
@@ -1197,7 +1197,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_normalize lcm_eq_normalizeₓ'. -/
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=
@@ -1214,7 +1214,7 @@ theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_left lcm_units_coe_leftₓ'. -/
 @[simp]
 theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (↑u) a = normalize a :=
@@ -1225,7 +1225,7 @@ theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_right lcm_units_coe_rightₓ'. -/
 @[simp]
 theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a ↑u = normalize a :=
@@ -1236,7 +1236,7 @@ theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_left lcm_one_leftₓ'. -/
 @[simp]
 theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :=
@@ -1247,7 +1247,7 @@ theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_right lcm_one_rightₓ'. -/
 @[simp]
 theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a :=
@@ -1258,7 +1258,7 @@ theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_same lcm_sameₓ'. -/
 @[simp]
 theorem lcm_same [NormalizedGCDMonoid α] (a : α) : lcm a a = normalize a :=
@@ -1282,7 +1282,7 @@ theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_left lcm_mul_leftₓ'. -/
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -1305,7 +1305,7 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_right lcm_mul_rightₓ'. -/
 @[simp]
 theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -1316,7 +1316,7 @@ theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_left_iff lcm_eq_left_iffₓ'. -/
 theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     lcm a b = a ↔ b ∣ a :=
@@ -1328,7 +1328,7 @@ theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_right_iff lcm_eq_right_iffₓ'. -/
 theorem lcm_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     lcm a b = b ↔ a ∣ b := by simpa only [lcm_comm b a] using lcm_eq_left_iff b a h
@@ -1491,7 +1491,7 @@ theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_eq normalize_eqₓ'. -/
 @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
@@ -1574,7 +1574,7 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) => (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverseₓ'. -/
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)
@@ -1638,7 +1638,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCDₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `gcd` and its properties. -/
 noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq α] (gcd : α → α → α)
@@ -1764,7 +1764,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_lcm normalizedGCDMonoidOfLCMₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
@@ -1957,7 +1957,7 @@ theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻
 lean 3 declaration is
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
 but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) _inst_1))))))))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₀) => G₀) a) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one

baba818b

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -373,7 +373,7 @@ theorem out_mul (a b : Associates α) : (a * b).out = a.out * b.out :=
 
 /- warning: associates.dvd_out_iff -> Associates.dvd_out_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (Associates.out.{u1} α _inst_1 _inst_2 b)) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a) b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (Associates.out.{u1} α _inst_1 _inst_2 b)) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (Associates.out.{u1} α _inst_1 _inst_2 b)) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a) b)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_out_iff Associates.dvd_out_iffₓ'. -/
@@ -384,7 +384,7 @@ theorem dvd_out_iff (a : α) (b : Associates α) : a ∣ b.out ↔ Associates.mk
 
 /- warning: associates.out_dvd_iff -> Associates.out_dvd_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.out.{u1} α _inst_1 _inst_2 b) a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) b (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.out.{u1} α _inst_1 _inst_2 b) a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) b (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α) (b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.out.{u1} α _inst_1 _inst_2 b) a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) b (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a))
 Case conversion may be inaccurate. Consider using '#align associates.out_dvd_iff Associates.out_dvd_iffₓ'. -/

baba818b

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -1525,7 +1525,7 @@ variable [CommRing α] [IsDomain α] [NormalizedGCDMonoid α]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (CommSemiring.toSemiring.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_rightₓ'. -/
 theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a c :=
   by
@@ -1548,7 +1548,7 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (CommSemiring.toSemiring.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_left gcd_eq_of_dvd_sub_leftₓ'. -/
 theorem gcd_eq_of_dvd_sub_left {a b c : α} (h : a ∣ b - c) : gcd b a = gcd c a := by
   rw [gcd_comm _ a, gcd_comm _ a, gcd_eq_of_dvd_sub_right h]

baba818b

bump to nightly-2023-04-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

0ff24cd7

Diff

@@ -1947,7 +1947,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
 lean 3 declaration is
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (coeBase.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (Units.hasCoe.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (DivInvMonoid.toHasInv.{u1} G₀ (GroupWithZero.toDivInvMonoid.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))) a))
 but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} G₀ (Units.val.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (CommGroupWithZero.toInv.{u1} G₀ _inst_1) a))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} G₀ (Units.val.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (CommGroupWithZero.toInv.{u1} G₀ _inst_1) a))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.coe_norm_unit CommGroupWithZero.coe_normUnitₓ'. -/
 @[simp]
 theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻¹ := by simp [norm_unit, h0]
@@ -1957,7 +1957,7 @@ theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻
 lean 3 declaration is
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
 but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) _inst_1))))))))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidToCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one

baba818b

bump to nightly-2023-04-11-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

8f9520b0

Diff

@@ -1945,7 +1945,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀
 
 /- warning: comm_group_with_zero.coe_norm_unit -> CommGroupWithZero.coe_normUnit is a dubious translation:
 lean 3 declaration is
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (coeBase.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (Units.hasCoe.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (DivInvMonoid.toHasInv.{u1} G₀ (GroupWithZero.toDivInvMonoid.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))) a))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (coeBase.{succ u1, succ u1} (Units.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (Units.hasCoe.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (DivInvMonoid.toHasInv.{u1} G₀ (GroupWithZero.toDivInvMonoid.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))) a))
 but is expected to have type
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} G₀ (Units.val.{u1} G₀ (MonoidWithZero.toMonoid.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (NormalizationMonoid.normUnit.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b))) a)) (Inv.inv.{u1} G₀ (CommGroupWithZero.toInv.{u1} G₀ _inst_1) a))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.coe_norm_unit CommGroupWithZero.coe_normUnitₓ'. -/
@@ -1955,7 +1955,7 @@ theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻
 
 /- warning: comm_group_with_zero.normalize_eq_one -> CommGroupWithZero.normalize_eq_one is a dubious translation:
 lean 3 declaration is
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.toCancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
 but is expected to have type
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/

baba818b

bump to nightly-2023-03-27-02

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

0e4ebd8c

Diff

@@ -1523,7 +1523,7 @@ variable [CommRing α] [IsDomain α] [NormalizedGCDMonoid α]
 
 /- warning: gcd_eq_of_dvd_sub_right -> gcd_eq_of_dvd_sub_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a b) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) a c))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_rightₓ'. -/
@@ -1546,7 +1546,7 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
 
 /- warning: gcd_eq_of_dvd_sub_left -> gcd_eq_of_dvd_sub_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1))))))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGcdMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : IsDomain.{u1} α (Ring.toSemiring.{u1} α (CommRing.toRing.{u1} α _inst_1))] [_inst_3 : NormalizedGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2)] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (NonUnitalSemiring.toSemigroupWithZero.{u1} α (NonUnitalRing.toNonUnitalSemiring.{u1} α (NonUnitalCommRing.toNonUnitalRing.{u1} α (CommRing.toNonUnitalCommRing.{u1} α _inst_1)))))) a (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (Ring.toSub.{u1} α (CommRing.toRing.{u1} α _inst_1))) b c)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) b a) (GCDMonoid.gcd.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) (NormalizedGCDMonoid.toGCDMonoid.{u1} α (IsDomain.toCancelCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1) _inst_2) _inst_3) c a))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_of_dvd_sub_left gcd_eq_of_dvd_sub_leftₓ'. -/

baba818b

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -1063,7 +1063,7 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GC
     IsUnit (gcd x' y') := by
   rw [← associated_one_iff_isUnit]
   refine' Associated.of_mul_left _ (Associated.refl <| gcd x y) h
-  convert (gcd_mul_left' _ _ _).symm using 1
+  convert(gcd_mul_left' _ _ _).symm using 1
   rw [← ex, ← ey, mul_one]
 #align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcd
 
@@ -1668,7 +1668,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
             exact gcd_dvd_left _ _
-          · convert @normalize_zero α _ _
+          · convert@normalize_zero α _ _
         have h1 : gcd a b ≠ 0 := by
           have hab : a * b ≠ 0 := mul_ne_zero a0 hb
           contrapose! hab

baba818b

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -126,7 +126,7 @@ def normalize : α →*₀ α where
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align associated_normalize associated_normalizeₓ'. -/
 theorem associated_normalize (x : α) : Associated x (normalize x) :=
   ⟨_, rfl⟩
@@ -136,7 +136,7 @@ theorem associated_normalize (x : α) : Associated x (normalize x) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_associated normalize_associatedₓ'. -/
 theorem normalize_associated (x : α) : Associated (normalize x) x :=
   (associated_normalize _).symm
@@ -146,7 +146,7 @@ theorem normalize_associated (x : α) : Associated (normalize x) x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align associated_normalize_iff associated_normalize_iffₓ'. -/
 theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Associated x y :=
   ⟨fun h => h.trans (normalize_associated y), fun h => h.trans (associated_normalize y)⟩
@@ -156,7 +156,7 @@ theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align normalize_associated_iff normalize_associated_iffₓ'. -/
 theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Associated x y :=
   ⟨fun h => (associated_normalize _).trans h, fun h => (normalize_associated _).trans h⟩
@@ -166,7 +166,7 @@ theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align associates.mk_normalize Associates.mk_normalizeₓ'. -/
 theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associates.mk x :=
   Associates.mk_eq_mk_iff_associated.2 (normalize_associated _)
@@ -176,7 +176,7 @@ theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associa
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 Case conversion may be inaccurate. Consider using '#align normalize_apply normalize_applyₓ'. -/
 @[simp]
 theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
@@ -187,7 +187,7 @@ theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align normalize_zero normalize_zeroₓ'. -/
 @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
@@ -198,7 +198,7 @@ theorem normalize_zero : normalize (0 : α) = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_one normalize_oneₓ'. -/
 @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
@@ -209,7 +209,7 @@ theorem normalize_one : normalize (1 : α) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_coe_units normalize_coe_unitsₓ'. -/
 theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 #align normalize_coe_units normalize_coe_units
@@ -218,7 +218,7 @@ theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_zero normalize_eq_zeroₓ'. -/
 theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
   ⟨fun hx => (associated_zero_iff_eq_zero x).1 <| hx ▸ associated_normalize _, by
@@ -229,7 +229,7 @@ theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align normalize_eq_one normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
@@ -254,7 +254,7 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align normalize_idem normalize_idemₓ'. -/
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
@@ -263,7 +263,7 @@ theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by si
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize normalize_eq_normalizeₓ'. -/
 theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
   by
@@ -282,7 +282,7 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize_iff normalize_eq_normalize_iffₓ'. -/
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
   ⟨fun h => ⟨Units.dvd_mul_right.1 ⟨_, h.symm⟩, Units.dvd_mul_right.1 ⟨_, h⟩⟩, fun ⟨hxy, hyx⟩ =>
@@ -293,7 +293,7 @@ theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 Case conversion may be inaccurate. Consider using '#align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eqₓ'. -/
 theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : normalize b = b)
     (hab : a ∣ b) (hba : b ∣ a) : a = b :=
@@ -304,7 +304,7 @@ theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : nor
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align dvd_normalize_iff dvd_normalize_iffₓ'. -/
 --can be proven by simp
 theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
@@ -315,7 +315,7 @@ theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_dvd_iff normalize_dvd_iffₓ'. -/
 --can be proven by simp
 theorem normalize_dvd_iff {a b : α} : normalize a ∣ b ↔ a ∣ b :=
@@ -342,7 +342,7 @@ protected def out : Associates α → α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
 Case conversion may be inaccurate. Consider using '#align associates.out_mk Associates.out_mkₓ'. -/
 @[simp]
 theorem out_mk (a : α) : (Associates.mk a).out = normalize a :=
@@ -408,7 +408,7 @@ theorem out_top : (⊤ : Associates α).out = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align associates.normalize_out Associates.normalize_outₓ'. -/
 @[simp]
 theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
@@ -474,7 +474,7 @@ variable [CancelCommMonoidWithZero α]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_gcd normalize_gcdₓ'. -/
 @[simp]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
@@ -547,7 +547,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_normalize gcd_eq_normalizeₓ'. -/
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
@@ -558,7 +558,7 @@ theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_left gcd_zero_leftₓ'. -/
 @[simp]
 theorem gcd_zero_left [NormalizedGCDMonoid α] (a : α) : gcd 0 a = normalize a :=
@@ -579,7 +579,7 @@ theorem gcd_zero_left' [GCDMonoid α] (a : α) : Associated (gcd 0 a) a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_right gcd_zero_rightₓ'. -/
 @[simp]
 theorem gcd_zero_right [NormalizedGCDMonoid α] (a : α) : gcd a 0 = normalize a :=
@@ -668,7 +668,7 @@ theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_same gcd_sameₓ'. -/
 @[simp]
 theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
@@ -679,7 +679,7 @@ theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_left gcd_mul_leftₓ'. -/
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -721,7 +721,7 @@ theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a *
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_right gcd_mul_rightₓ'. -/
 @[simp]
 theorem gcd_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -743,7 +743,7 @@ theorem gcd_mul_right' [GCDMonoid α] (a b c : α) : Associated (gcd (b * a) (c
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_left_iff gcd_eq_left_iffₓ'. -/
 theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     gcd a b = a ↔ a ∣ b :=
@@ -755,7 +755,7 @@ theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_right_iff gcd_eq_right_iffₓ'. -/
 theorem gcd_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     gcd a b = b ↔ b ∣ a := by simpa only [gcd_comm a b] using gcd_eq_left_iff b a h
@@ -1034,7 +1034,7 @@ theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (h
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_2 _inst_3) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
+  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 Case conversion may be inaccurate. Consider using '#align gcd_greatest gcd_greatestₓ'. -/
 theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
@@ -1145,7 +1145,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_lcm normalize_lcmₓ'. -/
 @[simp]
 theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
@@ -1197,7 +1197,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_normalize lcm_eq_normalizeₓ'. -/
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=
@@ -1214,7 +1214,7 @@ theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_left lcm_units_coe_leftₓ'. -/
 @[simp]
 theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (↑u) a = normalize a :=
@@ -1225,7 +1225,7 @@ theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_right lcm_units_coe_rightₓ'. -/
 @[simp]
 theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a ↑u = normalize a :=
@@ -1236,7 +1236,7 @@ theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_left lcm_one_leftₓ'. -/
 @[simp]
 theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :=
@@ -1247,7 +1247,7 @@ theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_right lcm_one_rightₓ'. -/
 @[simp]
 theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a :=
@@ -1258,7 +1258,7 @@ theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_same lcm_sameₓ'. -/
 @[simp]
 theorem lcm_same [NormalizedGCDMonoid α] (a : α) : lcm a a = normalize a :=
@@ -1282,7 +1282,7 @@ theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_left lcm_mul_leftₓ'. -/
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -1305,7 +1305,7 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_right lcm_mul_rightₓ'. -/
 @[simp]
 theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -1316,7 +1316,7 @@ theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_left_iff lcm_eq_left_iffₓ'. -/
 theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     lcm a b = a ↔ b ∣ a :=
@@ -1328,7 +1328,7 @@ theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_right_iff lcm_eq_right_iffₓ'. -/
 theorem lcm_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     lcm a b = b ↔ a ∣ b := by simpa only [lcm_comm b a] using lcm_eq_left_iff b a h
@@ -1491,7 +1491,7 @@ theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_eq normalize_eqₓ'. -/
 @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
@@ -1574,7 +1574,7 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) => (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverseₓ'. -/
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)
@@ -1638,7 +1638,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCDₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `gcd` and its properties. -/
 noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq α] (gcd : α → α → α)
@@ -1764,7 +1764,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_lcm normalizedGCDMonoidOfLCMₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
@@ -1957,7 +1957,7 @@ theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻
 lean 3 declaration is
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
 but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) _inst_1))))))))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₀) => G₀) a) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one

baba818b

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -110,8 +110,14 @@ def normalize : α →*₀ α where
   map_zero' := by simp
   map_one' := by rw [normUnit_one, Units.val_one, mul_one]
   map_mul' x y :=
-    by_cases (fun hx : x = 0 => by rw [hx, zero_mul, zero_mul, zero_mul]) fun hx =>
-      by_cases (fun hy : y = 0 => by rw [hy, mul_zero, zero_mul, mul_zero]) fun hy => by
+    by_cases
+      (fun hx : x = 0 => by
+        rw [hx, MulZeroClass.zero_mul, MulZeroClass.zero_mul, MulZeroClass.zero_mul])
+      fun hx =>
+      by_cases
+        (fun hy : y = 0 => by
+          rw [hy, MulZeroClass.mul_zero, MulZeroClass.zero_mul, MulZeroClass.mul_zero])
+        fun hy => by
         simp only [norm_unit_mul hx hy, Units.val_mul] <;> simp only [mul_assoc, mul_left_comm y]
 #align normalize normalize
 -/
@@ -240,7 +246,7 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
   by
   nontriviality α using Subsingleton.elim a 0
   obtain rfl | h := eq_or_ne a 0
-  · rw [norm_unit_zero, zero_mul, norm_unit_zero]
+  · rw [norm_unit_zero, MulZeroClass.zero_mul, norm_unit_zero]
   · rw [norm_unit_mul h (Units.ne_zero _), norm_unit_coe_units, mul_inv_eq_one]
 #align norm_unit_mul_norm_unit normUnit_mul_normUnit
 
@@ -263,7 +269,7 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
   by
   nontriviality α
   rcases associated_of_dvd_dvd hab hba with ⟨u, rfl⟩
-  refine' by_cases (by rintro rfl <;> simp only [zero_mul]) fun ha : a ≠ 0 => _
+  refine' by_cases (by rintro rfl <;> simp only [MulZeroClass.zero_mul]) fun ha : a ≠ 0 => _
   suffices a * ↑(norm_unit a) = a * ↑u * ↑(norm_unit a) * ↑u⁻¹ by
     simpa only [normalize_apply, mul_assoc, norm_unit_mul ha u.ne_zero, norm_unit_coe_units]
   calc
@@ -602,7 +608,7 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     (fun h => by
       let ⟨ca, ha⟩ := gcd_dvd_left a b
       let ⟨cb, hb⟩ := gcd_dvd_right a b
-      rw [h, zero_mul] at ha hb <;> exact ⟨ha, hb⟩)
+      rw [h, MulZeroClass.zero_mul] at ha hb <;> exact ⟨ha, hb⟩)
     fun ⟨ha, hb⟩ => by
     rw [ha, hb, ← zero_dvd_iff]
     apply dvd_gcd <;> rfl
@@ -678,7 +684,8 @@ Case conversion may be inaccurate. Consider using '#align gcd_mul_left gcd_mul_l
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     gcd (a * b) (a * c) = normalize a * gcd b c :=
-  by_cases (by rintro rfl <;> simp only [zero_mul, gcd_zero_left, normalize_zero]) fun ha : a ≠ 0 =>
+  by_cases (by rintro rfl <;> simp only [MulZeroClass.zero_mul, gcd_zero_left, normalize_zero])
+    fun ha : a ≠ 0 =>
     suffices gcd (a * b) (a * c) = normalize (a * gcd b c) by
       simpa only [normalize.map_mul, normalize_gcd]
     let ⟨d, Eq⟩ := dvd_gcd (dvd_mul_right a b) (dvd_mul_right a c)
@@ -699,7 +706,7 @@ Case conversion may be inaccurate. Consider using '#align gcd_mul_left' gcd_mul_
 theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a * c)) (a * gcd b c) :=
   by
   obtain rfl | ha := eq_or_ne a 0
-  · simp only [zero_mul, gcd_zero_left']
+  · simp only [MulZeroClass.zero_mul, gcd_zero_left']
   obtain ⟨d, eq⟩ := dvd_gcd (dvd_mul_right a b) (dvd_mul_right a c)
   apply associated_of_dvd_dvd
   · rw [Eq]
@@ -977,7 +984,7 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
     obtain rfl | hk := k.eq_zero_or_pos
     · exfalso
       revert h
-      rw [ha, zero_mul, pow_zero]
+      rw [ha, MulZeroClass.zero_mul, pow_zero]
       apply zero_ne_one
     · rw [zero_pow hk]
   by_cases hb : b = 0
@@ -1072,7 +1079,8 @@ theorem extract_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] (
   by_cases h : gcd x y = 0
   · obtain ⟨rfl, rfl⟩ := (gcd_eq_zero_iff x y).1 h
     simp_rw [← associated_one_iff_isUnit]
-    exact ⟨1, 1, by rw [h, zero_mul], by rw [h, zero_mul], gcd_one_left' 1⟩
+    exact
+      ⟨1, 1, by rw [h, MulZeroClass.zero_mul], by rw [h, MulZeroClass.zero_mul], gcd_one_left' 1⟩
   obtain ⟨x', ex⟩ := gcd_dvd_left x y
   obtain ⟨y', ey⟩ := gcd_dvd_right x y
   exact ⟨x', y', ex, ey, isUnit_gcd_of_eq_mul_gcd ex ey h⟩
@@ -1127,7 +1135,8 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
   Iff.intro
     (fun h : lcm a b = 0 =>
       by
-      have : Associated (a * b) 0 := (gcd_mul_lcm a b).symm.trans <| by rw [h, mul_zero]
+      have : Associated (a * b) 0 :=
+        (gcd_mul_lcm a b).symm.trans <| by rw [h, MulZeroClass.mul_zero]
       simpa only [associated_zero_iff_eq_zero, mul_eq_zero] )
     (by rintro (rfl | rfl) <;> [apply lcm_zero_left, apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
@@ -1278,7 +1287,8 @@ Case conversion may be inaccurate. Consider using '#align lcm_mul_left lcm_mul_l
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     lcm (a * b) (a * c) = normalize a * lcm b c :=
-  by_cases (by rintro rfl <;> simp only [zero_mul, lcm_zero_left, normalize_zero]) fun ha : a ≠ 0 =>
+  by_cases (by rintro rfl <;> simp only [MulZeroClass.zero_mul, lcm_zero_left, normalize_zero])
+    fun ha : a ≠ 0 =>
     suffices lcm (a * b) (a * c) = normalize (a * lcm b c) by
       simpa only [normalize.map_mul, normalize_lcm]
     have : a ∣ lcm (a * b) (a * c) := (dvd_mul_right _ _).trans (dvd_lcm_left _ _)
@@ -1608,7 +1618,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
       if a = 0 then 0 else Classical.choose ((gcd_dvd_left a b).trans (Dvd.intro b rfl))
     gcd_mul_lcm := fun a b => by
       split_ifs with a0
-      · rw [mul_zero, a0, zero_mul]
+      · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
       · rw [← Classical.choose_spec ((gcd_dvd_left a b).trans (Dvd.intro b rfl))]
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
@@ -1620,7 +1630,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
         rw [← associated_zero_iff_eq_zero, ← a0]
         exact associated_of_dvd_dvd (dvd_gcd (dvd_refl a) (dvd_zero a)) (gcd_dvd_left _ _)
       apply Or.resolve_left (mul_eq_zero.1 _) a0'
-      rw [h, mul_zero] }
+      rw [h, MulZeroClass.mul_zero] }
 #align gcd_monoid_of_gcd gcdMonoidOfGCD
 -/
 
@@ -1653,7 +1663,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
               (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))).symm
         set l := Classical.choose (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))
         obtain rfl | hb := eq_or_ne b 0
-        · simp only [normalize_zero, mul_zero, mul_eq_zero] at this
+        · simp only [normalize_zero, MulZeroClass.mul_zero, mul_eq_zero] at this
           obtain ha | hl := this
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
@@ -1662,13 +1672,13 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         have h1 : gcd a b ≠ 0 := by
           have hab : a * b ≠ 0 := mul_ne_zero a0 hb
           contrapose! hab
-          rw [← normalize_eq_zero, ← this, hab, zero_mul]
+          rw [← normalize_eq_zero, ← this, hab, MulZeroClass.zero_mul]
         have h2 : normalize (gcd a b * l) = gcd a b * l := by rw [this, normalize_idem]
         rw [← normalize_gcd] at this
         rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2
     gcd_mul_lcm := fun a b => by
       split_ifs with a0
-      · rw [mul_zero, a0, zero_mul]
+      · rw [MulZeroClass.mul_zero, a0, MulZeroClass.zero_mul]
       · rw [←
           Classical.choose_spec (dvd_normalize_iff.2 ((gcd_dvd_left a b).trans (Dvd.intro b rfl)))]
         exact normalize_associated (a * b)
@@ -1686,7 +1696,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         exact normalize_eq_normalize (gcd_dvd_left _ _) (dvd_gcd (dvd_refl a) (dvd_zero a))
       rw [← gcd0] at a0
       apply Or.resolve_left (mul_eq_zero.1 _) a0
-      rw [h, mul_zero, normalize_zero] }
+      rw [h, MulZeroClass.mul_zero, normalize_zero] }
 #align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCD
 
 #print gcdMonoidOfLCM /-
@@ -1699,8 +1709,8 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
     gcd := fun a b => if a = 0 then b else if b = 0 then a else Classical.choose (exists_gcd a b)
     gcd_mul_lcm := fun a b => by
       split_ifs
-      · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
-      · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), mul_zero]
+      · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), MulZeroClass.mul_zero, MulZeroClass.zero_mul]
+      · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), MulZeroClass.mul_zero]
       rw [mul_comm, ← Classical.choose_spec (exists_gcd a b)]
     lcm_zero_left := fun a => eq_zero_of_zero_dvd (dvd_lcm_left _ _)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
@@ -1769,8 +1779,10 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       else if b = 0 then normalize a else Classical.choose (exists_gcd a b)
     gcd_mul_lcm := fun a b => by
       split_ifs with h h_1
-      · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
-      · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), mul_zero, mul_zero]
+      · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), MulZeroClass.mul_zero, MulZeroClass.zero_mul]
+      ·
+        rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), MulZeroClass.mul_zero,
+          MulZeroClass.mul_zero]
       rw [mul_comm, ← Classical.choose_spec (exists_gcd a b)]
       exact normalize_associated (a * b)
     normalize_lcm

baba818b

bump to nightly-2023-03-08-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

10f15343

Diff

@@ -120,7 +120,7 @@ def normalize : α →*₀ α where
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align associated_normalize associated_normalizeₓ'. -/
 theorem associated_normalize (x : α) : Associated x (normalize x) :=
   ⟨_, rfl⟩
@@ -130,7 +130,7 @@ theorem associated_normalize (x : α) : Associated x (normalize x) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_associated normalize_associatedₓ'. -/
 theorem normalize_associated (x : α) : Associated (normalize x) x :=
   (associated_normalize _).symm
@@ -140,7 +140,7 @@ theorem normalize_associated (x : α) : Associated (normalize x) x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align associated_normalize_iff associated_normalize_iffₓ'. -/
 theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Associated x y :=
   ⟨fun h => h.trans (normalize_associated y), fun h => h.trans (associated_normalize y)⟩
@@ -150,7 +150,7 @@ theorem associated_normalize_iff {x y : α} : Associated x (normalize y) ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Associated.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) y) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x y)
 Case conversion may be inaccurate. Consider using '#align normalize_associated_iff normalize_associated_iffₓ'. -/
 theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Associated x y :=
   ⟨fun h => (associated_normalize _).trans h, fun h => (normalize_associated _).trans h⟩
@@ -160,7 +160,7 @@ theorem normalize_associated_iff {x y : α} : Associated (normalize x) y ↔ Ass
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} (Associates.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (Associates.mk.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align associates.mk_normalize Associates.mk_normalizeₓ'. -/
 theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associates.mk x :=
   Associates.mk_eq_mk_iff_associated.2 (normalize_associated _)
@@ -170,7 +170,7 @@ theorem Associates.mk_normalize (x : α) : Associates.mk (normalize x) = Associa
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) x (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (NormalizationMonoid.normUnit.{u1} α _inst_1 _inst_2 x)))
 Case conversion may be inaccurate. Consider using '#align normalize_apply normalize_applyₓ'. -/
 @[simp]
 theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
@@ -181,7 +181,7 @@ theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) _inst_1))))
 Case conversion may be inaccurate. Consider using '#align normalize_zero normalize_zeroₓ'. -/
 @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
@@ -192,7 +192,7 @@ theorem normalize_zero : normalize (0 : α) = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1], Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_one normalize_oneₓ'. -/
 @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
@@ -203,7 +203,7 @@ theorem normalize_one : normalize (1 : α) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align normalize_coe_units normalize_coe_unitsₓ'. -/
 theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 #align normalize_coe_units normalize_coe_units
@@ -212,7 +212,7 @@ theorem normalize_coe_units (u : αˣ) : normalize (u : α) = 1 := by simp
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (Eq.{succ u1} α x (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_zero normalize_eq_zeroₓ'. -/
 theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
   ⟨fun hx => (associated_zero_iff_eq_zero x).1 <| hx ▸ associated_normalize _, by
@@ -223,7 +223,7 @@ theorem normalize_eq_zero {x : α} : normalize x = 0 ↔ x = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (Monoid.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))))) (IsUnit.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align normalize_eq_one normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
@@ -248,7 +248,7 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1))))))) (normalize.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) _inst_1 _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x)
 Case conversion may be inaccurate. Consider using '#align normalize_idem normalize_idemₓ'. -/
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
@@ -257,7 +257,7 @@ theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by si
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize normalize_eq_normalizeₓ'. -/
 theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
   by
@@ -276,7 +276,7 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : norm
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) x) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {x : α} {y : α}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) y)) (And (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) x y) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) y x))
 Case conversion may be inaccurate. Consider using '#align normalize_eq_normalize_iff normalize_eq_normalize_iffₓ'. -/
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
   ⟨fun h => ⟨Units.dvd_mul_right.1 ⟨_, h.symm⟩, Units.dvd_mul_right.1 ⟨_, h⟩⟩, fun ⟨hxy, hyx⟩ =>
@@ -287,7 +287,7 @@ theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) a) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b) b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Eq.{succ u1} α a b)
 Case conversion may be inaccurate. Consider using '#align dvd_antisymm_of_normalize_eq dvd_antisymm_of_normalize_eqₓ'. -/
 theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : normalize b = b)
     (hab : a ∣ b) (hba : b ∣ a) : a = b :=
@@ -298,7 +298,7 @@ theorem dvd_antisymm_of_normalize_eq {a b : α} (ha : normalize a = a) (hb : nor
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align dvd_normalize_iff dvd_normalize_iffₓ'. -/
 --can be proven by simp
 theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
@@ -309,7 +309,7 @@ theorem dvd_normalize_iff {a b : α} : a ∣ normalize b ↔ a ∣ b :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] {a : α} {b : α}, Iff (Dvd.dvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (semigroupDvd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (SemigroupWithZero.toSemigroup.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toSemigroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_dvd_iff normalize_dvd_iffₓ'. -/
 --can be proven by simp
 theorem normalize_dvd_iff {a b : α} : normalize a ∣ b ↔ a ∣ b :=
@@ -336,7 +336,7 @@ protected def out : Associates α → α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (Associates.out.{u1} α _inst_1 _inst_2 (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) a)
 Case conversion may be inaccurate. Consider using '#align associates.out_mk Associates.out_mkₓ'. -/
 @[simp]
 theorem out_mk (a : α) : (Associates.mk a).out = normalize a :=
@@ -402,7 +402,7 @@ theorem out_top : (⊤ : Associates α).out = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] (a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (Associates.out.{u1} α _inst_1 _inst_2 a)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (Associates.out.{u1} α _inst_1 _inst_2 a)) (Associates.out.{u1} α _inst_1 _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align associates.normalize_out Associates.normalize_outₓ'. -/
 @[simp]
 theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
@@ -468,7 +468,7 @@ variable [CancelCommMonoidWithZero α]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_gcd normalize_gcdₓ'. -/
 @[simp]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
@@ -541,7 +541,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_normalize gcd_eq_normalizeₓ'. -/
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
@@ -552,7 +552,7 @@ theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_left gcd_zero_leftₓ'. -/
 @[simp]
 theorem gcd_zero_left [NormalizedGCDMonoid α] (a : α) : gcd 0 a = normalize a :=
@@ -573,7 +573,7 @@ theorem gcd_zero_left' [GCDMonoid α] (a : α) : Associated (gcd 0 a) a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_zero_right gcd_zero_rightₓ'. -/
 @[simp]
 theorem gcd_zero_right [NormalizedGCDMonoid α] (a : α) : gcd a 0 = normalize a :=
@@ -662,7 +662,7 @@ theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align gcd_same gcd_sameₓ'. -/
 @[simp]
 theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
@@ -673,7 +673,7 @@ theorem gcd_same [NormalizedGCDMonoid α] (a : α) : gcd a a = normalize a :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_left gcd_mul_leftₓ'. -/
 @[simp]
 theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -714,7 +714,7 @@ theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a *
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align gcd_mul_right gcd_mul_rightₓ'. -/
 @[simp]
 theorem gcd_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -736,7 +736,7 @@ theorem gcd_mul_right' [GCDMonoid α] (a b c : α) : Associated (gcd (b * a) (c
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_left_iff gcd_eq_left_iffₓ'. -/
 theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     gcd a b = a ↔ a ∣ b :=
@@ -748,7 +748,7 @@ theorem gcd_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align gcd_eq_right_iff gcd_eq_right_iffₓ'. -/
 theorem gcd_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     gcd a b = b ↔ b ∣ a := by simpa only [gcd_comm a b] using gcd_eq_left_iff b a h
@@ -1027,7 +1027,7 @@ theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (h
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_2 _inst_3) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
+  forall {α : Type.{u1}} [_inst_2 : CancelCommMonoidWithZero.{u1} α] [_inst_3 : NormalizedGCDMonoid.{u1} α _inst_2] {a : α} {b : α} {d : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) d b) -> (forall (e : α), (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) e d)) -> (Eq.{succ u1} α (GCDMonoid.gcd.{u1} α _inst_2 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_2 _inst_3) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_2))))))) (normalize.{u1} α _inst_2 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_2 _inst_3)) d))
 Case conversion may be inaccurate. Consider using '#align gcd_greatest gcd_greatestₓ'. -/
 theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
@@ -1136,7 +1136,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)
 Case conversion may be inaccurate. Consider using '#align normalize_lcm normalize_lcmₓ'. -/
 @[simp]
 theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
@@ -1188,7 +1188,7 @@ instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b)) -> (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) c))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_normalize lcm_eq_normalizeₓ'. -/
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=
@@ -1205,7 +1205,7 @@ theorem lcm_dvd_lcm [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_left lcm_units_coe_leftₓ'. -/
 @[simp]
 theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (↑u) a = normalize a :=
@@ -1216,7 +1216,7 @@ theorem lcm_units_coe_left [NormalizedGCDMonoid α] (u : αˣ) (a : α) : lcm (
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (coeBase.{succ u1, succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (Units.hasCoe.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) u)) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (u : Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (Units.val.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) u)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_units_coe_right lcm_units_coe_rightₓ'. -/
 @[simp]
 theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a ↑u = normalize a :=
@@ -1227,7 +1227,7 @@ theorem lcm_units_coe_right [NormalizedGCDMonoid α] (a : α) (u : αˣ) : lcm a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))))) a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_left lcm_one_leftₓ'. -/
 @[simp]
 theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :=
@@ -1238,7 +1238,7 @@ theorem lcm_one_left [NormalizedGCDMonoid α] (a : α) : lcm 1 a = normalize a :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_one_right lcm_one_rightₓ'. -/
 @[simp]
 theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a :=
@@ -1249,7 +1249,7 @@ theorem lcm_one_right [NormalizedGCDMonoid α] (a : α) : lcm a 1 = normalize a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a a) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align lcm_same lcm_sameₓ'. -/
 @[simp]
 theorem lcm_same [NormalizedGCDMonoid α] (a : α) : lcm a a = normalize a :=
@@ -1273,7 +1273,7 @@ theorem lcm_eq_one_iff [NormalizedGCDMonoid α] (a b : α) : lcm a b = 1 ↔ a 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MulZeroOneClass.toMulZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (MonoidWithZero.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CommMonoidWithZero.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_left lcm_mul_leftₓ'. -/
 @[simp]
 theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
@@ -1295,7 +1295,7 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) b c) (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α) (c : α), Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) c a)) (HMul.hMul.{u1, u1, u1} α ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) b c) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a))
 Case conversion may be inaccurate. Consider using '#align lcm_mul_right lcm_mul_rightₓ'. -/
 @[simp]
 theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
@@ -1306,7 +1306,7 @@ theorem lcm_mul_right [NormalizedGCDMonoid α] (a b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) a) a) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_left_iff lcm_eq_left_iffₓ'. -/
 theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a) :
     lcm a b = a ↔ b ∣ a :=
@@ -1318,7 +1318,7 @@ theorem lcm_eq_left_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize a = a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGcdMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizedGCDMonoid.{u1} α _inst_1] (a : α) (b : α), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) b) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (NormalizedGCDMonoid.toNormalizationMonoid.{u1} α _inst_1 _inst_2)) b) b) -> (Iff (Eq.{succ u1} α (GCDMonoid.lcm.{u1} α _inst_1 (NormalizedGCDMonoid.toGCDMonoid.{u1} α _inst_1 _inst_2) a b) b) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align lcm_eq_right_iff lcm_eq_right_iffₓ'. -/
 theorem lcm_eq_right_iff [NormalizedGCDMonoid α] (a b : α) (h : normalize b = b) :
     lcm a b = b ↔ a ∣ b := by simpa only [lcm_comm b a] using lcm_eq_left_iff b a h
@@ -1481,7 +1481,7 @@ theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : Unique.{succ u1} (Units.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))] (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 (normalizationMonoidOfUniqueUnits.{u1} α _inst_1 _inst_2)) x) x
 Case conversion may be inaccurate. Consider using '#align normalize_eq normalize_eqₓ'. -/
 @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
@@ -1564,7 +1564,7 @@ private theorem map_mk_unit_aux [DecidableEq α] {f : Associates α →* α}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) => (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.commMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (f : MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))), (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulOneClass.toMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (MulZeroOneClass.toMulOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (CommMonoidWithZero.toMonoidWithZero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) f) (Associates.mk.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (NormalizationMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalization_monoid_of_monoid_hom_right_inverse normalizationMonoidOfMonoidHomRightInverseₓ'. -/
 /-- Define `normalization_monoid` on a structure from a `monoid_hom` inverse to `associates.mk`. -/
 def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates α →* α)
@@ -1628,7 +1628,7 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (gcd : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) a) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (gcd a b) b) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a c) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (gcd c b))) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (gcd a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (gcd a b)) (gcd a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_gcd normalizedGCDMonoidOfGCDₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `gcd` and its properties. -/
 noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq α] (gcd : α → α → α)
@@ -1754,7 +1754,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (fun (_x : MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) => α -> α) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] [_inst_2 : NormalizationMonoid.{u1} α _inst_1] [_inst_3 : DecidableEq.{succ u1} α] (lcm : α -> α -> α), (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a (lcm a b)) -> (forall (a : α) (b : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b (lcm a b)) -> (forall {a : α} {b : α} {c : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) c a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) b a) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (lcm c b) a)) -> (forall (a : α) (b : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) (lcm a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MulOneClass.toMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} α α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))) (normalize.{u1} α _inst_1 _inst_2) (lcm a b)) (lcm a b)) -> (NormalizedGCDMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align normalized_gcd_monoid_of_lcm normalizedGCDMonoidOfLCMₓ'. -/
 /-- Define `normalized_gcd_monoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
@@ -1945,7 +1945,7 @@ theorem coe_normUnit {a : G₀} (h0 : a ≠ 0) : (↑(normUnit a) : G₀) = a⁻
 lean 3 declaration is
   forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (OfNat.mk.{u1} G₀ 0 (Zero.zero.{u1} G₀ (MulZeroClass.toHasZero.{u1} G₀ (MulZeroOneClass.toMulZeroClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1))))))))) -> (Eq.{succ u1} G₀ (coeFn.{succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (fun (_x : MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) => G₀ -> G₀) (MonoidWithZeroHom.hasCoeToFun.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.normalizedGcdMonoid.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} G₀ 1 (OfNat.mk.{u1} G₀ 1 (One.one.{u1} G₀ (MulOneClass.toHasOne.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ (CommGroupWithZero.toGroupWithZero.{u1} G₀ _inst_1)))))))))
 but is expected to have type
-  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₀) => G₀) a) _inst_1))))))))
+  forall (G₀ : Type.{u1}) [_inst_1 : CommGroupWithZero.{u1} G₀] [_inst_2 : DecidableEq.{succ u1} G₀] {a : G₀}, (Ne.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (CommMonoidWithZero.toZero.{u1} G₀ (CommGroupWithZero.toCommMonoidWithZero.{u1} G₀ _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ (fun (_x : G₀) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MulOneClass.toMul.{u1} G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MulZeroOneClass.toMulOneClass.{u1} G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) (MonoidWithZeroHomClass.toMonoidHomClass.{u1, u1, u1} (MonoidWithZeroHom.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1))))) G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZeroHom.monoidWithZeroHomClass.{u1, u1} G₀ G₀ (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))) (MonoidWithZero.toMulZeroOneClass.{u1} G₀ (CommMonoidWithZero.toMonoidWithZero.{u1} G₀ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1)))))))) (normalize.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (NormalizedGCDMonoid.toNormalizationMonoid.{u1} G₀ (CommGroupWithZero.cancelCommMonoidWithZero.{u1} G₀ _inst_1) (CommGroupWithZero.instNormalizedGCDMonoidCancelCommMonoidWithZero.{u1} G₀ _inst_1 (fun (a : G₀) (b : G₀) => _inst_2 a b)))) a) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (InvOneClass.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivInvOneMonoid.toInvOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivisionMonoid.toDivInvOneMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (DivisionCommMonoid.toDivisionMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) (CommGroupWithZero.toDivisionCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₀) => G₀) a) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_oneₓ'. -/
 theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp [normalize_apply, h0]
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one

baba818b

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

550b5853

chore(Associated): add simps, golf (#11435)

New `simp` tags or `simp` lemmas

associated_one_iff_isUnit, associated_zero_iff_eq_zero, Associates.mk_eq_one, Associates.mk_dvd_mk, Associates.mk_isRelPrime_iff, Associates.mk_zero, Associates.quot_out_zero, Associates.le_zero, Associates.prime_mk, Associates.irreducible_mk, Associates.mk_dvdNotUnit_mk_iff, Associates.factors_le, Associates.prod_factors

New `gcongr` tags

Associates.factors_mono, Associates.prod_mono

Change explicit args to implicit

Associates.prime_mk, Associates.irreducible_mk, Associates.one_or_eq_of_le_of_prime

Change typeclass assumptions

drop [Nontrivial _] here and there, mostly in cases when a lemma has _ ≠ _ assumption
drop all decidability assumptions in Associates.FactorSetMem
drop decidability assumptions when they aren't needed to formulate a theorem

Use `WithTop` API

Use WithTop.some and ⊤ instead of Option.some and none in UniqueFactorizationDomain.

Renames

Associates.isPrimal_iff → Associates.isPrimal_mk;
Associates.mk_le_mk_iff_dvd_iff → Associates.mk_le_mk_iff_dvd;
Associates.factors_0 → Associates.factors_zero;
Associates.factors_eq_none_iff_zero → Associates.factors_eq_top_iff_zero

42466cc7

Diff

@@ -207,8 +207,6 @@ namespace Associates
 
 variable [CancelCommMonoidWithZero α] [NormalizationMonoid α]
 
-attribute [local instance] Associated.setoid
-
 /-- Maps an element of `Associates` back to the normalized element of its associate class -/
 protected def out : Associates α → α :=
   (Quotient.lift (normalize : α → α)) fun a _ ⟨_, hu⟩ =>
@@ -232,12 +230,12 @@ theorem out_mul (a b : Associates α) : (a * b).out = a.out * b.out :=
 
 theorem dvd_out_iff (a : α) (b : Associates α) : a ∣ b.out ↔ Associates.mk a ≤ b :=
   Quotient.inductionOn b <| by
-    simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
+    simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd]
 #align associates.dvd_out_iff Associates.dvd_out_iff
 
 theorem out_dvd_iff (a : α) (b : Associates α) : b.out ∣ a ↔ b ≤ Associates.mk a :=
   Quotient.inductionOn b <| by
-    simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd_iff]
+    simp [Associates.out_mk, Associates.quotient_mk_eq_mk, mk_le_mk_iff_dvd]
 #align associates.out_dvd_iff Associates.out_dvd_iff
 
 @[simp]
@@ -415,8 +413,10 @@ theorem gcd_one_left [NormalizedGCDMonoid α] (a : α) : gcd 1 a = 1 :=
 #align gcd_one_left gcd_one_left
 
 @[simp]
-theorem gcd_one_left' [GCDMonoid α] (a : α) : Associated (gcd 1 a) 1 :=
-  associated_of_dvd_dvd (gcd_dvd_left _ _) (one_dvd _)
+theorem isUnit_gcd_one_left [GCDMonoid α] (a : α) : IsUnit (gcd 1 a) :=
+  isUnit_of_dvd_one (gcd_dvd_left _ _)
+
+theorem gcd_one_left' [GCDMonoid α] (a : α) : Associated (gcd 1 a) 1 := by simp
 #align gcd_one_left' gcd_one_left'
 
 @[simp]
@@ -425,8 +425,10 @@ theorem gcd_one_right [NormalizedGCDMonoid α] (a : α) : gcd a 1 = 1 :=
 #align gcd_one_right gcd_one_right
 
 @[simp]
-theorem gcd_one_right' [GCDMonoid α] (a : α) : Associated (gcd a 1) 1 :=
-  associated_of_dvd_dvd (gcd_dvd_right _ _) (one_dvd _)
+theorem isUnit_gcd_one_right [GCDMonoid α] (a : α) : IsUnit (gcd a 1) :=
+  isUnit_of_dvd_one (gcd_dvd_right _ _)
+
+theorem gcd_one_right' [GCDMonoid α] (a : α) : Associated (gcd a 1) 1 := by simp
 #align gcd_one_right' gcd_one_right'
 
 theorem gcd_dvd_gcd [GCDMonoid α] {a b c d : α} (hab : a ∣ b) (hcd : c ∣ d) : gcd a c ∣ gcd b d :=

550b5853

chore: classify porting notes about additional necessary beta reduction (#12130)

This subsumes some of the notes in #10752 and #10971. I'm on the fence as to whether replacing the dsimp only by beta_reduce is useful; this is easy to revert if needed.

7eeaaffb

Diff

@@ -1048,15 +1048,15 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
     lcm := fun a b =>
       if a = 0 then 0 else Classical.choose ((gcd_dvd_left a b).trans (Dvd.intro b rfl))
     gcd_mul_lcm := fun a b => by
-      -- Porting note (#10971): need `dsimp only` before `split_ifs`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with a0
       · rw [mul_zero, a0, zero_mul]
       · rw [← Classical.choose_spec ((gcd_dvd_left a b).trans (Dvd.intro b rfl))]
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      -- Porting note (#10971): need `dsimp only` before `split_ifs`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with a0
       · rfl
       have h := (Classical.choose_spec ((gcd_dvd_left a 0).trans (Dvd.intro 0 rfl))).symm
@@ -1108,8 +1108,8 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         rw [← normalize_gcd] at this
         rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2
     gcd_mul_lcm := fun a b => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with a0
       · rw [mul_zero, a0, zero_mul]
       · rw [←
@@ -1117,8 +1117,8 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         exact normalize_associated (a * b)
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with a0
       · rfl
       rw [← normalize_eq_zero] at a0
@@ -1141,8 +1141,8 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
   { lcm
     gcd := fun a b => if a = 0 then b else if b = 0 then a else Classical.choose (exists_gcd a b)
     gcd_mul_lcm := fun a b => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with h h_1
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
       · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _)]
@@ -1150,8 +1150,8 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
     lcm_zero_left := fun a => eq_zero_of_zero_dvd (dvd_lcm_left _ _)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
     gcd_dvd_left := fun a b => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with h h_1
       · rw [h]
         apply dvd_zero
@@ -1167,8 +1167,8 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
         mul_dvd_mul_iff_right h]
       apply dvd_lcm_right
     gcd_dvd_right := fun a b => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with h h_1
       · exact dvd_rfl
       · rw [h_1]
@@ -1184,8 +1184,8 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
         mul_dvd_mul_iff_right h_1]
       apply dvd_lcm_left
     dvd_gcd := fun {a b c} ac ab => by
-      -- Porting note (#10971): need `dsimp only`
-      dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      beta_reduce
       split_ifs with h h_1
       · exact ab
       · exact ac
@@ -1219,7 +1219,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
       if a = 0 then normalize b
       else if b = 0 then normalize a else Classical.choose (exists_gcd a b)
     gcd_mul_lcm := fun a b => by
-      dsimp only
+      beta_reduce
       split_ifs with h h_1
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
       · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), mul_zero, mul_zero]
@@ -1247,7 +1247,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
     lcm_zero_left := fun a => eq_zero_of_zero_dvd (dvd_lcm_left _ _)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
     gcd_dvd_left := fun a b => by
-      dsimp only
+      beta_reduce
       split_ifs with h h_1
       · rw [h]
         apply dvd_zero
@@ -1263,7 +1263,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
         mul_comm, mul_dvd_mul_iff_right h]
       apply dvd_lcm_right
     gcd_dvd_right := fun a b => by
-      dsimp only
+      beta_reduce
       split_ifs with h h_1
       · exact (normalize_associated _).dvd
       · rw [h_1]
@@ -1279,7 +1279,7 @@ noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq
         mul_dvd_mul_iff_right h_1]
       apply dvd_lcm_left
     dvd_gcd := fun {a b c} ac ab => by
-      dsimp only
+      beta_reduce
       split_ifs with h h_1
       · apply dvd_normalize_iff.2 ab
       · apply dvd_normalize_iff.2 ac
@@ -1357,9 +1357,10 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹
   normUnit_zero := dif_pos rfl
   normUnit_mul := fun {x y} x0 y0 => Units.eq_iff.1 (by
-    -- Porting note (#10971): need `dsimp only`, also `simp` reaches maximum heartbeat
+    -- Porting note(#12129): additional beta reduction needed
+    -- Porting note: `simp` reaches maximum heartbeat
     -- by Units.eq_iff.mp (by simp only [x0, y0, mul_comm])
-    dsimp only
+    beta_reduce
     split_ifs with h
     · rw [mul_eq_zero] at h
       cases h
@@ -1367,26 +1368,26 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
       · exact absurd ‹y = 0› y0
     · rw [Units.mk0_mul, mul_inv_rev, mul_comm] )
   normUnit_coe_units u := by
-    -- Porting note (#10971): need `dsimp only`
-    dsimp only
+    -- Porting note(#12129): additional beta reduction needed
+    beta_reduce
     rw [dif_neg (Units.ne_zero _), Units.mk0_val]
   gcd a b := if a = 0 ∧ b = 0 then 0 else 1
   lcm a b := if a = 0 ∨ b = 0 then 0 else 1
   gcd_dvd_left a b := by
-    -- Porting note (#10971): need `dsimp only`
-    dsimp only
+    -- Porting note(#12129): additional beta reduction needed
+    beta_reduce
     split_ifs with h
     · rw [h.1]
     · exact one_dvd _
   gcd_dvd_right a b := by
-    -- Porting note (#10971): need `dsimp only`
-    dsimp only
+    -- Porting note(#12129): additional beta reduction needed
+    beta_reduce
     split_ifs with h
     · rw [h.2]
     · exact one_dvd _
   dvd_gcd := fun {a b c} hac hab => by
-    -- Porting note (#10971): need `dsimp only`
-    dsimp only
+    -- Porting note(#12129): additional beta reduction needed
+    beta_reduce
     split_ifs with h
     · apply dvd_zero
     · rw [not_and_or] at h
@@ -1402,8 +1403,8 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
     · by_cases hb : b = 0
       · simp only [hb, and_true, or_true, ite_true, mul_zero]
         exact Associated.refl _
-      -- Porting note (#10971): need `dsimp only`
-      · dsimp only
+      -- Porting note(#12129): additional beta reduction needed
+      · beta_reduce
         rw [if_neg (not_and_of_not_left _ ha), one_mul, if_neg (not_or_of_not ha hb)]
         exact (associated_one_iff_isUnit.mpr ((IsUnit.mk0 _ ha).mul (IsUnit.mk0 _ hb))).symm
   lcm_zero_left b := if_pos (Or.inl rfl)

550b5853

feat: GCDMonoid (Associates α) instance (#11618)

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

92f24cbd

Diff

@@ -1420,3 +1420,39 @@ theorem normalize_eq_one {a : G₀} (h0 : a ≠ 0) : normalize a = 1 := by simp
 #align comm_group_with_zero.normalize_eq_one CommGroupWithZero.normalize_eq_one
 
 end CommGroupWithZero
+
+theorem Associated.gcd [CancelCommMonoidWithZero α] [GCDMonoid α]
+    {a₁ a₂ b₁ b₂ : α} (ha : Associated a₁ a₂) (hb : Associated b₁ b₂) :
+    Associated (gcd a₁ b₁) (gcd a₂ b₂) :=
+  associated_of_dvd_dvd (gcd_dvd_gcd ha.dvd hb.dvd) (gcd_dvd_gcd ha.symm.dvd hb.symm.dvd)
+
+theorem Associated.lcm [CancelCommMonoidWithZero α] [GCDMonoid α]
+    {a₁ a₂ b₁ b₂ : α} (ha : Associated a₁ a₂) (hb : Associated b₁ b₂) :
+    Associated (lcm a₁ b₁) (lcm a₂ b₂) :=
+  associated_of_dvd_dvd (lcm_dvd_lcm ha.dvd hb.dvd) (lcm_dvd_lcm ha.symm.dvd hb.symm.dvd)
+
+namespace Associates
+
+variable [CancelCommMonoidWithZero α] [GCDMonoid α]
+
+instance instGCDMonoid : GCDMonoid (Associates α) where
+  gcd := Quotient.map₂' gcd fun a₁ a₂ (ha : Associated _ _) b₁ b₂ (hb : Associated _ _) => ha.gcd hb
+  lcm := Quotient.map₂' lcm fun a₁ a₂ (ha : Associated _ _) b₁ b₂ (hb : Associated _ _) => ha.lcm hb
+  gcd_dvd_left := by rintro ⟨a⟩ ⟨b⟩; exact mk_le_mk_of_dvd (gcd_dvd_left _ _)
+  gcd_dvd_right := by rintro ⟨a⟩ ⟨b⟩; exact mk_le_mk_of_dvd (gcd_dvd_right _ _)
+  dvd_gcd := by
+    rintro ⟨a⟩ ⟨b⟩ ⟨c⟩ hac hbc
+    exact mk_le_mk_of_dvd (dvd_gcd (dvd_of_mk_le_mk hac) (dvd_of_mk_le_mk hbc))
+  gcd_mul_lcm := by
+    rintro ⟨a⟩ ⟨b⟩
+    rw [associated_iff_eq]
+    exact Quotient.sound <| gcd_mul_lcm _ _
+  lcm_zero_left := by rintro ⟨a⟩; exact congr_arg Associates.mk <| lcm_zero_left _
+  lcm_zero_right := by rintro ⟨a⟩; exact congr_arg Associates.mk <| lcm_zero_right _
+
+theorem gcd_mk_mk {a b : α} : gcd (Associates.mk a) (Associates.mk b) = Associates.mk (gcd a b) :=
+  rfl
+theorem lcm_mk_mk {a b : α} : lcm (Associates.mk a) (Associates.mk b) = Associates.mk (lcm a b) :=
+  rfl
+
+end Associates

550b5853

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -576,7 +576,7 @@ theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} :
   · induction' k with k hk
     · rw [pow_zero, pow_zero]
       exact (gcd_one_right' a).dvd
-    rw [pow_succ, pow_succ]
+    rw [pow_succ', pow_succ']
     trans gcd a b * gcd a (b ^ k)
     · exact gcd_mul_dvd_mul_gcd a b (b ^ k)
     · exact (mul_dvd_mul_iff_left hg).mpr hk

550b5853

chore: Rename mul-div cancellation lemmas (#11530)

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

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

4ea4a86a

Diff

@@ -988,7 +988,7 @@ theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a
     rcases gcd_dvd_right a c with ⟨e, he⟩
     rcases gcd_dvd_left a c with ⟨f, hf⟩
     use e + f * d
-    rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel]
+    rw [mul_add, ← he, ← mul_assoc, ← hf, ← hd, ← add_sub_assoc, add_comm c b, add_sub_cancel_right]
 #align gcd_eq_of_dvd_sub_right gcd_eq_of_dvd_sub_right
 
 theorem gcd_eq_of_dvd_sub_left {a b c : α} (h : a ∣ b - c) : gcd b a = gcd c a := by

550b5853

chore: classify slow / slower porting notes (#11084)

Classifies by adding issue number #11083 to porting notes claiming anything semantically equivalent to:

"very slow; improve performance?"
"quite slow; improve performance?"
"`tactic" was slow"
"removed attribute because it caused extremely slow tactic"
"proof was rewritten, because it was too slow"
"doing this make things very slow"
"slower implementation"

e6a09f7c

Diff

@@ -94,7 +94,7 @@ theorem normUnit_one : normUnit (1 : α) = 1 :=
   normUnit_coe_units 1
 #align norm_unit_one normUnit_one
 
--- Porting note: quite slow. Improve performance?
+-- Porting note (#11083): quite slow. Improve performance?
 /-- Chooses an element of each associate class, by multiplying by `normUnit` -/
 def normalize : α →*₀ α where
   toFun x := x * normUnit x
@@ -157,7 +157,7 @@ theorem normalize_eq_one {x : α} : normalize x = 1 ↔ IsUnit x :=
   ⟨fun hx => isUnit_iff_exists_inv.2 ⟨_, hx⟩, fun ⟨u, hu⟩ => hu ▸ normalize_coe_units u⟩
 #align normalize_eq_one normalize_eq_one
 
--- Porting note: quite slow. Improve performance?
+-- Porting note (#11083): quite slow. Improve performance?
 @[simp]
 theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 := by
   nontriviality α using Subsingleton.elim a 0
@@ -1206,7 +1206,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       apply ac }
 #align gcd_monoid_of_lcm gcdMonoidOfLCM
 
--- Porting note: very slow; improve performance?
+-- Porting note (#11083): very slow; improve performance?
 /-- Define `NormalizedGCDMonoid` on a structure just from the `lcm` and its properties. -/
 noncomputable def normalizedGCDMonoidOfLCM [NormalizationMonoid α] [DecidableEq α] (lcm : α → α → α)
     (dvd_lcm_left : ∀ a b, a ∣ lcm a b) (dvd_lcm_right : ∀ a b, b ∣ lcm a b)
@@ -1351,7 +1351,7 @@ namespace CommGroupWithZero
 
 variable (G₀ : Type*) [CommGroupWithZero G₀] [DecidableEq G₀]
 
--- Porting note: very slow; improve performance?
+-- Porting note (#11083): very slow; improve performance?
 -- see Note [lower instance priority]
 instance (priority := 100) : NormalizedGCDMonoid G₀ where
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹

550b5853

chore: classify need dsimp only porting notes (#10972)

Classifies by adding issue number #10971 to porting notes claiming:

need dsimp only.

ea286e3c

Diff

@@ -1048,14 +1048,14 @@ noncomputable def gcdMonoidOfGCD [DecidableEq α] (gcd : α → α → α)
     lcm := fun a b =>
       if a = 0 then 0 else Classical.choose ((gcd_dvd_left a b).trans (Dvd.intro b rfl))
     gcd_mul_lcm := fun a b => by
-      -- Porting note: need `dsimp only` before `split_ifs`
+      -- Porting note (#10971): need `dsimp only` before `split_ifs`
       dsimp only
       split_ifs with a0
       · rw [mul_zero, a0, zero_mul]
       · rw [← Classical.choose_spec ((gcd_dvd_left a b).trans (Dvd.intro b rfl))]
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      -- Porting note: need `dsimp only` before `split_ifs`
+      -- Porting note (#10971): need `dsimp only` before `split_ifs`
       dsimp only
       split_ifs with a0
       · rfl
@@ -1108,7 +1108,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         rw [← normalize_gcd] at this
         rwa [normalize.map_mul, normalize_gcd, mul_right_inj' h1] at h2
     gcd_mul_lcm := fun a b => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with a0
       · rw [mul_zero, a0, zero_mul]
@@ -1117,7 +1117,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         exact normalize_associated (a * b)
     lcm_zero_left := fun a => if_pos rfl
     lcm_zero_right := fun a => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with a0
       · rfl
@@ -1141,7 +1141,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
   { lcm
     gcd := fun a b => if a = 0 then b else if b = 0 then a else Classical.choose (exists_gcd a b)
     gcd_mul_lcm := fun a b => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with h h_1
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
@@ -1150,7 +1150,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
     lcm_zero_left := fun a => eq_zero_of_zero_dvd (dvd_lcm_left _ _)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)
     gcd_dvd_left := fun a b => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with h h_1
       · rw [h]
@@ -1167,7 +1167,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
         mul_dvd_mul_iff_right h]
       apply dvd_lcm_right
     gcd_dvd_right := fun a b => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with h h_1
       · exact dvd_rfl
@@ -1184,7 +1184,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
         mul_dvd_mul_iff_right h_1]
       apply dvd_lcm_left
     dvd_gcd := fun {a b c} ac ab => by
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       dsimp only
       split_ifs with h h_1
       · exact ab
@@ -1357,7 +1357,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹
   normUnit_zero := dif_pos rfl
   normUnit_mul := fun {x y} x0 y0 => Units.eq_iff.1 (by
-    -- Porting note: need `dsimp only`, also `simp` reaches maximum heartbeat
+    -- Porting note (#10971): need `dsimp only`, also `simp` reaches maximum heartbeat
     -- by Units.eq_iff.mp (by simp only [x0, y0, mul_comm])
     dsimp only
     split_ifs with h
@@ -1367,25 +1367,25 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
       · exact absurd ‹y = 0› y0
     · rw [Units.mk0_mul, mul_inv_rev, mul_comm] )
   normUnit_coe_units u := by
-    -- Porting note: need `dsimp only`
+    -- Porting note (#10971): need `dsimp only`
     dsimp only
     rw [dif_neg (Units.ne_zero _), Units.mk0_val]
   gcd a b := if a = 0 ∧ b = 0 then 0 else 1
   lcm a b := if a = 0 ∨ b = 0 then 0 else 1
   gcd_dvd_left a b := by
-    -- Porting note: need `dsimp only`
+    -- Porting note (#10971): need `dsimp only`
     dsimp only
     split_ifs with h
     · rw [h.1]
     · exact one_dvd _
   gcd_dvd_right a b := by
-    -- Porting note: need `dsimp only`
+    -- Porting note (#10971): need `dsimp only`
     dsimp only
     split_ifs with h
     · rw [h.2]
     · exact one_dvd _
   dvd_gcd := fun {a b c} hac hab => by
-    -- Porting note: need `dsimp only`
+    -- Porting note (#10971): need `dsimp only`
     dsimp only
     split_ifs with h
     · apply dvd_zero
@@ -1402,7 +1402,7 @@ instance (priority := 100) : NormalizedGCDMonoid G₀ where
     · by_cases hb : b = 0
       · simp only [hb, and_true, or_true, ite_true, mul_zero]
         exact Associated.refl _
-      -- Porting note: need `dsimp only`
+      -- Porting note (#10971): need `dsimp only`
       · dsimp only
         rw [if_neg (not_and_of_not_left _ ha), one_mul, if_neg (not_or_of_not ha hb)]
         exact (associated_one_iff_isUnit.mpr ((IsUnit.mk0 _ ha).mul (IsUnit.mk0 _ hb))).symm

550b5853

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -133,13 +133,13 @@ theorem normalize_apply (x : α) : normalize x = x * normUnit x :=
   rfl
 #align normalize_apply normalize_apply
 
--- Porting note: `simp` can prove this
+-- Porting note (#10618): `simp` can prove this
 -- @[simp]
 theorem normalize_zero : normalize (0 : α) = 0 :=
   normalize.map_zero
 #align normalize_zero normalize_zero
 
--- Porting note: `simp` can prove this
+-- Porting note (#10618): `simp` can prove this
 -- @[simp]
 theorem normalize_one : normalize (1 : α) = 1 :=
   normalize.map_one
@@ -951,7 +951,7 @@ theorem normUnit_eq_one (x : α) : normUnit x = 1 :=
   rfl
 #align norm_unit_eq_one normUnit_eq_one
 
--- Porting note: `simp` can prove this
+-- Porting note (#10618): `simp` can prove this
 -- @[simp]
 theorem normalize_eq (x : α) : normalize x = x :=
   mul_one x

550b5853

chore: Remove unnecessary "rw"s (#10704)

Remove unnecessary "rw"s.

db5a9376

Diff

@@ -1145,7 +1145,7 @@ noncomputable def gcdMonoidOfLCM [DecidableEq α] (lcm : α → α → α)
       dsimp only
       split_ifs with h h_1
       · rw [h, eq_zero_of_zero_dvd (dvd_lcm_left _ _), mul_zero, zero_mul]
-      · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _), mul_zero]
+      · rw [h_1, eq_zero_of_zero_dvd (dvd_lcm_right _ _)]
       rw [mul_comm, ← Classical.choose_spec (exists_gcd a b)]
     lcm_zero_left := fun a => eq_zero_of_zero_dvd (dvd_lcm_left _ _)
     lcm_zero_right := fun a => eq_zero_of_zero_dvd (dvd_lcm_right _ _)

550b5853

feat: introduce IsRelPrime and DecompositionMonoid and refactor (#10327)

Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.
Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.
Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.
Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.
Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.
Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

b569e065

Diff

@@ -309,6 +309,18 @@ section GCDMonoid
 
 variable [CancelCommMonoidWithZero α]
 
+instance [NormalizationMonoid α] : Nonempty (NormalizationMonoid α) := ⟨‹_›⟩
+instance [GCDMonoid α] : Nonempty (GCDMonoid α) := ⟨‹_›⟩
+instance [NormalizedGCDMonoid α] : Nonempty (NormalizedGCDMonoid α) := ⟨‹_›⟩
+instance [h : Nonempty (NormalizedGCDMonoid α)] : Nonempty (NormalizationMonoid α) :=
+  h.elim fun _ ↦ inferInstance
+instance [h : Nonempty (NormalizedGCDMonoid α)] : Nonempty (GCDMonoid α) :=
+  h.elim fun _ ↦ inferInstance
+
+theorem gcd_isUnit_iff_isRelPrime [GCDMonoid α] {a b : α} :
+    IsUnit (gcd a b) ↔ IsRelPrime a b :=
+  ⟨fun h _ ha hb ↦ isUnit_of_dvd_unit (dvd_gcd ha hb) h, (· (gcd_dvd_left a b) (gcd_dvd_right a b))⟩
+
 -- Porting note: lower priority to avoid linter complaints about simp-normal form
 @[simp 1100]
 theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
@@ -520,35 +532,26 @@ theorem dvd_mul_gcd_iff_dvd_mul [GCDMonoid α] {m n k : α} : k ∣ m * gcd k n
 
 /-- Represent a divisor of `m * n` as a product of a divisor of `m` and a divisor of `n`.
 
-In other words, the nonzero elements of a `GCDMonoid` form a decomposition monoid
-(more widely known as a pre-Schreier domain in the context of rings).
-
 Note: In general, this representation is highly non-unique.
 
 See `Nat.prodDvdAndDvdOfDvdProd` for a constructive version on `ℕ`.  -/
-theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) :
-    ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ := by
-  by_cases h0 : gcd k m = 0
-  · rw [gcd_eq_zero_iff] at h0
-    rcases h0 with ⟨rfl, rfl⟩
-    refine' ⟨0, n, dvd_refl 0, dvd_refl n, _⟩
-    simp
-  · obtain ⟨a, ha⟩ := gcd_dvd_left k m
-    refine' ⟨gcd k m, a, gcd_dvd_right _ _, _, ha⟩
-    suffices h : gcd k m * a ∣ gcd k m * n by
-      cases' h with b hb
-      use b
-      rw [mul_assoc] at hb
-      apply mul_left_cancel₀ h0 hb
-    rw [← ha]
-    exact dvd_gcd_mul_of_dvd_mul H
-#align exists_dvd_and_dvd_of_dvd_mul exists_dvd_and_dvd_of_dvd_mul
-
-theorem dvd_mul [GCDMonoid α] {k m n : α} : k ∣ m * n ↔ ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ := by
-  refine' ⟨exists_dvd_and_dvd_of_dvd_mul, _⟩
-  rintro ⟨d₁, d₂, hy, hz, rfl⟩
-  exact mul_dvd_mul hy hz
-#align dvd_mul dvd_mul
+instance [h : Nonempty (GCDMonoid α)] : DecompositionMonoid α where
+  primal k m n H := by
+    cases h
+    by_cases h0 : gcd k m = 0
+    · rw [gcd_eq_zero_iff] at h0
+      rcases h0 with ⟨rfl, rfl⟩
+      refine' ⟨0, n, dvd_refl 0, dvd_refl n, _⟩
+      simp
+    · obtain ⟨a, ha⟩ := gcd_dvd_left k m
+      refine' ⟨gcd k m, a, gcd_dvd_right _ _, _, ha⟩
+      suffices h : gcd k m * a ∣ gcd k m * n by
+        cases' h with b hb
+        use b
+        rw [mul_assoc] at hb
+        apply mul_left_cancel₀ h0 hb
+      rw [← ha]
+      exact dvd_gcd_mul_of_dvd_mul H
 
 theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd k m * gcd k n := by
   obtain ⟨m', n', hm', hn', h⟩ := exists_dvd_and_dvd_of_dvd_mul (gcd_dvd_right k (m * n))
@@ -604,7 +607,7 @@ theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠
   rw [mul_comm] at h2
   have h3 : d₁ ^ k ∣ a := by
     apply (dvd_gcd_mul_of_dvd_mul h2).trans
-    rw [IsUnit.mul_left_dvd _ _ _ h1]
+    rw [h1.mul_left_dvd]
   have h4 : d₁ ^ k ≠ 0 := by
     intro hdk
     rw [hdk] at h3
@@ -887,28 +890,10 @@ theorem lcm_eq_of_associated_right [NormalizedGCDMonoid α] {m n : α} (h : Asso
 
 end LCM
 
-namespace GCDMonoid
-
-theorem prime_of_irreducible [GCDMonoid α] {x : α} (hi : Irreducible x) : Prime x :=
-  ⟨hi.ne_zero,
-    ⟨hi.1, fun a b h => by
-      cases' gcd_dvd_left x a with y hy
-      cases' hi.isUnit_or_isUnit hy with hu hu
-      · right
-        trans gcd (x * b) (a * b)
-        apply dvd_gcd (dvd_mul_right x b) h
-        rw [(gcd_mul_right' b x a).dvd_iff_dvd_left]
-        exact (associated_unit_mul_left _ _ hu).dvd
-      · left
-        rw [hy]
-        exact dvd_trans (associated_mul_unit_left _ _ hu).dvd (gcd_dvd_right x a)⟩⟩
-#align gcd_monoid.prime_of_irreducible GCDMonoid.prime_of_irreducible
-
-theorem irreducible_iff_prime [GCDMonoid α] {p : α} : Irreducible p ↔ Prime p :=
-  ⟨prime_of_irreducible, Prime.irreducible⟩
-#align gcd_monoid.irreducible_iff_prime GCDMonoid.irreducible_iff_prime
-
-end GCDMonoid
+@[deprecated] alias GCDMonoid.prime_of_irreducible := Irreducible.prime
+#align gcd_monoid.prime_of_irreducible Irreducible.prime
+@[deprecated] alias GCDMonoid.irreducible_iff_prime := irreducible_iff_prime
+#align gcd_monoid.irreducible_iff_prime irreducible_iff_prime
 
 end GCDMonoid

550b5853

chore: move to v4.6.0-rc1, merging adaptations from bump/v4.6.0 (#10176)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

490d2d48

Diff

@@ -355,11 +355,11 @@ theorem gcd_assoc' [GCDMonoid α] (m n k : α) : Associated (gcd (gcd m n) k) (g
       ((gcd_dvd_right m (gcd n k)).trans (gcd_dvd_right n k)))
 #align gcd_assoc' gcd_assoc'
 
-instance [NormalizedGCDMonoid α] : IsCommutative α gcd :=
-  ⟨gcd_comm⟩
+instance [NormalizedGCDMonoid α] : Std.Commutative (α := α) gcd where
+  comm := gcd_comm
 
-instance [NormalizedGCDMonoid α] : IsAssociative α gcd :=
-  ⟨gcd_assoc⟩
+instance [NormalizedGCDMonoid α] : Std.Associative (α := α) gcd where
+  assoc := gcd_assoc
 
 theorem gcd_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : gcd a b ∣ c)
     (hcab : c ∣ gcd a b) : gcd a b = normalize c :=
@@ -779,11 +779,11 @@ theorem lcm_assoc' [GCDMonoid α] (m n k : α) : Associated (lcm (lcm m n) k) (l
       (lcm_dvd ((dvd_lcm_right _ _).trans (dvd_lcm_left _ _)) (dvd_lcm_right _ _)))
 #align lcm_assoc' lcm_assoc'
 
-instance [NormalizedGCDMonoid α] : IsCommutative α lcm :=
-  ⟨lcm_comm⟩
+instance [NormalizedGCDMonoid α] : Std.Commutative (α := α) lcm where
+  comm := lcm_comm
 
-instance [NormalizedGCDMonoid α] : IsAssociative α lcm :=
-  ⟨lcm_assoc⟩
+instance [NormalizedGCDMonoid α] : Std.Associative (α := α) lcm where
+  assoc := lcm_assoc
 
 theorem lcm_eq_normalize [NormalizedGCDMonoid α] {a b c : α} (habc : lcm a b ∣ c)
     (hcab : c ∣ lcm a b) : lcm a b = normalize c :=

550b5853

feat: The support of f ^ n (#9617)

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

From LeanAPAP

9d1a7d26

Diff

@@ -619,13 +619,9 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
     rw [Subsingleton.elim a (0 ^ k)]
   by_cases ha : a = 0
   · use 0
-    rw [ha]
-    obtain rfl | hk := k.eq_zero_or_pos
-    · exfalso
-      revert h
-      rw [ha, zero_mul, pow_zero]
-      apply zero_ne_one
-    · rw [zero_pow hk]
+    obtain rfl | hk := eq_or_ne k 0
+    · simp [ha] at h
+    · rw [ha, zero_pow hk]
   by_cases hb : b = 0
   · use 1
     rw [one_pow]

550b5853

chore: Move zpow lemmas (#9720)

These lemmas can be proved much earlier with little to no change to their proofs.

Part of #9411

1564a327

Diff

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker
 -/
 import Mathlib.Algebra.Associated
-import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Ring.Regular
 import Mathlib.Tactic.Common

550b5853

fix: attribute [simp] ... in -> attribute [local simp] ... in (#7678)

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

1fe87718

Diff

@@ -931,7 +931,7 @@ instance (priority := 100) normalizationMonoidOfUniqueUnits : NormalizationMonoi
 
 instance uniqueNormalizationMonoidOfUniqueUnits : Unique (NormalizationMonoid α) where
   default := normalizationMonoidOfUniqueUnits
-  uniq := fun ⟨u, _, _, _⟩ => by congr; simp
+  uniq := fun ⟨u, _, _, _⟩ => by congr; simp [eq_iff_true_of_subsingleton]
 #align unique_normalization_monoid_of_unique_units uniqueNormalizationMonoidOfUniqueUnits
 
 instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=

550b5853

feat: some lemmas about associated and prime elements (#7453)

From flt-regular.

Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

Co-authored-by: timotree3 <timorcb@gmail.com>

51089d8f

Diff

@@ -508,11 +508,17 @@ theorem dvd_gcd_mul_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k
   (dvd_gcd (dvd_mul_right _ n) H).trans (gcd_mul_right' n k m).dvd
 #align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mul
 
+theorem dvd_gcd_mul_iff_dvd_mul [GCDMonoid α] {m n k : α} : k ∣ gcd k m * n ↔ k ∣ m * n :=
+  ⟨fun h => h.trans (mul_dvd_mul (gcd_dvd_right k m) dvd_rfl), dvd_gcd_mul_of_dvd_mul⟩
+
 theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
   rw [mul_comm] at H ⊢
   exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
 
+theorem dvd_mul_gcd_iff_dvd_mul [GCDMonoid α] {m n k : α} : k ∣ m * gcd k n ↔ k ∣ m * n :=
+  ⟨fun h => h.trans (mul_dvd_mul dvd_rfl (gcd_dvd_right k n)), dvd_mul_gcd_of_dvd_mul⟩
+
 /-- Represent a divisor of `m * n` as a product of a divisor of `m` and a divisor of `n`.
 
 In other words, the nonzero elements of a `GCDMonoid` form a decomposition monoid
@@ -692,6 +698,22 @@ theorem extract_gcd {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α] (x
   exact ⟨x', y', ex, ey, isUnit_gcd_of_eq_mul_gcd ex ey h⟩
 #align extract_gcd extract_gcd
 
+theorem associated_gcd_left_iff [GCDMonoid α] {x y : α} : Associated x (gcd x y) ↔ x ∣ y :=
+  ⟨fun hx => hx.dvd.trans (gcd_dvd_right x y),
+    fun hxy => associated_of_dvd_dvd (dvd_gcd dvd_rfl hxy) (gcd_dvd_left x y)⟩
+
+theorem associated_gcd_right_iff [GCDMonoid α] {x y : α} : Associated y (gcd x y) ↔ y ∣ x :=
+  ⟨fun hx => hx.dvd.trans (gcd_dvd_left x y),
+    fun hxy => associated_of_dvd_dvd (dvd_gcd hxy dvd_rfl) (gcd_dvd_right x y)⟩
+
+theorem Irreducible.isUnit_gcd_iff [GCDMonoid α] {x y : α} (hx : Irreducible x) :
+    IsUnit (gcd x y) ↔ ¬(x ∣ y) := by
+  rw [hx.isUnit_iff_not_associated_of_dvd (gcd_dvd_left x y), not_iff_not, associated_gcd_left_iff]
+
+theorem Irreducible.gcd_eq_one_iff [NormalizedGCDMonoid α] {x y : α} (hx : Irreducible x) :
+    gcd x y = 1 ↔ ¬(x ∣ y) := by
+  rw [← hx.isUnit_gcd_iff, ← normalize_eq_one, NormalizedGCDMonoid.normalize_gcd]
+
 end GCD
 
 section LCM

550b5853

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -248,8 +248,7 @@ theorem out_top : (⊤ : Associates α).out = 0 :=
 
 -- Porting note: lower priority to avoid linter complaints about simp-normal form
 @[simp 1100]
-theorem normalize_out (a : Associates α) :
-  normalize a.out = a.out :=
+theorem normalize_out (a : Associates α) : normalize a.out = a.out :=
   Quotient.inductionOn a normalize_idem
 #align associates.normalize_out Associates.normalize_out
 
@@ -313,8 +312,7 @@ variable [CancelCommMonoidWithZero α]
 
 -- Porting note: lower priority to avoid linter complaints about simp-normal form
 @[simp 1100]
-theorem normalize_gcd [NormalizedGCDMonoid α] :
-  ∀ a b : α, normalize (gcd a b) = gcd a b :=
+theorem normalize_gcd [NormalizedGCDMonoid α] : ∀ a b : α, normalize (gcd a b) = gcd a b :=
   NormalizedGCDMonoid.normalize_gcd
 #align normalize_gcd normalize_gcd
 
@@ -733,8 +731,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
 
 -- Porting note: lower priority to avoid linter complaints about simp-normal form
 @[simp 1100]
-theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) :
-  normalize (lcm a b) = lcm a b :=
+theorem normalize_lcm [NormalizedGCDMonoid α] (a b : α) : normalize (lcm a b) = lcm a b :=
   NormalizedGCDMonoid.normalize_lcm a b
 #align normalize_lcm normalize_lcm

550b5853

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

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

bdc47f68

Diff

@@ -532,8 +532,8 @@ theorem exists_dvd_and_dvd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m *
     simp
   · obtain ⟨a, ha⟩ := gcd_dvd_left k m
     refine' ⟨gcd k m, a, gcd_dvd_right _ _, _, ha⟩
-    suffices h : gcd k m * a ∣ gcd k m * n
-    · cases' h with b hb
+    suffices h : gcd k m * a ∣ gcd k m * n by
+      cases' h with b hb
       use b
       rw [mul_assoc] at hb
       apply mul_left_cancel₀ h0 hb

550b5853

chore: delay import of Tactic.Common (#7000)

I know that this is contrary to what we've done previously, but:

I'm trying to upstream a great many tactics from Mathlib to Std (essentially, everything that non-mathematicians want too).
This makes it much easier for me to see what is going on, and understand the import requirements (particularly for the "big" tactics norm_num / ring / linarith)
It's actually not as bad as it looks here, because as these tactics move up to Std they will start disappearing again from explicit imports, but Mathlib can happily import all of Std.

(Oh

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

4f3418a7

Diff

@@ -6,6 +6,7 @@ Authors: Johannes Hölzl, Jens Wagemaker
 import Mathlib.Algebra.Associated
 import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Ring.Regular
+import Mathlib.Tactic.Common
 
 #align_import algebra.gcd_monoid.basic from "leanprover-community/mathlib"@"550b58538991c8977703fdeb7c9d51a5aa27df11"

550b5853

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -64,13 +64,13 @@ divisibility, gcd, lcm, normalize
 -/
 
 
-variable {α : Type _}
+variable {α : Type*}
 
 -- Porting note: mathlib3 had a `@[protect_proj]` here, but adding `protected` to all the fields
 -- adds unnecessary clutter to later code
 /-- Normalization monoid: multiplying with `normUnit` gives a normal form for associated
 elements. -/
-class NormalizationMonoid (α : Type _) [CancelCommMonoidWithZero α] where
+class NormalizationMonoid (α : Type*) [CancelCommMonoidWithZero α] where
   /-- `normUnit` assigns to each element of the monoid a unit of the monoid. -/
   normUnit : α → αˣ
   /-- The proposition that `normUnit` maps `0` to the identity. -/
@@ -269,7 +269,7 @@ end Associates
 `lcm` (least common multiple) operations, determined up to a unit. The type class focuses on `gcd`
 and we derive the corresponding `lcm` facts from `gcd`.
 -/
-class GCDMonoid (α : Type _) [CancelCommMonoidWithZero α] where
+class GCDMonoid (α : Type*) [CancelCommMonoidWithZero α] where
   /-- The greatest common divisor between two elements. -/
   gcd : α → α → α
   /-- The least common multiple between two elements. -/
@@ -294,7 +294,7 @@ class GCDMonoid (α : Type _) [CancelCommMonoidWithZero α] where
 supremum, `1` is bottom, and `0` is top. The type class focuses on `gcd` and we derive the
 corresponding `lcm` facts from `gcd`.
 -/
-class NormalizedGCDMonoid (α : Type _) [CancelCommMonoidWithZero α] extends NormalizationMonoid α,
+class NormalizedGCDMonoid (α : Type*) [CancelCommMonoidWithZero α] extends NormalizationMonoid α,
   GCDMonoid α where
   /-- The GCD is normalized to itself. -/
   normalize_gcd : ∀ a b, normalize (gcd a b) = gcd a b
@@ -659,21 +659,21 @@ theorem exists_eq_pow_of_mul_eq_pow [GCDMonoid α] [Unique αˣ] {a b c : α} (h
   ⟨d, (associated_iff_eq.mp hd).symm⟩
 #align exists_eq_pow_of_mul_eq_pow exists_eq_pow_of_mul_eq_pow
 
-theorem gcd_greatest {α : Type _} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
+theorem gcd_greatest {α : Type*} [CancelCommMonoidWithZero α] [NormalizedGCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
     GCDMonoid.gcd a b = normalize d :=
   haveI h := hd _ (GCDMonoid.gcd_dvd_left a b) (GCDMonoid.gcd_dvd_right a b)
   gcd_eq_normalize h (GCDMonoid.dvd_gcd hda hdb)
 #align gcd_greatest gcd_greatest
 
-theorem gcd_greatest_associated {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] {a b d : α}
+theorem gcd_greatest_associated {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α] {a b d : α}
     (hda : d ∣ a) (hdb : d ∣ b) (hd : ∀ e : α, e ∣ a → e ∣ b → e ∣ d) :
     Associated d (GCDMonoid.gcd a b) :=
   haveI h := hd _ (GCDMonoid.gcd_dvd_left a b) (GCDMonoid.gcd_dvd_right a b)
   associated_of_dvd_dvd (GCDMonoid.dvd_gcd hda hdb) h
 #align gcd_greatest_associated gcd_greatest_associated
 
-theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α]
+theorem isUnit_gcd_of_eq_mul_gcd {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α]
     {x y x' y' : α} (ex : x = gcd x y * x') (ey : y = gcd x y * y') (h : gcd x y ≠ 0) :
     IsUnit (gcd x' y') := by
   rw [← associated_one_iff_isUnit]
@@ -682,7 +682,7 @@ theorem isUnit_gcd_of_eq_mul_gcd {α : Type _} [CancelCommMonoidWithZero α] [GC
   rw [← ex, ← ey, mul_one]
 #align is_unit_gcd_of_eq_mul_gcd isUnit_gcd_of_eq_mul_gcd
 
-theorem extract_gcd {α : Type _} [CancelCommMonoidWithZero α] [GCDMonoid α] (x y : α) :
+theorem extract_gcd {α : Type*} [CancelCommMonoidWithZero α] [GCDMonoid α] (x y : α) :
     ∃ x' y', x = gcd x y * x' ∧ y = gcd x y * y' ∧ IsUnit (gcd x' y') := by
   by_cases h : gcd x y = 0
   · obtain ⟨rfl, rfl⟩ := (gcd_eq_zero_iff x y).1 h
@@ -1349,7 +1349,7 @@ end Constructors
 
 namespace CommGroupWithZero
 
-variable (G₀ : Type _) [CommGroupWithZero G₀] [DecidableEq G₀]
+variable (G₀ : Type*) [CommGroupWithZero G₀] [DecidableEq G₀]
 
 -- Porting note: very slow; improve performance?
 -- see Note [lower instance priority]

550b5853

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker
-
-! This file was ported from Lean 3 source module algebra.gcd_monoid.basic
-! leanprover-community/mathlib commit 550b58538991c8977703fdeb7c9d51a5aa27df11
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Associated
 import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Ring.Regular
 
+#align_import algebra.gcd_monoid.basic from "leanprover-community/mathlib"@"550b58538991c8977703fdeb7c9d51a5aa27df11"
+
 /-!
 # Monoids with normalization functions, `gcd`, and `lcm`

550b5853

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -930,7 +930,7 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
       -- Porting note: Lean4 seems to need help specifying `g₁` and `g₂`
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _)
       · exact (@lcm_dvd_iff _ _ g₁ ..).mpr ⟨@dvd_lcm_left _ _ g₂ _ _, @dvd_lcm_right _ _ g₂ _ _⟩
-      · exact lcm_dvd_iff.mpr ⟨@dvd_lcm_left  _ _ g₁ _ _, @dvd_lcm_right _ _ g₁  _ _⟩
+      · exact lcm_dvd_iff.mpr ⟨@dvd_lcm_left _ _ g₁ _ _, @dvd_lcm_right _ _ g₁ _ _⟩
     cases g₁
     cases g₂
     dsimp only at hgcd hlcm

550b5853

chore: tidy various files (#5449)

ff656fa9

Diff

@@ -1106,7 +1106,6 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
         have h1 : gcd a b ≠ 0 := by
           have hab : a * b ≠ 0 := mul_ne_zero a0 hb
           contrapose! hab
-          push_neg at hab
           rw [← normalize_eq_zero, ← this, hab, zero_mul]
         have h2 : normalize (gcd a b * l) = gcd a b * l := by rw [this, normalize_idem]
         rw [← normalize_gcd] at this

550b5853

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -513,7 +513,7 @@ theorem dvd_gcd_mul_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k
 #align dvd_gcd_mul_of_dvd_mul dvd_gcd_mul_of_dvd_mul
 
 theorem dvd_mul_gcd_of_dvd_mul [GCDMonoid α] {m n k : α} (H : k ∣ m * n) : k ∣ m * gcd k n := by
-  rw [mul_comm] at H⊢
+  rw [mul_comm] at H ⊢
   exact dvd_gcd_mul_of_dvd_mul H
 #align dvd_mul_gcd_of_dvd_mul dvd_mul_gcd_of_dvd_mul
 
@@ -633,7 +633,7 @@ theorem exists_associated_pow_of_mul_eq_pow [GCDMonoid α] {a b c : α} (hab : I
     exact gcd_zero_right' a
   obtain rfl | hk := k.eq_zero_or_pos
   · use 1
-    rw [pow_zero] at h⊢
+    rw [pow_zero] at h ⊢
     use Units.mkOfMulEqOne _ _ h
     rw [Units.val_mkOfMulEqOne, one_mul]
   have hc : c ∣ a * b := by

550b5853

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -920,13 +920,13 @@ instance uniqueNormalizationMonoidOfUniqueUnits : Unique (NormalizationMonoid α
 instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
   ⟨fun g₁ g₂ => by
     have hgcd : g₁.gcd = g₂.gcd := by
-      ext (a b)
+      ext a b
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _)
       -- Porting note: Lean4 seems to need help specifying `g₁` and `g₂`
       · exact dvd_gcd (@gcd_dvd_left _ _ g₁ _ _) (@gcd_dvd_right _ _ g₁ _ _)
       · exact @dvd_gcd _ _ g₁ _ _ _ (@gcd_dvd_left _ _ g₂ _ _) (@gcd_dvd_right _ _ g₂ _ _)
     have hlcm : g₁.lcm = g₂.lcm := by
-      ext (a b)
+      ext a b
       -- Porting note: Lean4 seems to need help specifying `g₁` and `g₂`
       refine' associated_iff_eq.mp (associated_of_dvd_dvd _ _)
       · exact (@lcm_dvd_iff _ _ g₁ ..).mpr ⟨@dvd_lcm_left _ _ g₂ _ _, @dvd_lcm_right _ _ g₂ _ _⟩

550b5853

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -281,7 +281,7 @@ class GCDMonoid (α : Type _) [CancelCommMonoidWithZero α] where
   gcd_dvd_left : ∀ a b, gcd a b ∣ a
   /-- The GCD is a divisor of the second element. -/
   gcd_dvd_right : ∀ a b, gcd a b ∣ b
-  /-- Tny common divisor of both elements is a divisor of the GCD. -/
+  /-- Any common divisor of both elements is a divisor of the GCD. -/
   dvd_gcd : ∀ {a b c}, a ∣ c → a ∣ b → a ∣ gcd c b
   /-- The product of two elements is `Associated` with the product of their GCD and LCM. -/
   gcd_mul_lcm : ∀ a b, Associated (gcd a b * lcm a b) (a * b)

550b5853

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -730,7 +730,7 @@ theorem lcm_eq_zero_iff [GCDMonoid α] (a b : α) : lcm a b = 0 ↔ a = 0 ∨ b
     (fun h : lcm a b = 0 => by
       have : Associated (a * b) 0 := (gcd_mul_lcm a b).symm.trans <| by rw [h, mul_zero]
       rwa [← mul_eq_zero, ← associated_zero_iff_eq_zero])
-    (by rintro (rfl | rfl) <;> [apply lcm_zero_left, apply lcm_zero_right])
+    (by rintro (rfl | rfl) <;> [apply lcm_zero_left; apply lcm_zero_right])
 #align lcm_eq_zero_iff lcm_eq_zero_iff
 
 -- Porting note: lower priority to avoid linter complaints about simp-normal form

550b5853

feat: add Mathlib.Tactic.Common, and import (#4056)

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

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

a4eaf1c4

Diff

@@ -11,7 +11,6 @@ Authors: Johannes Hölzl, Jens Wagemaker
 import Mathlib.Algebra.Associated
 import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Ring.Regular
-import Mathlib.Tactic.Set
 
 /-!
 # Monoids with normalization functions, `gcd`, and `lcm`

550b5853

chore: bye-bye, solo bys! (#3825)

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

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

14167e48

Diff

@@ -1022,16 +1022,14 @@ def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates
   normUnit_zero := if_pos rfl
   normUnit_mul {a b} ha hb := by
     simp_rw [if_neg (mul_ne_zero ha hb), if_neg ha, if_neg hb, Units.ext_iff, Units.val_mul]
-    suffices
-      a * b * ↑(Classical.choose (associated_map_mk hinv (a * b))) =
+    suffices a * b * ↑(Classical.choose (associated_map_mk hinv (a * b))) =
         a * ↑(Classical.choose (associated_map_mk hinv a)) *
-          (b * ↑(Classical.choose (associated_map_mk hinv b)))
-      by
-        apply mul_left_cancel₀ (mul_ne_zero ha hb) _
-        -- Porting note: original `simpa` fails with `unexpected bound variable #1`
-        -- simpa only [mul_assoc, mul_comm, mul_left_comm] using this
-        rw [this, mul_assoc, ← mul_assoc _ b, mul_comm _ b, ← mul_assoc, ← mul_assoc,
-          mul_assoc (a * b)]
+        (b * ↑(Classical.choose (associated_map_mk hinv b))) by
+      apply mul_left_cancel₀ (mul_ne_zero ha hb) _
+      -- Porting note: original `simpa` fails with `unexpected bound variable #1`
+      -- simpa only [mul_assoc, mul_comm, mul_left_comm] using this
+      rw [this, mul_assoc, ← mul_assoc _ b, mul_comm _ b, ← mul_assoc, ← mul_assoc,
+        mul_assoc (a * b)]
     rw [map_mk_unit_aux hinv a, map_mk_unit_aux hinv (a * b), map_mk_unit_aux hinv b, ←
       MonoidHom.map_mul, Associates.mk_mul_mk]
   normUnit_coe_units u := by

550b5853

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -183,7 +183,6 @@ theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) :
   calc
     a * ↑(normUnit a) = a * ↑(normUnit a) * ↑u * ↑u⁻¹ := (Units.mul_inv_cancel_right _ _).symm
     _ = a * ↑u * ↑(normUnit a) * ↑u⁻¹ := by rw [mul_right_comm a]
-
 #align normalize_eq_normalize normalize_eq_normalize
 
 theorem normalize_eq_normalize_iff {x y : α} : normalize x = normalize y ↔ x ∣ y ∧ y ∣ x :=
@@ -585,7 +584,6 @@ theorem gcd_pow_left_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd (a ^
     gcd (a ^ k) b ∣ gcd b (a ^ k) := (gcd_comm' _ _).dvd
     _ ∣ gcd b a ^ k := gcd_pow_right_dvd_pow_gcd
     _ ∣ gcd a b ^ k := pow_dvd_pow_of_dvd (gcd_comm' _ _).dvd _
-
 #align gcd_pow_left_dvd_pow_gcd gcd_pow_left_dvd_pow_gcd
 
 theorem pow_dvd_of_mul_eq_pow [GCDMonoid α] {a b c d₁ d₂ : α} (ha : a ≠ 0) (hab : IsUnit (gcd a b))

550b5853

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -1107,7 +1107,7 @@ noncomputable def normalizedGCDMonoidOfGCD [NormalizationMonoid α] [DecidableEq
           · apply (a0 _).elim
             rw [← zero_dvd_iff, ← ha]
             exact gcd_dvd_left _ _
-          · convert @normalize_zero α _ _
+          · rw [hl, zero_mul]
         have h1 : gcd a b ≠ 0 := by
           have hab : a * b ≠ 0 := mul_ne_zero a0 hb
           contrapose! hab

550b5853

chore: add missing hypothesis names to by_cases (#2679)

5d07683a

Diff

@@ -704,7 +704,7 @@ end GCD
 section LCM
 
 theorem lcm_dvd_iff [GCDMonoid α] {a b c : α} : lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c := by
-  by_cases a = 0 ∨ b = 0
+  by_cases h : a = 0 ∨ b = 0
   · rcases h with (rfl | rfl) <;>
       simp (config := { contextual := true }) only [iff_def, lcm_zero_left, lcm_zero_right,
         zero_dvd_iff, dvd_zero, eq_self_iff_true, and_true_iff, imp_true_iff]

550b5853

chore: don't inline DivInvMonoid default value for Div, for better instance transparency (#1897)

See Zulip. This will make particular DivInvMonoids whose Div field is constructed using the default value (such as ℝ) behave the same way as generic ones, at the instance transparency level, fixing examples such as the following:

import Mathlib.Data.Real.Basic

variable [LinearOrderedField α]

/- `.reducible` transparency works correctly over `ℝ`. -/
example {a b : ℝ} : a / 2 ≤ b / 2 := by
  with_reducible (apply mul_le_mul) -- fails, as desired

/- `.instance` transparency works correctly over a generic field. -/
example {a b : α} : a / 2 ≤ b / 2 := by
  with_reducible_and_instances (apply mul_le_mul) -- fails, as desired

/- `.instance` transparency does not work correctly over `ℝ`. -/
example {a b : ℝ} : a / 2 ≤ b / 2 := by
  with_reducible_and_instances (apply mul_le_mul) -- succeeds, wanted it not to
  all_goals sorry

eb83c3de

Diff

@@ -102,7 +102,9 @@ theorem normUnit_one : normUnit (1 : α) = 1 :=
 /-- Chooses an element of each associate class, by multiplying by `normUnit` -/
 def normalize : α →*₀ α where
   toFun x := x * normUnit x
-  map_zero' := by simp only [normUnit_zero, Units.val_one, mul_one]
+  map_zero' := by
+    simp only [normUnit_zero]
+    exact mul_one (0:α)
   map_one' := by dsimp only; rw [normUnit_one, one_mul]; rfl
   map_mul' x y :=
     (by_cases fun hx : x = 0 => by dsimp only; rw [hx, zero_mul, zero_mul, zero_mul]) fun hx =>

550b5853

fix: replace symmApply by symm_apply (#2560)

9aade17b

Diff

@@ -970,7 +970,7 @@ def associatesEquivOfUniqueUnits : Associates α ≃* α where
   right_inv _ := (Associates.out_mk _).trans <| normalize_eq _
   map_mul' := Associates.out_mul
 #align associates_equiv_of_unique_units associatesEquivOfUniqueUnits
-#align associates_equiv_of_unique_units_symm_apply associatesEquivOfUniqueUnits_symmApply
+#align associates_equiv_of_unique_units_symm_apply associatesEquivOfUniqueUnits_symm_apply
 #align associates_equiv_of_unique_units_apply associatesEquivOfUniqueUnits_apply
 
 end UniqueUnit

550b5853

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -970,6 +970,8 @@ def associatesEquivOfUniqueUnits : Associates α ≃* α where
   right_inv _ := (Associates.out_mk _).trans <| normalize_eq _
   map_mul' := Associates.out_mul
 #align associates_equiv_of_unique_units associatesEquivOfUniqueUnits
+#align associates_equiv_of_unique_units_symm_apply associatesEquivOfUniqueUnits_symmApply
+#align associates_equiv_of_unique_units_apply associatesEquivOfUniqueUnits_apply
 
 end UniqueUnit

550b5853

chore: format by line breaks with long lines (#1529)

This was done semi-automatically with some regular expressions in vim in contrast to the fully automatic https://github.com/leanprover-community/mathlib4/pull/1523.

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

1050066f

Diff

@@ -171,8 +171,8 @@ theorem normUnit_mul_normUnit (a : α) : normUnit (a * normUnit a) = 1 := by
 theorem normalize_idem (x : α) : normalize (normalize x) = normalize x := by simp
 #align normalize_idem normalize_idem
 
-theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) : normalize a = normalize b :=
-  by
+theorem normalize_eq_normalize {a b : α} (hab : a ∣ b) (hba : b ∣ a) :
+    normalize a = normalize b := by
   nontriviality α
   rcases associated_of_dvd_dvd hab hba with ⟨u, rfl⟩
   refine' by_cases (by rintro rfl; simp only [zero_mul]) fun ha : a ≠ 0 => _
@@ -446,8 +446,8 @@ theorem gcd_mul_left [NormalizedGCDMonoid α] (a b c : α) :
       (dvd_gcd (mul_dvd_mul_left a <| gcd_dvd_left _ _) (mul_dvd_mul_left a <| gcd_dvd_right _ _))
 #align gcd_mul_left gcd_mul_left
 
-theorem gcd_mul_left' [GCDMonoid α] (a b c : α) : Associated (gcd (a * b) (a * c)) (a * gcd b c) :=
-  by
+theorem gcd_mul_left' [GCDMonoid α] (a b c : α) :
+    Associated (gcd (a * b) (a * c)) (a * gcd b c) := by
   obtain rfl | ha := eq_or_ne a 0
   · simp only [zero_mul, gcd_zero_left']
   obtain ⟨d, eq⟩ := dvd_gcd (dvd_mul_right a b) (dvd_mul_right a c)
@@ -561,8 +561,8 @@ theorem gcd_mul_dvd_mul_gcd [GCDMonoid α] (k m n : α) : gcd k (m * n) ∣ gcd
     exact dvd_gcd hn'k hn'
 #align gcd_mul_dvd_mul_gcd gcd_mul_dvd_mul_gcd
 
-theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} : gcd a (b ^ k) ∣ gcd a b ^ k :=
-  by
+theorem gcd_pow_right_dvd_pow_gcd [GCDMonoid α] {a b : α} {k : ℕ} :
+    gcd a (b ^ k) ∣ gcd a b ^ k := by
   by_cases hg : gcd a b = 0
   · rw [gcd_eq_zero_iff] at hg
     rcases hg with ⟨rfl, rfl⟩

550b5853

chore: the style linter shouldn't complain about long #align lines (#1643)

54af0498

Diff

@@ -948,9 +948,7 @@ instance subsingleton_normalizedGCDMonoid_of_unique_units : Subsingleton (Normal
     have := Subsingleton.elim a_norm b_norm
     subst this
     rfl⟩
-#align
-  subsingleton_normalized_gcd_monoid_of_unique_units
-  subsingleton_normalizedGCDMonoid_of_unique_units
+#align subsingleton_normalized_gcd_monoid_of_unique_units subsingleton_normalizedGCDMonoid_of_unique_units
 
 @[simp]
 theorem normUnit_eq_one (x : α) : normUnit x = 1 :=

550b5853

chore: tidy various files (#1412)

0ee6552e

Diff

@@ -212,7 +212,7 @@ variable [CancelCommMonoidWithZero α] [NormalizationMonoid α]
 
 attribute [local instance] Associated.setoid
 
-/-- Maps an element of `associates` back to the normalized element of its associate class -/
+/-- Maps an element of `Associates` back to the normalized element of its associate class -/
 protected def out : Associates α → α :=
   (Quotient.lift (normalize : α → α)) fun a _ ⟨_, hu⟩ =>
     hu ▸ normalize_eq_normalize ⟨_, rfl⟩ (Units.mul_right_dvd.2 <| dvd_refl a)
@@ -395,7 +395,8 @@ theorem gcd_eq_zero_iff [GCDMonoid α] (a b : α) : gcd a b = 0 ↔ a = 0 ∧ b
     (fun h => by
       let ⟨ca, ha⟩ := gcd_dvd_left a b
       let ⟨cb, hb⟩ := gcd_dvd_right a b
-      rw [h, zero_mul] at ha hb; exact ⟨ha, hb⟩)
+      rw [h, zero_mul] at ha hb
+      exact ⟨ha, hb⟩)
     fun ⟨ha, hb⟩ => by
     rw [ha, hb, ← zero_dvd_iff]
     apply dvd_gcd <;> rfl
@@ -821,13 +822,13 @@ theorem lcm_mul_left [NormalizedGCDMonoid α] (a b c : α) :
     fun ha : a ≠ 0 =>
     suffices lcm (a * b) (a * c) = normalize (a * lcm b c) by simpa
     have : a ∣ lcm (a * b) (a * c) := (dvd_mul_right _ _).trans (dvd_lcm_left _ _)
-    let ⟨d, Eq⟩ := this
+    let ⟨d, eq⟩ := this
     lcm_eq_normalize
       (lcm_dvd (mul_dvd_mul_left a (dvd_lcm_left _ _)) (mul_dvd_mul_left a (dvd_lcm_right _ _)))
-      (Eq.symm ▸
+      (eq.symm ▸
         (mul_dvd_mul_left a <|
-          lcm_dvd ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ dvd_lcm_left _ _)
-            ((mul_dvd_mul_iff_left ha).1 <| Eq ▸ dvd_lcm_right _ _)))
+          lcm_dvd ((mul_dvd_mul_iff_left ha).1 <| eq ▸ dvd_lcm_left _ _)
+            ((mul_dvd_mul_iff_left ha).1 <| eq ▸ dvd_lcm_right _ _)))
 #align lcm_mul_left lcm_mul_left
 
 @[simp]
@@ -905,16 +906,14 @@ section UniqueUnit
 variable [CancelCommMonoidWithZero α] [Unique αˣ]
 
 -- see Note [lower instance priority]
-instance (priority := 100) normalizationMonoidOfUniqueUnits :
-    NormalizationMonoid α where
+instance (priority := 100) normalizationMonoidOfUniqueUnits : NormalizationMonoid α where
   normUnit _ := 1
   normUnit_zero := rfl
   normUnit_mul _ _ := (mul_one 1).symm
   normUnit_coe_units _ := Subsingleton.elim _ _
 #align normalization_monoid_of_unique_units normalizationMonoidOfUniqueUnits
 
-instance uniqueNormalizationMonoidOfUniqueUnits :
-    Unique (NormalizationMonoid α) where
+instance uniqueNormalizationMonoidOfUniqueUnits : Unique (NormalizationMonoid α) where
   default := normalizationMonoidOfUniqueUnits
   uniq := fun ⟨u, _, _, _⟩ => by congr; simp
 #align unique_normalization_monoid_of_unique_units uniqueNormalizationMonoidOfUniqueUnits
@@ -939,8 +938,7 @@ instance subsingleton_gcdMonoid_of_unique_units : Subsingleton (GCDMonoid α) :=
     simp only [hgcd, hlcm]⟩
 #align subsingleton_gcd_monoid_of_unique_units subsingleton_gcdMonoid_of_unique_units
 
-instance subsingleton_normalizedGCDMonoid_of_unique_units :
-    Subsingleton (NormalizedGCDMonoid α) :=
+instance subsingleton_normalizedGCDMonoid_of_unique_units : Subsingleton (NormalizedGCDMonoid α) :=
   ⟨by
     intro a b
     cases' a with a_norm a_gcd
@@ -967,8 +965,7 @@ theorem normalize_eq (x : α) : normalize x = x :=
 
 /-- If a monoid's only unit is `1`, then it is isomorphic to its associates. -/
 @[simps]
-def associatesEquivOfUniqueUnits :
-    Associates α ≃* α where
+def associatesEquivOfUniqueUnits : Associates α ≃* α where
   toFun := Associates.out
   invFun := Associates.mk
   left_inv := Associates.mk_out
@@ -984,7 +981,7 @@ variable [CommRing α] [IsDomain α] [NormalizedGCDMonoid α]
 
 theorem gcd_eq_of_dvd_sub_right {a b c : α} (h : a ∣ b - c) : gcd a b = gcd a c := by
   apply dvd_antisymm_of_normalize_eq (normalize_gcd _ _) (normalize_gcd _ _) <;>
-      rw [dvd_gcd_iff] <;>
+    rw [dvd_gcd_iff] <;>
     refine' ⟨gcd_dvd_left _ _, _⟩
   · rcases h with ⟨d, hd⟩
     rcases gcd_dvd_right a b with ⟨e, he⟩
@@ -1023,7 +1020,7 @@ def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates
     if a = 0 then 1
     else Classical.choose (Associates.mk_eq_mk_iff_associated.1 (hinv (Associates.mk a)).symm)
   normUnit_zero := if_pos rfl
-  normUnit_mul := fun {a b} ha hb => by
+  normUnit_mul {a b} ha hb := by
     simp_rw [if_neg (mul_ne_zero ha hb), if_neg ha, if_neg hb, Units.ext_iff, Units.val_mul]
     suffices
       a * b * ↑(Classical.choose (associated_map_mk hinv (a * b))) =
@@ -1363,9 +1360,7 @@ variable (G₀ : Type _) [CommGroupWithZero G₀] [DecidableEq G₀]
 
 -- Porting note: very slow; improve performance?
 -- see Note [lower instance priority]
-instance (priority := 100) :
-    NormalizedGCDMonoid
-      G₀ where
+instance (priority := 100) : NormalizedGCDMonoid G₀ where
   normUnit x := if h : x = 0 then 1 else (Units.mk0 x h)⁻¹
   normUnit_zero := dif_pos rfl
   normUnit_mul := fun {x y} x0 y0 => Units.eq_iff.1 (by

550b5853

chore: deal with some old porting notes (#1405)

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

1a8e98c7

Diff

@@ -1031,10 +1031,10 @@ def normalizationMonoidOfMonoidHomRightInverse [DecidableEq α] (f : Associates
           (b * ↑(Classical.choose (associated_map_mk hinv b)))
       by
         apply mul_left_cancel₀ (mul_ne_zero ha hb) _
+        -- Porting note: original `simpa` fails with `unexpected bound variable #1`
+        -- simpa only [mul_assoc, mul_comm, mul_left_comm] using this
         rw [this, mul_assoc, ← mul_assoc _ b, mul_comm _ b, ← mul_assoc, ← mul_assoc,
           mul_assoc (a * b)]
-        -- Porting note: original `simpa` fails
-        -- simpa only [mul_assoc, mul_comm, mul_left_comm] using this
     rw [map_mk_unit_aux hinv a, map_mk_unit_aux hinv (a * b), map_mk_unit_aux hinv b, ←
       MonoidHom.map_mul, Associates.mk_mul_mk]
   normUnit_coe_units u := by

550b5853

feat: port Algebra.GCDMonoid.Basic (#1135)

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

bfe06a77

`algebra.gcd_monoid.basic` ⟷ `Mathlib.Algebra.GCDMonoid.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

New `simp` tags or `simp` lemmas

New `gcongr` tags

Change explicit args to implicit

Change typeclass assumptions

Use `WithTop` API

Renames

Dependencies 3 + 130

algebra.gcd_monoid.basic ⟷ Mathlib.Algebra.GCDMonoid.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

New simp tags or simp lemmas

New gcongr tags

Change explicit args to implicit

Change typeclass assumptions

Use WithTop API

Renames

Dependencies 3 + 130

`algebra.gcd_monoid.basic` ⟷ `Mathlib.Algebra.GCDMonoid.Basic`

New `simp` tags or `simp` lemmas

New `gcongr` tags

Use `WithTop` API