algebra.associated ⟷ Mathlib.Algebra.Associated

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

@@ -1151,10 +1151,10 @@ theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.
 #align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvd
 -/
 
-#print Associates.mk_le_mk_iff_dvd_iff /-
-theorem mk_le_mk_iff_dvd_iff {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=
+#print Associates.mk_le_mk_iff_dvd /-
+theorem mk_le_mk_iff_dvd {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=
   Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
-#align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd_iff
+#align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd
 -/
 
 #print Associates.mk_dvd_mk /-

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

@@ -71,7 +71,7 @@ theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p 
     have := isUnit_of_dvd_one _ h
     have := not_unit hp
     contradiction
-  rw [pow_succ] at h
+  rw [pow_succ'] at h
   cases' dvd_or_dvd hp h with dvd_a dvd_pow
   · assumption
   exact ih dvd_pow
@@ -135,9 +135,9 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
   induction' n with n ih
   · rw [pow_zero]; exact one_dvd b
   · obtain ⟨c, rfl⟩ := ih (dvd_trans (pow_dvd_pow p n.le_succ) h')
-    rw [pow_succ']
+    rw [pow_succ]
     apply mul_dvd_mul_left _ ((hp.dvd_or_dvd _).resolve_left h)
-    rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ', mul_left_comm]
+    rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ, mul_left_comm]
 #align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_left
 -/
 
@@ -161,7 +161,7 @@ theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWith
   have : a ^ n.succ * x ^ n = p * y :=
     by
     refine' mul_left_cancel₀ (pow_ne_zero n hp.ne_zero) _
-    rw [← mul_assoc _ p, ← pow_succ', ← hy, mul_pow, ← mul_assoc (a ^ n.succ), mul_comm _ (p ^ n),
+    rw [← mul_assoc _ p, ← pow_succ, ← hy, mul_pow, ← mul_assoc (a ^ n.succ), mul_comm _ (p ^ n),
       mul_assoc]
   -- So `p ∣ a` (and we're done) or `p ∣ x`, which can't be the case since it implies `p^2 ∣ b`.
   refine' hp.dvd_of_dvd_pow ((hp.dvd_or_dvd ⟨_, this⟩).resolve_right fun hdvdx => hb _)
@@ -180,7 +180,7 @@ theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x
   induction' i with i ih generalizing x
   · simp only [zero_add, pow_one] at *
     exact (h.dvd_or_dvd hxy).resolve_right hy
-  rw [pow_succ] at hxy ⊢
+  rw [pow_succ'] at hxy ⊢
   obtain ⟨x', rfl⟩ := (h.dvd_or_dvd (dvd_of_mul_right_dvd hxy)).resolve_right hy
   rw [mul_assoc] at hxy
   exact mul_dvd_mul_left p (ih ((mul_dvd_mul_iff_left h.ne_zero).mp hxy))
@@ -263,7 +263,7 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
   · simp only [nat.lt_one_iff.mp hn, IsEmpty.forall_iff, not_irreducible_one, pow_zero]
   intro h
   obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_lt hn
-  rw [pow_succ, add_comm] at h
+  rw [pow_succ', add_comm] at h
   exact (or_iff_left_of_imp is_unit_pow_succ_iff.mp).mp (of_irreducible_mul h)
 #align of_irreducible_pow of_irreducible_pow
 
@@ -413,8 +413,8 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l
   have hp0 : p ^ (k + l) ≠ 0 := pow_ne_zero _ hp.NeZero
   have hpd : p ∣ x * y := ⟨z, by rwa [mul_right_inj' hp0] at h⟩
   (hp.dvd_or_dvd hpd).elim
-    (fun ⟨d, hd⟩ => Or.inl ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩)
-    fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩
+    (fun ⟨d, hd⟩ => Or.inl ⟨d, by simp [*, pow_succ', mul_comm, mul_left_comm, mul_assoc]⟩)
+    fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ', mul_comm, mul_left_comm, mul_assoc]⟩
 #align succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
 -/
 
@@ -651,7 +651,7 @@ theorem Associated.mul_right [CommMonoid α] {a b : α} (h : a ~ᵤ b) (c : α)
 theorem Associated.pow_pow [CommMonoid α] {a b : α} {n : ℕ} (h : a ~ᵤ b) : a ^ n ~ᵤ b ^ n :=
   by
   induction' n with n ih; · simp [h]
-  convert h.mul_mul ih <;> rw [pow_succ]
+  convert h.mul_mul ih <;> rw [pow_succ']
 #align associated.pow_pow Associated.pow_pow
 -/
 
@@ -1038,7 +1038,7 @@ theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInve
 
 #print Associates.mk_pow /-
 theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n := by
-  induction n <;> simp [*, pow_succ, associates.mk_mul_mk.symm]
+  induction n <;> simp [*, pow_succ', associates.mk_mul_mk.symm]
 #align associates.mk_pow Associates.mk_pow
 -/
 
@@ -1473,12 +1473,12 @@ theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n
   induction' n with n ih generalizing q
   · simp [← isUnit_iff_dvd_one, associated_one_iff_isUnit]
   refine' ⟨fun h => _, fun ⟨i, hi, hq⟩ => hq.dvd.trans (pow_dvd_pow p hi)⟩
-  rw [pow_succ] at h
+  rw [pow_succ'] at h
   rcases hp.left_dvd_or_dvd_right_of_dvd_mul h with (⟨q, rfl⟩ | hno)
   · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h
     rcases h with ⟨i, hi, hq⟩
     refine' ⟨i + 1, Nat.succ_le_succ hi, (hq.mul_left p).trans _⟩
-    rw [pow_succ]
+    rw [pow_succ']
   · obtain ⟨i, hi, hq⟩ := ih.mp hno
     exact ⟨i, hi.trans n.le_succ, hq⟩
 #align dvd_prime_pow dvd_prime_pow

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

@@ -67,11 +67,11 @@ theorem dvd_or_dvd (hp : Prime p) {a b : α} (h : p ∣ a * b) : p ∣ a ∨ p 
 theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p ∣ a :=
   by
   induction' n with n ih
-  · rw [pow_zero] at h 
+  · rw [pow_zero] at h
     have := isUnit_of_dvd_one _ h
     have := not_unit hp
     contradiction
-  rw [pow_succ] at h 
+  rw [pow_succ] at h
   cases' dvd_or_dvd hp h with dvd_a dvd_pow
   · assumption
   exact ih dvd_pow
@@ -123,7 +123,7 @@ theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p
   rintro ⟨c, hc⟩
   rcases hp.2.2 a c (hc ▸ dvd_mul_right _ _) with (h | ⟨x, rfl⟩)
   · exact Or.inl h
-  · rw [mul_left_comm, mul_right_inj' hp.ne_zero] at hc 
+  · rw [mul_left_comm, mul_right_inj' hp.ne_zero] at hc
     exact Or.inr (hc.symm ▸ dvd_mul_right _ _)
 #align prime.left_dvd_or_dvd_right_of_dvd_mul Prime.left_dvd_or_dvd_right_of_dvd_mul
 -/
@@ -143,7 +143,7 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
 
 #print Prime.pow_dvd_of_dvd_mul_right /-
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
-    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h' ;
+    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h';
   exact hp.pow_dvd_of_dvd_mul_left n h h'
 #align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_right
 -/
@@ -182,7 +182,7 @@ theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x
     exact (h.dvd_or_dvd hxy).resolve_right hy
   rw [pow_succ] at hxy ⊢
   obtain ⟨x', rfl⟩ := (h.dvd_or_dvd (dvd_of_mul_right_dvd hxy)).resolve_right hy
-  rw [mul_assoc] at hxy 
+  rw [mul_assoc] at hxy
   exact mul_dvd_mul_left p (ih ((mul_dvd_mul_iff_left h.ne_zero).mp hxy))
 #align prime_pow_succ_dvd_mul prime_pow_succ_dvd_mul
 -/
@@ -263,7 +263,7 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
   · simp only [nat.lt_one_iff.mp hn, IsEmpty.forall_iff, not_irreducible_one, pow_zero]
   intro h
   obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_lt hn
-  rw [pow_succ, add_comm] at h 
+  rw [pow_succ, add_comm] at h
   exact (or_iff_left_of_imp is_unit_pow_succ_iff.mp).mp (of_irreducible_mul h)
 #align of_irreducible_pow of_irreducible_pow
 
@@ -275,7 +275,7 @@ theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
   refine' Classical.or_iff_not_imp_right.2 fun H => _
   simp [h, irreducible_iff] at H ⊢
   refine' fun a b h => by_contradiction fun o => _
-  simp [not_or] at o 
+  simp [not_or] at o
   exact H _ o.1 _ o.2 h.symm
 #align irreducible_or_factor irreducible_or_factor
 -/
@@ -348,8 +348,8 @@ theorem irreducible_mul_iff {a b : α} :
   by
   constructor
   · refine' fun h => Or.imp (fun h' => ⟨_, h'⟩) (fun h' => ⟨_, h'⟩) (h.isUnit_or_isUnit rfl).symm
-    · rwa [irreducible_mul_isUnit h'] at h 
-    · rwa [irreducible_isUnit_mul h'] at h 
+    · rwa [irreducible_mul_isUnit h'] at h
+    · rwa [irreducible_isUnit_mul h'] at h
   · rintro (⟨ha, hb⟩ | ⟨hb, ha⟩)
     · rwa [irreducible_mul_isUnit hb]
     · rwa [irreducible_isUnit_mul ha]
@@ -364,7 +364,7 @@ variable [CommMonoid α] {a : α}
 
 #print Irreducible.not_square /-
 theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a := by rintro ⟨b, rfl⟩;
-  simp only [irreducible_mul_iff, or_self_iff] at ha ; exact ha.1.not_unit ha.2
+  simp only [irreducible_mul_iff, or_self_iff] at ha; exact ha.1.not_unit ha.2
 #align irreducible.not_square Irreducible.not_square
 -/
 
@@ -411,7 +411,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l
   have h : p ^ (k + l) * (x * y) = p ^ (k + l) * (p * z) := by
     simpa [mul_comm, pow_add, hx, hy, mul_assoc, mul_left_comm] using hz
   have hp0 : p ^ (k + l) ≠ 0 := pow_ne_zero _ hp.NeZero
-  have hpd : p ∣ x * y := ⟨z, by rwa [mul_right_inj' hp0] at h ⟩
+  have hpd : p ∣ x * y := ⟨z, by rwa [mul_right_inj' hp0] at h⟩
   (hp.dvd_or_dvd hpd).elim
     (fun ⟨d, hd⟩ => Or.inl ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩)
     fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩
@@ -674,7 +674,7 @@ theorem associated_of_dvd_dvd [CancelMonoidWithZero α] {a b : α} (hab : a ∣
   rcases hba with ⟨d, a_eq⟩
   by_cases ha0 : a = 0
   · simp_all
-  have hac0 : a * c ≠ 0 := by intro con; rw [Con, MulZeroClass.zero_mul] at a_eq ; apply ha0 a_eq
+  have hac0 : a * c ≠ 0 := by intro con; rw [Con, MulZeroClass.zero_mul] at a_eq; apply ha0 a_eq
   have : a * (c * d) = a * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
   have hcd : c * d = 1 := mul_left_cancel₀ ha0 this
   have : a * c * (d * c) = a * c * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
@@ -1054,7 +1054,7 @@ theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
     (Quotient.induction_on₂ x y fun a b h =>
       have : a * b ~ᵤ 1 := Quotient.exact h
       ⟨Quotient.sound <| associated_one_of_associated_mul_one this,
-        Quotient.sound <| associated_one_of_associated_mul_one <| by rwa [mul_comm] at this ⟩)
+        Quotient.sound <| associated_one_of_associated_mul_one <| by rwa [mul_comm] at this⟩)
     (by simp (config := { contextual := true }))
 #align associates.mul_eq_one_iff Associates.mul_eq_one_iff
 -/
@@ -1260,7 +1260,7 @@ theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible
   · intro h x y
     refine' Quotient.induction_on₂ x y fun x y a_eq => _
     rcases Quotient.exact a_eq.symm with ⟨u, a_eq⟩
-    rw [mul_assoc] at a_eq 
+    rw [mul_assoc] at a_eq
     show IsUnit (Associates.mk x) ∨ IsUnit (Associates.mk y)
     simpa [is_unit_mk] using h _ _ a_eq.symm
 #align associates.irreducible_mk Associates.irreducible_mk
@@ -1275,10 +1275,10 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
   constructor
   · contrapose!; rw [forall_associated]
     intro h x hx hbax
-    rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax 
+    rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax
     cases' hbax with u hu
     apply h (x * ↑u⁻¹)
-    · rw [is_unit_mk] at hx 
+    · rw [is_unit_mk] at hx
       rw [Associated.isUnit_iff]
       apply hx
       use u
@@ -1337,7 +1337,7 @@ instance : CancelCommMonoidWithZero (Associates α) :=
     hMul_left_cancel_of_ne_zero := by
       rintro ⟨a⟩ ⟨b⟩ ⟨c⟩ ha h
       rcases Quotient.exact' h with ⟨u, hu⟩
-      rw [mul_assoc] at hu 
+      rw [mul_assoc] at hu
       exact Quotient.sound' ⟨u, mul_left_cancel₀ (mk_ne_zero.1 ha) hu⟩ }
 
 #print Associates.le_of_mul_le_mul_left /-
@@ -1358,7 +1358,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
         have : d = 1 := bot_unique this
         simp [this]
     | Or.inr h =>
-      by_cases (fun this : d = 0 => by simp [this] at hp0  <;> contradiction) fun this : d ≠ 0 =>
+      by_cases (fun this : d = 0 => by simp [this] at hp0 <;> contradiction) fun this : d ≠ 0 =>
         have : d * m ≤ d * 1 := by simpa [mul_comm] using h
         Or.inl <| bot_unique <| Associates.le_of_mul_le_mul_left d m 1 ‹d ≠ 0› this
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
@@ -1451,7 +1451,7 @@ theorem DvdNotUnit.ne [CancelCommMonoidWithZero α] {p q : α} (h : DvdNotUnit p
   by_contra hcontra
   obtain ⟨hp, x, hx', hx''⟩ := h
   conv_lhs at hx'' => rw [← hcontra, ← mul_one p]
-  rw [(mul_left_cancel₀ hp hx'').symm] at hx' 
+  rw [(mul_left_cancel₀ hp hx'').symm] at hx'
   exact hx' isUnit_one
 #align dvd_not_unit.ne DvdNotUnit.ne
 -/
@@ -1473,9 +1473,9 @@ theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n
   induction' n with n ih generalizing q
   · simp [← isUnit_iff_dvd_one, associated_one_iff_isUnit]
   refine' ⟨fun h => _, fun ⟨i, hi, hq⟩ => hq.dvd.trans (pow_dvd_pow p hi)⟩
-  rw [pow_succ] at h 
+  rw [pow_succ] at h
   rcases hp.left_dvd_or_dvd_right_of_dvd_mul h with (⟨q, rfl⟩ | hno)
-  · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h 
+  · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h
     rcases h with ⟨i, hi, hq⟩
     refine' ⟨i + 1, Nat.succ_le_succ hi, (hq.mul_left p).trans _⟩
     rw [pow_succ]

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

@@ -256,7 +256,6 @@ theorem of_irreducible_mul {α} [Monoid α] {x y : α} : Irreducible (x * y) →
 #align of_irreducible_mul of_irreducible_mul
 -/
 
-#print of_irreducible_pow /-
 theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
     Irreducible (x ^ n) → IsUnit x :=
   by
@@ -267,7 +266,6 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
   rw [pow_succ, add_comm] at h 
   exact (or_iff_left_of_imp is_unit_pow_succ_iff.mp).mp (of_irreducible_mul h)
 #align of_irreducible_pow of_irreducible_pow
--/
 
 #print irreducible_or_factor /-
 theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
@@ -431,10 +429,10 @@ theorem IsSquare.not_prime (ha : IsSquare a) : ¬Prime a := fun h => h.not_squar
 #align is_square.not_prime IsSquare.not_prime
 -/
 
-#print pow_not_prime /-
-theorem pow_not_prime {n : ℕ} (hn : n ≠ 1) : ¬Prime (a ^ n) := fun hp =>
+#print not_prime_pow /-
+theorem not_prime_pow {n : ℕ} (hn : n ≠ 1) : ¬Prime (a ^ n) := fun hp =>
   hp.not_unit <| IsUnit.pow _ <| of_irreducible_pow hn <| hp.Irreducible
-#align pow_not_prime pow_not_prime
+#align pow_not_prime not_prime_pow
 -/
 
 end CancelCommMonoidWithZero
@@ -1366,7 +1364,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
 -/
 
-instance : CanonicallyOrderedCommMonoid (Associates α) :=
+instance : CanonicallyOrderedAddCommMonoid (Associates α) :=
   { Associates.cancelCommMonoidWithZero, Associates.boundedOrder,
     Associates.orderedCommMonoid with
     exists_hMul_of_le := fun a b => id

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

@@ -175,7 +175,7 @@ theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWith
 theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x y : α} (h : Prime p)
     {i : ℕ} (hxy : p ^ (i + 1) ∣ x * y) : p ^ (i + 1) ∣ x ∨ p ∣ y :=
   by
-  rw [or_iff_not_imp_right]
+  rw [Classical.or_iff_not_imp_right]
   intro hy
   induction' i with i ih generalizing x
   · simp only [zero_add, pow_one] at *
@@ -274,7 +274,7 @@ theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
     Irreducible x ∨ ∃ a b, ¬IsUnit a ∧ ¬IsUnit b ∧ a * b = x :=
   by
   haveI := Classical.dec
-  refine' or_iff_not_imp_right.2 fun H => _
+  refine' Classical.or_iff_not_imp_right.2 fun H => _
   simp [h, irreducible_iff] at H ⊢
   refine' fun a b h => by_contradiction fun o => _
   simp [not_or] at o 

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

@@ -1366,7 +1366,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
 -/
 
-instance : CanonicallyOrderedMonoid (Associates α) :=
+instance : CanonicallyOrderedCommMonoid (Associates α) :=
   { Associates.cancelCommMonoidWithZero, Associates.boundedOrder,
     Associates.orderedCommMonoid with
     exists_hMul_of_le := fun a b => id

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

@@ -734,12 +734,10 @@ protected theorem Associated.prime [CommMonoidWithZero α] {p q : α} (h : p ~
 #align associated.prime Associated.prime
 -/
 
-#print Irreducible.associated_of_dvd /-
 theorem Irreducible.associated_of_dvd [CancelMonoidWithZero α] {p q : α} (p_irr : Irreducible p)
     (q_irr : Irreducible q) (dvd : p ∣ q) : Associated p q :=
   associated_of_dvd_dvd dvd (p_irr.dvd_symm q_irr dvd)
-#align irreducible.associated_of_dvd Irreducible.associated_of_dvd
--/
+#align irreducible.associated_of_dvd Irreducible.associated_of_dvdₓ
 
 #print Irreducible.dvd_irreducible_iff_associated /-
 theorem Irreducible.dvd_irreducible_iff_associated [CancelMonoidWithZero α] {p q : α}
@@ -751,7 +749,7 @@ theorem Irreducible.dvd_irreducible_iff_associated [CancelMonoidWithZero α] {p
 #print Prime.associated_of_dvd /-
 theorem Prime.associated_of_dvd [CancelCommMonoidWithZero α] {p q : α} (p_prime : Prime p)
     (q_prime : Prime q) (dvd : p ∣ q) : Associated p q :=
-  p_prime.Irreducible.associated_of_dvd q_prime.Irreducible dvd
+  p_prime.Irreducible.associated_of_dvdₓ q_prime.Irreducible dvd
 #align prime.associated_of_dvd Prime.associated_of_dvd
 -/
 

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

@@ -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.Divisibility.Basic
-import Mathbin.Algebra.GroupPower.Lemmas
-import Mathbin.Algebra.Parity
+import Algebra.Divisibility.Basic
+import Algebra.GroupPower.Lemmas
+import Algebra.Parity
 
 #align_import algebra.associated from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 

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

@@ -1338,7 +1338,7 @@ instance : NoZeroDivisors (Associates α) :=
 
 instance : CancelCommMonoidWithZero (Associates α) :=
   { (inferInstance : CommMonoidWithZero (Associates α)) with
-    mul_left_cancel_of_ne_zero := by
+    hMul_left_cancel_of_ne_zero := by
       rintro ⟨a⟩ ⟨b⟩ ⟨c⟩ ha h
       rcases Quotient.exact' h with ⟨u, hu⟩
       rw [mul_assoc] at hu 
@@ -1371,7 +1371,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
 instance : CanonicallyOrderedMonoid (Associates α) :=
   { Associates.cancelCommMonoidWithZero, Associates.boundedOrder,
     Associates.orderedCommMonoid with
-    exists_mul_of_le := fun a b => id
+    exists_hMul_of_le := fun a b => id
     le_self_mul := fun a b => ⟨b, rfl⟩ }
 
 #print Associates.dvdNotUnit_iff_lt /-

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

@@ -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.associated
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Divisibility.Basic
 import Mathbin.Algebra.GroupPower.Lemmas
 import Mathbin.Algebra.Parity
 
+#align_import algebra.associated from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Associated, prime, and irreducible elements.
 

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

@@ -37,11 +37,11 @@ namespace Prime
 
 variable {p : α} (hp : Prime p)
 
-include hp
-
+#print Prime.ne_zero /-
 theorem ne_zero : p ≠ 0 :=
   hp.1
 #align prime.ne_zero Prime.ne_zero
+-/
 
 #print Prime.not_unit /-
 theorem not_unit : ¬IsUnit p :=
@@ -49,16 +49,22 @@ theorem not_unit : ¬IsUnit p :=
 #align prime.not_unit Prime.not_unit
 -/
 
+#print Prime.not_dvd_one /-
 theorem not_dvd_one : ¬p ∣ 1 :=
   mt (isUnit_of_dvd_one _) hp.not_unit
 #align prime.not_dvd_one Prime.not_dvd_one
+-/
 
+#print Prime.ne_one /-
 theorem ne_one : p ≠ 1 := fun h => hp.2.1 (h.symm ▸ isUnit_one)
 #align prime.ne_one Prime.ne_one
+-/
 
+#print Prime.dvd_or_dvd /-
 theorem dvd_or_dvd (hp : Prime p) {a b : α} (h : p ∣ a * b) : p ∣ a ∨ p ∣ b :=
   hp.2.2 a b h
 #align prime.dvd_or_dvd Prime.dvd_or_dvd
+-/
 
 #print Prime.dvd_of_dvd_pow /-
 theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p ∣ a :=
@@ -77,34 +83,43 @@ theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p 
 
 end Prime
 
+#print not_prime_zero /-
 @[simp]
 theorem not_prime_zero : ¬Prime (0 : α) := fun h => h.NeZero rfl
 #align not_prime_zero not_prime_zero
+-/
 
+#print not_prime_one /-
 @[simp]
 theorem not_prime_one : ¬Prime (1 : α) := fun h => h.not_unit isUnit_one
 #align not_prime_one not_prime_one
+-/
 
 section Map
 
 variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomClass F α β]
   [MulHomClass G β α] (f : F) (g : G) {p : α}
 
+#print comap_prime /-
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
     refine' (hp.2.2 (f a) (f b) <| by convert map_dvd f h; simp).imp _ _ <;>
       · intro h; convert ← map_dvd g h <;> apply hinv⟩
 #align comap_prime comap_prime
+-/
 
+#print MulEquiv.prime_iff /-
 theorem MulEquiv.prime_iff (e : α ≃* β) : Prime p ↔ Prime (e p) :=
   ⟨fun h => (comap_prime e.symm e fun a => by simp) <| (e.symm_apply_apply p).substr h,
     comap_prime e e.symm fun a => by simp⟩
 #align mul_equiv.prime_iff MulEquiv.prime_iff
+-/
 
 end Map
 
 end Prime
 
+#print Prime.left_dvd_or_dvd_right_of_dvd_mul /-
 theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p : α} (hp : Prime p)
     {a b : α} : a ∣ p * b → p ∣ a ∨ a ∣ b :=
   by
@@ -114,7 +129,9 @@ theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p
   · rw [mul_left_comm, mul_right_inj' hp.ne_zero] at hc 
     exact Or.inr (hc.symm ▸ dvd_mul_right _ _)
 #align prime.left_dvd_or_dvd_right_of_dvd_mul Prime.left_dvd_or_dvd_right_of_dvd_mul
+-/
 
+#print Prime.pow_dvd_of_dvd_mul_left /-
 theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
     (n : ℕ) (h : ¬p ∣ a) (h' : p ^ n ∣ a * b) : p ^ n ∣ b :=
   by
@@ -125,12 +142,16 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
     apply mul_dvd_mul_left _ ((hp.dvd_or_dvd _).resolve_left h)
     rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ', mul_left_comm]
 #align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_left
+-/
 
+#print Prime.pow_dvd_of_dvd_mul_right /-
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
     (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h' ;
   exact hp.pow_dvd_of_dvd_mul_left n h h'
 #align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_right
+-/
 
+#print Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd /-
 theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWithZero α] {p a b : α}
     {n : ℕ} (hp : Prime p) (hpow : p ^ n.succ ∣ a ^ n.succ * b ^ n) (hb : ¬p ^ 2 ∣ b) : p ∣ a :=
   by
@@ -151,7 +172,9 @@ theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWith
   rw [pow_two, ← mul_assoc]
   exact dvd_mul_right _ _
 #align prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd
+-/
 
+#print prime_pow_succ_dvd_mul /-
 theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x y : α} (h : Prime p)
     {i : ℕ} (hxy : p ^ (i + 1) ∣ x * y) : p ^ (i + 1) ∣ x ∨ p ∣ y :=
   by
@@ -165,6 +188,7 @@ theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x
   rw [mul_assoc] at hxy 
   exact mul_dvd_mul_left p (ih ((mul_dvd_mul_iff_left h.ne_zero).mp hxy))
 #align prime_pow_succ_dvd_mul prime_pow_succ_dvd_mul
+-/
 
 #print Irreducible /-
 /-- `irreducible p` states that `p` is non-unit and only factors into units.
@@ -180,44 +204,60 @@ structure Irreducible [Monoid α] (p : α) : Prop where
 
 namespace Irreducible
 
+#print Irreducible.not_dvd_one /-
 theorem not_dvd_one [CommMonoid α] {p : α} (hp : Irreducible p) : ¬p ∣ 1 :=
   mt (isUnit_of_dvd_one _) hp.not_unit
 #align irreducible.not_dvd_one Irreducible.not_dvd_one
+-/
 
+#print Irreducible.isUnit_or_isUnit /-
 theorem isUnit_or_isUnit [Monoid α] {p : α} (hp : Irreducible p) {a b : α} (h : p = a * b) :
     IsUnit a ∨ IsUnit b :=
   hp.isUnit_or_is_unit' a b h
 #align irreducible.is_unit_or_is_unit Irreducible.isUnit_or_isUnit
+-/
 
 end Irreducible
 
+#print irreducible_iff /-
 theorem irreducible_iff [Monoid α] {p : α} :
     Irreducible p ↔ ¬IsUnit p ∧ ∀ a b, p = a * b → IsUnit a ∨ IsUnit b :=
   ⟨fun h => ⟨h.1, h.2⟩, fun h => ⟨h.1, h.2⟩⟩
 #align irreducible_iff irreducible_iff
+-/
 
+#print not_irreducible_one /-
 @[simp]
 theorem not_irreducible_one [Monoid α] : ¬Irreducible (1 : α) := by simp [irreducible_iff]
 #align not_irreducible_one not_irreducible_one
+-/
 
+#print Irreducible.ne_one /-
 theorem Irreducible.ne_one [Monoid α] : ∀ {p : α}, Irreducible p → p ≠ 1
   | _, hp, rfl => not_irreducible_one hp
 #align irreducible.ne_one Irreducible.ne_one
+-/
 
+#print not_irreducible_zero /-
 @[simp]
 theorem not_irreducible_zero [MonoidWithZero α] : ¬Irreducible (0 : α)
   | ⟨hn0, h⟩ =>
     have : IsUnit (0 : α) ∨ IsUnit (0 : α) := h 0 0 (MulZeroClass.mul_zero 0).symm
     this.elim hn0 hn0
 #align not_irreducible_zero not_irreducible_zero
+-/
 
+#print Irreducible.ne_zero /-
 theorem Irreducible.ne_zero [MonoidWithZero α] : ∀ {p : α}, Irreducible p → p ≠ 0
   | _, hp, rfl => not_irreducible_zero hp
 #align irreducible.ne_zero Irreducible.ne_zero
+-/
 
+#print of_irreducible_mul /-
 theorem of_irreducible_mul {α} [Monoid α] {x y : α} : Irreducible (x * y) → IsUnit x ∨ IsUnit y
   | ⟨_, h⟩ => h _ _ rfl
 #align of_irreducible_mul of_irreducible_mul
+-/
 
 #print of_irreducible_pow /-
 theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
@@ -232,6 +272,7 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
 #align of_irreducible_pow of_irreducible_pow
 -/
 
+#print irreducible_or_factor /-
 theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
     Irreducible x ∨ ∃ a b, ¬IsUnit a ∧ ¬IsUnit b ∧ a * b = x :=
   by
@@ -242,6 +283,7 @@ theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
   simp [not_or] at o 
   exact H _ o.1 _ o.2 h.symm
 #align irreducible_or_factor irreducible_or_factor
+-/
 
 #print Irreducible.dvd_symm /-
 /-- If `p` and `q` are irreducible, then `p ∣ q` implies `q ∣ p`. -/
@@ -263,6 +305,7 @@ section
 
 variable [Monoid α]
 
+#print irreducible_units_mul /-
 theorem irreducible_units_mul (a : αˣ) (b : α) : Irreducible (↑a * b) ↔ Irreducible b :=
   by
   simp only [irreducible_iff, Units.isUnit_units_mul, and_congr_right_iff]
@@ -274,12 +317,16 @@ theorem irreducible_units_mul (a : αˣ) (b : α) : Irreducible (↑a * b) ↔ I
     apply h
     rw [mul_assoc, ← HAB, Units.inv_mul_cancel_left]
 #align irreducible_units_mul irreducible_units_mul
+-/
 
+#print irreducible_isUnit_mul /-
 theorem irreducible_isUnit_mul {a b : α} (h : IsUnit a) : Irreducible (a * b) ↔ Irreducible b :=
   let ⟨a, ha⟩ := h
   ha ▸ irreducible_units_mul a b
 #align irreducible_is_unit_mul irreducible_isUnit_mul
+-/
 
+#print irreducible_mul_units /-
 theorem irreducible_mul_units (a : αˣ) (b : α) : Irreducible (b * ↑a) ↔ Irreducible b :=
   by
   simp only [irreducible_iff, Units.isUnit_mul_units, and_congr_right_iff]
@@ -291,12 +338,16 @@ theorem irreducible_mul_units (a : αˣ) (b : α) : Irreducible (b * ↑a) ↔ I
     apply h
     rw [← mul_assoc, ← HAB, Units.mul_inv_cancel_right]
 #align irreducible_mul_units irreducible_mul_units
+-/
 
+#print irreducible_mul_isUnit /-
 theorem irreducible_mul_isUnit {a b : α} (h : IsUnit a) : Irreducible (b * a) ↔ Irreducible b :=
   let ⟨a, ha⟩ := h
   ha ▸ irreducible_mul_units a b
 #align irreducible_mul_is_unit irreducible_mul_isUnit
+-/
 
+#print irreducible_mul_iff /-
 theorem irreducible_mul_iff {a b : α} :
     Irreducible (a * b) ↔ Irreducible a ∧ IsUnit b ∨ Irreducible b ∧ IsUnit a :=
   by
@@ -308,6 +359,7 @@ theorem irreducible_mul_iff {a b : α} :
     · rwa [irreducible_mul_isUnit hb]
     · rwa [irreducible_isUnit_mul ha]
 #align irreducible_mul_iff irreducible_mul_iff
+-/
 
 end
 
@@ -315,12 +367,16 @@ section CommMonoid
 
 variable [CommMonoid α] {a : α}
 
+#print Irreducible.not_square /-
 theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a := by rintro ⟨b, rfl⟩;
   simp only [irreducible_mul_iff, or_self_iff] at ha ; exact ha.1.not_unit ha.2
 #align irreducible.not_square Irreducible.not_square
+-/
 
+#print IsSquare.not_irreducible /-
 theorem IsSquare.not_irreducible (ha : IsSquare a) : ¬Irreducible a := fun h => h.not_square ha
 #align is_square.not_irreducible IsSquare.not_irreducible
+-/
 
 end CommMonoid
 
@@ -353,6 +409,7 @@ protected theorem Prime.irreducible (hp : Prime p) : Irreducible p :=
 #align prime.irreducible Prime.irreducible
 -/
 
+#print succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul /-
 theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l : ℕ} :
     p ^ k ∣ a → p ^ l ∣ b → p ^ (k + l + 1) ∣ a * b → p ^ (k + 1) ∣ a ∨ p ^ (l + 1) ∣ b :=
   fun ⟨x, hx⟩ ⟨y, hy⟩ ⟨z, hz⟩ =>
@@ -364,13 +421,18 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l
     (fun ⟨d, hd⟩ => Or.inl ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩)
     fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩
 #align succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
+-/
 
+#print Prime.not_square /-
 theorem Prime.not_square (hp : Prime p) : ¬IsSquare p :=
   hp.Irreducible.not_square
 #align prime.not_square Prime.not_square
+-/
 
+#print IsSquare.not_prime /-
 theorem IsSquare.not_prime (ha : IsSquare a) : ¬Prime a := fun h => h.not_square ha
 #align is_square.not_prime IsSquare.not_prime
+-/
 
 #print pow_not_prime /-
 theorem pow_not_prime {n : ℕ} (hn : n ≠ 1) : ¬Prime (a ^ n) := fun hp =>
@@ -388,7 +450,6 @@ def Associated [Monoid α] (x y : α) : Prop :=
 #align associated Associated
 -/
 
--- mathport name: «expr ~ᵤ »
 local infixl:50 " ~ᵤ " => Associated
 
 namespace Associated
@@ -442,10 +503,13 @@ end Associated
 
 attribute [local instance] Associated.setoid
 
+#print unit_associated_one /-
 theorem unit_associated_one [Monoid α] {u : αˣ} : (u : α) ~ᵤ 1 :=
   ⟨u⁻¹, Units.mul_inv u⟩
 #align unit_associated_one unit_associated_one
+-/
 
+#print associated_one_iff_isUnit /-
 theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsUnit a :=
   Iff.intro
     (fun h =>
@@ -453,7 +517,9 @@ theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsU
       h ▸ ⟨c, (one_mul _).symm⟩)
     fun ⟨c, h⟩ => Associated.symm ⟨c, by simp [h]⟩
 #align associated_one_iff_is_unit associated_one_iff_isUnit
+-/
 
+#print associated_zero_iff_eq_zero /-
 theorem associated_zero_iff_eq_zero [MonoidWithZero α] (a : α) : a ~ᵤ 0 ↔ a = 0 :=
   Iff.intro
     (fun h => by
@@ -461,95 +527,130 @@ theorem associated_zero_iff_eq_zero [MonoidWithZero α] (a : α) : a ~ᵤ 0 ↔
       simpa using h.symm)
     fun h => h ▸ Associated.refl a
 #align associated_zero_iff_eq_zero associated_zero_iff_eq_zero
+-/
 
+#print associated_one_of_mul_eq_one /-
 theorem associated_one_of_mul_eq_one [CommMonoid α] {a : α} (b : α) (hab : a * b = 1) : a ~ᵤ 1 :=
   show (Units.mkOfMulEqOne a b hab : α) ~ᵤ 1 from unit_associated_one
 #align associated_one_of_mul_eq_one associated_one_of_mul_eq_one
+-/
 
+#print associated_one_of_associated_mul_one /-
 theorem associated_one_of_associated_mul_one [CommMonoid α] {a b : α} : a * b ~ᵤ 1 → a ~ᵤ 1
   | ⟨u, h⟩ => associated_one_of_mul_eq_one (b * u) <| by simpa [mul_assoc] using h
 #align associated_one_of_associated_mul_one associated_one_of_associated_mul_one
+-/
 
+#print associated_mul_unit_left /-
 theorem associated_mul_unit_left {β : Type _} [Monoid β] (a u : β) (hu : IsUnit u) :
     Associated (a * u) a :=
   let ⟨u', hu⟩ := hu
   ⟨u'⁻¹, hu ▸ Units.mul_inv_cancel_right _ _⟩
 #align associated_mul_unit_left associated_mul_unit_left
+-/
 
+#print associated_unit_mul_left /-
 theorem associated_unit_mul_left {β : Type _} [CommMonoid β] (a u : β) (hu : IsUnit u) :
     Associated (u * a) a := by
   rw [mul_comm]
   exact associated_mul_unit_left _ _ hu
 #align associated_unit_mul_left associated_unit_mul_left
+-/
 
+#print associated_mul_unit_right /-
 theorem associated_mul_unit_right {β : Type _} [Monoid β] (a u : β) (hu : IsUnit u) :
     Associated a (a * u) :=
   (associated_mul_unit_left a u hu).symm
 #align associated_mul_unit_right associated_mul_unit_right
+-/
 
+#print associated_unit_mul_right /-
 theorem associated_unit_mul_right {β : Type _} [CommMonoid β] (a u : β) (hu : IsUnit u) :
     Associated a (u * a) :=
   (associated_unit_mul_left a u hu).symm
 #align associated_unit_mul_right associated_unit_mul_right
+-/
 
+#print associated_mul_isUnit_left_iff /-
 theorem associated_mul_isUnit_left_iff {β : Type _} [Monoid β] {a u b : β} (hu : IsUnit u) :
     Associated (a * u) b ↔ Associated a b :=
   ⟨trans (associated_mul_unit_right _ _ hu), trans (associated_mul_unit_left _ _ hu)⟩
 #align associated_mul_is_unit_left_iff associated_mul_isUnit_left_iff
+-/
 
+#print associated_isUnit_mul_left_iff /-
 theorem associated_isUnit_mul_left_iff {β : Type _} [CommMonoid β] {u a b : β} (hu : IsUnit u) :
     Associated (u * a) b ↔ Associated a b :=
   by
   rw [mul_comm]
   exact associated_mul_isUnit_left_iff hu
 #align associated_is_unit_mul_left_iff associated_isUnit_mul_left_iff
+-/
 
+#print associated_mul_isUnit_right_iff /-
 theorem associated_mul_isUnit_right_iff {β : Type _} [Monoid β] {a b u : β} (hu : IsUnit u) :
     Associated a (b * u) ↔ Associated a b :=
   Associated.comm.trans <| (associated_mul_isUnit_left_iff hu).trans Associated.comm
 #align associated_mul_is_unit_right_iff associated_mul_isUnit_right_iff
+-/
 
+#print associated_isUnit_mul_right_iff /-
 theorem associated_isUnit_mul_right_iff {β : Type _} [CommMonoid β] {a u b : β} (hu : IsUnit u) :
     Associated a (u * b) ↔ Associated a b :=
   Associated.comm.trans <| (associated_isUnit_mul_left_iff hu).trans Associated.comm
 #align associated_is_unit_mul_right_iff associated_isUnit_mul_right_iff
+-/
 
+#print associated_mul_unit_left_iff /-
 @[simp]
 theorem associated_mul_unit_left_iff {β : Type _} [Monoid β] {a b : β} {u : Units β} :
     Associated (a * u) b ↔ Associated a b :=
   associated_mul_isUnit_left_iff u.IsUnit
 #align associated_mul_unit_left_iff associated_mul_unit_left_iff
+-/
 
+#print associated_unit_mul_left_iff /-
 @[simp]
 theorem associated_unit_mul_left_iff {β : Type _} [CommMonoid β] {a b : β} {u : Units β} :
     Associated (↑u * a) b ↔ Associated a b :=
   associated_isUnit_mul_left_iff u.IsUnit
 #align associated_unit_mul_left_iff associated_unit_mul_left_iff
+-/
 
+#print associated_mul_unit_right_iff /-
 @[simp]
 theorem associated_mul_unit_right_iff {β : Type _} [Monoid β] {a b : β} {u : Units β} :
     Associated a (b * u) ↔ Associated a b :=
   associated_mul_isUnit_right_iff u.IsUnit
 #align associated_mul_unit_right_iff associated_mul_unit_right_iff
+-/
 
+#print associated_unit_mul_right_iff /-
 @[simp]
 theorem associated_unit_mul_right_iff {β : Type _} [CommMonoid β] {a b : β} {u : Units β} :
     Associated a (↑u * b) ↔ Associated a b :=
   associated_isUnit_mul_right_iff u.IsUnit
 #align associated_unit_mul_right_iff associated_unit_mul_right_iff
+-/
 
+#print Associated.mul_mul /-
 theorem Associated.mul_mul [CommMonoid α] {a₁ a₂ b₁ b₂ : α} :
     a₁ ~ᵤ b₁ → a₂ ~ᵤ b₂ → a₁ * a₂ ~ᵤ b₁ * b₂
   | ⟨c₁, h₁⟩, ⟨c₂, h₂⟩ => ⟨c₁ * c₂, by simp [h₁.symm, h₂.symm, mul_assoc, mul_comm, mul_left_comm]⟩
 #align associated.mul_mul Associated.mul_mul
+-/
 
+#print Associated.mul_left /-
 theorem Associated.mul_left [CommMonoid α] (a : α) {b c : α} (h : b ~ᵤ c) : a * b ~ᵤ a * c :=
   (Associated.refl a).mul_mul h
 #align associated.mul_left Associated.mul_left
+-/
 
+#print Associated.mul_right /-
 theorem Associated.mul_right [CommMonoid α] {a b : α} (h : a ~ᵤ b) (c : α) : a * c ~ᵤ b * c :=
   h.mul_mul (Associated.refl c)
 #align associated.mul_right Associated.mul_right
+-/
 
 #print Associated.pow_pow /-
 theorem Associated.pow_pow [CommMonoid α] {a b : α} {n : ℕ} (h : a ~ᵤ b) : a ^ n ~ᵤ b ^ n :=
@@ -610,6 +711,7 @@ theorem Associated.dvd_iff_dvd_right [Monoid α] {a b c : α} (h : b ~ᵤ c) : a
 #align associated.dvd_iff_dvd_right Associated.dvd_iff_dvd_right
 -/
 
+#print Associated.eq_zero_iff /-
 theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a = 0 ↔ b = 0 :=
   ⟨fun ha => by
     let ⟨u, hu⟩ := h
@@ -617,10 +719,13 @@ theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a
     let ⟨u, hu⟩ := h.symm
     simp [hu.symm, hb]⟩
 #align associated.eq_zero_iff Associated.eq_zero_iff
+-/
 
+#print Associated.ne_zero_iff /-
 theorem Associated.ne_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a ≠ 0 ↔ b ≠ 0 :=
   not_congr h.eq_zero_iff
 #align associated.ne_zero_iff Associated.ne_zero_iff
+-/
 
 #print Associated.prime /-
 protected theorem Associated.prime [CommMonoidWithZero α] {p q : α} (h : p ~ᵤ q) (hp : Prime p) :
@@ -700,6 +805,7 @@ protected theorem Associated.irreducible_iff [Monoid α] {p q : α} (h : p ~ᵤ
 #align associated.irreducible_iff Associated.irreducible_iff
 -/
 
+#print Associated.of_mul_left /-
 theorem Associated.of_mul_left [CancelCommMonoidWithZero α] {a b c d : α} (h : a * b ~ᵤ c * d)
     (h₁ : a ~ᵤ c) (ha : a ≠ 0) : b ~ᵤ d :=
   let ⟨u, hu⟩ := h
@@ -710,11 +816,14 @@ theorem Associated.of_mul_left [CancelCommMonoidWithZero α] {a b c d : α} (h :
         rw [← hv, mul_assoc c (v : α) d, mul_left_comm c, ← hu]
         simp [hv.symm, mul_assoc, mul_comm, mul_left_comm])⟩
 #align associated.of_mul_left Associated.of_mul_left
+-/
 
+#print Associated.of_mul_right /-
 theorem Associated.of_mul_right [CancelCommMonoidWithZero α] {a b c d : α} :
     a * b ~ᵤ c * d → b ~ᵤ d → b ≠ 0 → a ~ᵤ c := by
   rw [mul_comm a, mul_comm c] <;> exact Associated.of_mul_left
 #align associated.of_mul_right Associated.of_mul_right
+-/
 
 #print Associated.of_pow_associated_of_prime /-
 theorem Associated.of_pow_associated_of_prime [CancelCommMonoidWithZero α] {p₁ p₂ : α} {k₁ k₂ : ℕ}
@@ -739,9 +848,11 @@ section UniqueUnits
 
 variable [Monoid α] [Unique αˣ]
 
+#print units_eq_one /-
 theorem units_eq_one (u : αˣ) : u = 1 :=
   Subsingleton.elim u 1
 #align units_eq_one units_eq_one
+-/
 
 #print associated_iff_eq /-
 theorem associated_iff_eq {x y : α} : x ~ᵤ y ↔ x = y :=
@@ -843,21 +954,27 @@ theorem mk_surjective [Monoid α] : Function.Surjective (@Associates.mk α _) :=
 instance [Monoid α] : One (Associates α) :=
   ⟨⟦1⟧⟩
 
+#print Associates.mk_one /-
 @[simp]
 theorem mk_one [Monoid α] : Associates.mk (1 : α) = 1 :=
   rfl
 #align associates.mk_one Associates.mk_one
+-/
 
+#print Associates.one_eq_mk_one /-
 theorem one_eq_mk_one [Monoid α] : (1 : Associates α) = Associates.mk 1 :=
   rfl
 #align associates.one_eq_mk_one Associates.one_eq_mk_one
+-/
 
 instance [Monoid α] : Bot (Associates α) :=
   ⟨1⟩
 
+#print Associates.bot_eq_one /-
 theorem bot_eq_one [Monoid α] : (⊥ : Associates α) = 1 :=
   rfl
 #align associates.bot_eq_one Associates.bot_eq_one
+-/
 
 #print Associates.exists_rep /-
 theorem exists_rep [Monoid α] (a : Associates α) : ∃ a0 : α, Associates.mk a0 = a :=
@@ -885,9 +1002,11 @@ instance : Mul (Associates α) :=
     Quotient.liftOn₂ a' b' (fun a b => ⟦a * b⟧) fun a₁ a₂ b₁ b₂ ⟨c₁, h₁⟩ ⟨c₂, h₂⟩ =>
       Quotient.sound <| ⟨c₁ * c₂, by simp [h₁.symm, h₂.symm, mul_assoc, mul_comm, mul_left_comm]⟩⟩
 
+#print Associates.mk_mul_mk /-
 theorem mk_mul_mk {x y : α} : Associates.mk x * Associates.mk y = Associates.mk (x * y) :=
   rfl
 #align associates.mk_mul_mk Associates.mk_mul_mk
+-/
 
 instance : CommMonoid (Associates α) where
   one := 1
@@ -903,29 +1022,40 @@ instance : Preorder (Associates α) where
   le_refl := dvd_refl
   le_trans a b c := dvd_trans
 
+#print Associates.mkMonoidHom /-
 /-- `associates.mk` as a `monoid_hom`. -/
 protected def mkMonoidHom : α →* Associates α :=
   ⟨Associates.mk, mk_one, fun x y => mk_mul_mk⟩
 #align associates.mk_monoid_hom Associates.mkMonoidHom
+-/
 
+#print Associates.mkMonoidHom_apply /-
 @[simp]
 theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a :=
   rfl
 #align associates.mk_monoid_hom_apply Associates.mkMonoidHom_apply
+-/
 
+#print Associates.associated_map_mk /-
 theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInverse f Associates.mk)
     (a : α) : a ~ᵤ f (Associates.mk a) :=
   Associates.mk_eq_mk_iff_associated.1 (hinv (Associates.mk a)).symm
 #align associates.associated_map_mk Associates.associated_map_mk
+-/
 
+#print Associates.mk_pow /-
 theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n := by
   induction n <;> simp [*, pow_succ, associates.mk_mul_mk.symm]
 #align associates.mk_pow Associates.mk_pow
+-/
 
+#print Associates.dvd_eq_le /-
 theorem dvd_eq_le : ((· ∣ ·) : Associates α → Associates α → Prop) = (· ≤ ·) :=
   rfl
 #align associates.dvd_eq_le Associates.dvd_eq_le
+-/
 
+#print Associates.mul_eq_one_iff /-
 theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
   Iff.intro
     (Quotient.induction_on₂ x y fun a b h =>
@@ -934,53 +1064,74 @@ theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
         Quotient.sound <| associated_one_of_associated_mul_one <| by rwa [mul_comm] at this ⟩)
     (by simp (config := { contextual := true }))
 #align associates.mul_eq_one_iff Associates.mul_eq_one_iff
+-/
 
+#print Associates.units_eq_one /-
 theorem units_eq_one (u : (Associates α)ˣ) : u = 1 :=
   Units.ext (mul_eq_one_iff.1 u.val_inv).1
 #align associates.units_eq_one Associates.units_eq_one
+-/
 
+#print Associates.uniqueUnits /-
 instance uniqueUnits : Unique (Associates α)ˣ
     where
   default := 1
   uniq := Associates.units_eq_one
 #align associates.unique_units Associates.uniqueUnits
+-/
 
+#print Associates.coe_unit_eq_one /-
 theorem coe_unit_eq_one (u : (Associates α)ˣ) : (u : Associates α) = 1 := by simp
 #align associates.coe_unit_eq_one Associates.coe_unit_eq_one
+-/
 
+#print Associates.isUnit_iff_eq_one /-
 theorem isUnit_iff_eq_one (a : Associates α) : IsUnit a ↔ a = 1 :=
   Iff.intro (fun ⟨u, h⟩ => h ▸ coe_unit_eq_one _) fun h => h.symm ▸ isUnit_one
 #align associates.is_unit_iff_eq_one Associates.isUnit_iff_eq_one
+-/
 
+#print Associates.isUnit_iff_eq_bot /-
 theorem isUnit_iff_eq_bot {a : Associates α} : IsUnit a ↔ a = ⊥ := by
   rw [Associates.isUnit_iff_eq_one, bot_eq_one]
 #align associates.is_unit_iff_eq_bot Associates.isUnit_iff_eq_bot
+-/
 
+#print Associates.isUnit_mk /-
 theorem isUnit_mk {a : α} : IsUnit (Associates.mk a) ↔ IsUnit a :=
   calc
     IsUnit (Associates.mk a) ↔ a ~ᵤ 1 := by
       rw [is_unit_iff_eq_one, one_eq_mk_one, mk_eq_mk_iff_associated]
     _ ↔ IsUnit a := associated_one_iff_isUnit
 #align associates.is_unit_mk Associates.isUnit_mk
+-/
 
 section Order
 
+#print Associates.mul_mono /-
 theorem mul_mono {a b c d : Associates α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a * c ≤ b * d :=
   let ⟨x, hx⟩ := h₁
   let ⟨y, hy⟩ := h₂
   ⟨x * y, by simp [hx, hy, mul_comm, mul_assoc, mul_left_comm]⟩
 #align associates.mul_mono Associates.mul_mono
+-/
 
+#print Associates.one_le /-
 theorem one_le {a : Associates α} : 1 ≤ a :=
   Dvd.intro _ (one_mul a)
 #align associates.one_le Associates.one_le
+-/
 
+#print Associates.le_mul_right /-
 theorem le_mul_right {a b : Associates α} : a ≤ a * b :=
   ⟨b, rfl⟩
 #align associates.le_mul_right Associates.le_mul_right
+-/
 
+#print Associates.le_mul_left /-
 theorem le_mul_left {a b : Associates α} : a ≤ b * a := by rw [mul_comm] <;> exact le_mul_right
 #align associates.le_mul_left Associates.le_mul_left
+-/
 
 instance : OrderBot (Associates α) where
   bot := 1
@@ -988,6 +1139,7 @@ instance : OrderBot (Associates α) where
 
 end Order
 
+#print Associates.dvd_of_mk_le_mk /-
 theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a ∣ b
   | ⟨c', hc'⟩ =>
     (Quotient.inductionOn c' fun c hc =>
@@ -998,18 +1150,25 @@ theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a 
             _ = a * (↑d * c) := by ac_rfl⟩)
       hc'
 #align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mk
+-/
 
+#print Associates.mk_le_mk_of_dvd /-
 theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.mk b := fun ⟨c, hc⟩ =>
   ⟨Associates.mk c, by simp [hc] <;> rfl⟩
 #align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvd
+-/
 
+#print Associates.mk_le_mk_iff_dvd_iff /-
 theorem mk_le_mk_iff_dvd_iff {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=
   Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
 #align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd_iff
+-/
 
+#print Associates.mk_dvd_mk /-
 theorem mk_dvd_mk {a b : α} : Associates.mk a ∣ Associates.mk b ↔ a ∣ b :=
   Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
 #align associates.mk_dvd_mk Associates.mk_dvd_mk
+-/
 
 end CommMonoid
 
@@ -1023,14 +1182,18 @@ section MonoidWithZero
 
 variable [MonoidWithZero α]
 
+#print Associates.mk_eq_zero /-
 @[simp]
 theorem mk_eq_zero {a : α} : Associates.mk a = 0 ↔ a = 0 :=
   ⟨fun h => (associated_zero_iff_eq_zero a).1 <| Quotient.exact h, fun h => h.symm ▸ rfl⟩
 #align associates.mk_eq_zero Associates.mk_eq_zero
+-/
 
+#print Associates.mk_ne_zero /-
 theorem mk_ne_zero {a : α} : Associates.mk a ≠ 0 ↔ a ≠ 0 :=
   not_congr mk_eq_zero
 #align associates.mk_ne_zero Associates.mk_ne_zero
+-/
 
 instance [Nontrivial α] : Nontrivial (Associates α) :=
   ⟨⟨0, 1, fun h =>
@@ -1038,9 +1201,11 @@ instance [Nontrivial α] : Nontrivial (Associates α) :=
       have : (0 : α) = 1 := ((associated_zero_iff_eq_zero 1).1 this.symm).symm
       zero_ne_one this⟩⟩
 
+#print Associates.exists_non_zero_rep /-
 theorem exists_non_zero_rep {a : Associates α} : a ≠ 0 → ∃ a0 : α, a0 ≠ 0 ∧ Associates.mk a0 = a :=
   Quotient.inductionOn a fun b nz => ⟨b, mt (congr_arg Quotient.mk') nz, rfl⟩
 #align associates.exists_non_zero_rep Associates.exists_non_zero_rep
+-/
 
 end MonoidWithZero
 
@@ -1067,11 +1232,14 @@ instance [DecidableRel ((· ∣ ·) : α → α → Prop)] :
     DecidableRel ((· ∣ ·) : Associates α → Associates α → Prop) := fun a b =>
   Quotient.recOnSubsingleton₂ a b fun a b => decidable_of_iff' _ mk_dvd_mk
 
+#print Associates.Prime.le_or_le /-
 theorem Prime.le_or_le {p : Associates α} (hp : Prime p) {a b : Associates α} (h : p ≤ a * b) :
     p ≤ a ∨ p ≤ b :=
   hp.2.2 a b h
 #align associates.prime.le_or_le Associates.Prime.le_or_le
+-/
 
+#print Associates.prime_mk /-
 theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p :=
   by
   rw [Prime, _root_.prime, forall_associated]
@@ -1086,7 +1254,9 @@ theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p :=
   refine' forall₂_congr fun a b => _
   rw [mk_mul_mk, mk_dvd_mk, mk_dvd_mk, mk_dvd_mk]
 #align associates.prime_mk Associates.prime_mk
+-/
 
+#print Associates.irreducible_mk /-
 theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible a :=
   by
   simp only [irreducible_iff, is_unit_mk]
@@ -1101,7 +1271,9 @@ theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible
     show IsUnit (Associates.mk x) ∨ IsUnit (Associates.mk y)
     simpa [is_unit_mk] using h _ _ a_eq.symm
 #align associates.irreducible_mk Associates.irreducible_mk
+-/
 
+#print Associates.mk_dvdNotUnit_mk_iff /-
 theorem mk_dvdNotUnit_mk_iff {a b : α} :
     DvdNotUnit (Associates.mk a) (Associates.mk b) ↔ DvdNotUnit a b :=
   by
@@ -1123,7 +1295,9 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
     use Associates.mk x
     simp [is_unit_mk, mk_mul_mk, hx]
 #align associates.mk_dvd_not_unit_mk_iff Associates.mk_dvdNotUnit_mk_iff
+-/
 
+#print Associates.dvdNotUnit_of_lt /-
 theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b :=
   by
   constructor; · rintro rfl; apply not_lt_of_le _ hlt; apply dvd_zero
@@ -1133,11 +1307,14 @@ theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b :=
   rcases ndvd with ⟨u, rfl⟩
   simp
 #align associates.dvd_not_unit_of_lt Associates.dvdNotUnit_of_lt
+-/
 
+#print Associates.irreducible_iff_prime_iff /-
 theorem irreducible_iff_prime_iff :
     (∀ a : α, Irreducible a ↔ Prime a) ↔ ∀ a : Associates α, Irreducible a ↔ Prime a := by
   simp_rw [forall_associated, irreducible_mk, prime_mk]
 #align associates.irreducible_iff_prime_iff Associates.irreducible_iff_prime_iff
+-/
 
 end CommMonoidWithZero
 
@@ -1170,10 +1347,13 @@ instance : CancelCommMonoidWithZero (Associates α) :=
       rw [mul_assoc] at hu 
       exact Quotient.sound' ⟨u, mul_left_cancel₀ (mk_ne_zero.1 ha) hu⟩ }
 
+#print Associates.le_of_mul_le_mul_left /-
 theorem le_of_mul_le_mul_left (a b c : Associates α) (ha : a ≠ 0) : a * b ≤ a * c → b ≤ c
   | ⟨d, hd⟩ => ⟨d, mul_left_cancel₀ ha <| by rwa [← mul_assoc]⟩
 #align associates.le_of_mul_le_mul_left Associates.le_of_mul_le_mul_left
+-/
 
+#print Associates.one_or_eq_of_le_of_prime /-
 theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p → m = 1 ∨ m = p
   | _, m, ⟨hp0, hp1, h⟩, ⟨d, rfl⟩ =>
     match h m d dvd_rfl with
@@ -1189,6 +1369,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
         have : d * m ≤ d * 1 := by simpa [mul_comm] using h
         Or.inl <| bot_unique <| Associates.le_of_mul_le_mul_left d m 1 ‹d ≠ 0› this
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
+-/
 
 instance : CanonicallyOrderedMonoid (Associates α) :=
   { Associates.cancelCommMonoidWithZero, Associates.boundedOrder,
@@ -1196,12 +1377,16 @@ instance : CanonicallyOrderedMonoid (Associates α) :=
     exists_mul_of_le := fun a b => id
     le_self_mul := fun a b => ⟨b, rfl⟩ }
 
+#print Associates.dvdNotUnit_iff_lt /-
 theorem dvdNotUnit_iff_lt {a b : Associates α} : DvdNotUnit a b ↔ a < b :=
   dvd_and_not_dvd_iff.symm
 #align associates.dvd_not_unit_iff_lt Associates.dvdNotUnit_iff_lt
+-/
 
+#print Associates.le_one_iff /-
 theorem le_one_iff {p : Associates α} : p ≤ 1 ↔ p = 1 := by rw [← Associates.bot_eq_one, le_bot_iff]
 #align associates.le_one_iff Associates.le_one_iff
+-/
 
 end CancelCommMonoidWithZero
 
@@ -1248,12 +1433,14 @@ end CommMonoidWithZero
 
 section CancelCommMonoidWithZero
 
+#print isUnit_of_associated_mul /-
 theorem isUnit_of_associated_mul [CancelCommMonoidWithZero α] {p b : α} (h : Associated (p * b) p)
     (hp : p ≠ 0) : IsUnit b := by
   cases' h with a ha
   refine' isUnit_of_mul_eq_one b a ((mul_right_inj' hp).mp _)
   rwa [← mul_assoc, mul_one]
 #align is_unit_of_associated_mul isUnit_of_associated_mul
+-/
 
 #print DvdNotUnit.not_associated /-
 theorem DvdNotUnit.not_associated [CancelCommMonoidWithZero α] {p q : α} (h : DvdNotUnit p q) :
@@ -1276,6 +1463,7 @@ theorem DvdNotUnit.ne [CancelCommMonoidWithZero α] {p q : α} (h : DvdNotUnit p
 #align dvd_not_unit.ne DvdNotUnit.ne
 -/
 
+#print pow_injective_of_not_unit /-
 theorem pow_injective_of_not_unit [CancelCommMonoidWithZero α] {q : α} (hq : ¬IsUnit q)
     (hq' : q ≠ 0) : Function.Injective fun n : ℕ => q ^ n :=
   by
@@ -1283,7 +1471,9 @@ theorem pow_injective_of_not_unit [CancelCommMonoidWithZero α] {q : α} (hq : 
   · exact not_isUnit_of_not_isUnit_dvd hq (dvd_pow (dvd_refl _) (Nat.sub_pos_of_lt h).ne')
   · exact (pow_mul_pow_sub q h.le).symm
 #align pow_injective_of_not_unit pow_injective_of_not_unit
+-/
 
+#print dvd_prime_pow /-
 theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n : ℕ) :
     q ∣ p ^ n ↔ ∃ i ≤ n, Associated q (p ^ i) :=
   by
@@ -1299,6 +1489,7 @@ theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n
   · obtain ⟨i, hi, hq⟩ := ih.mp hno
     exact ⟨i, hi.trans n.le_succ, hq⟩
 #align dvd_prime_pow dvd_prime_pow
+-/
 
 end CancelCommMonoidWithZero
 

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

@@ -689,7 +689,6 @@ protected theorem Associated.irreducible [Monoid α] {p q : α} (h : p ~ᵤ q) (
       calc
         p = p * u * (u⁻¹ : αˣ) := by simp
         _ = _ := by rw [hu] <;> simp [hab, mul_assoc]
-        
     (hp.isUnit_or_isUnit hpab).elim Or.inl fun ⟨v, hv⟩ => Or.inr ⟨v * u, by simp [hv]⟩⟩
 #align associated.irreducible Associated.irreducible
 -/
@@ -962,7 +961,6 @@ theorem isUnit_mk {a : α} : IsUnit (Associates.mk a) ↔ IsUnit a :=
     IsUnit (Associates.mk a) ↔ a ~ᵤ 1 := by
       rw [is_unit_iff_eq_one, one_eq_mk_one, mk_eq_mk_iff_associated]
     _ ↔ IsUnit a := associated_one_iff_isUnit
-    
 #align associates.is_unit_mk Associates.isUnit_mk
 
 section Order
@@ -997,8 +995,7 @@ theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a 
         ⟨↑d * c,
           calc
             b = a * c * ↑d := hd.symm
-            _ = a * (↑d * c) := by ac_rfl
-            ⟩)
+            _ = a * (↑d * c) := by ac_rfl⟩)
       hc'
 #align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mk
 

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

@@ -93,7 +93,7 @@ variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomCla
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
     refine' (hp.2.2 (f a) (f b) <| by convert map_dvd f h; simp).imp _ _ <;>
-      · intro h; convert← map_dvd g h <;> apply hinv⟩
+      · intro h; convert ← map_dvd g h <;> apply hinv⟩
 #align comap_prime comap_prime
 
 theorem MulEquiv.prime_iff (e : α ≃* β) : Prime p ↔ Prime (e p) :=

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

@@ -64,11 +64,11 @@ theorem dvd_or_dvd (hp : Prime p) {a b : α} (h : p ∣ a * b) : p ∣ a ∨ p 
 theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p ∣ a :=
   by
   induction' n with n ih
-  · rw [pow_zero] at h
+  · rw [pow_zero] at h 
     have := isUnit_of_dvd_one _ h
     have := not_unit hp
     contradiction
-  rw [pow_succ] at h
+  rw [pow_succ] at h 
   cases' dvd_or_dvd hp h with dvd_a dvd_pow
   · assumption
   exact ih dvd_pow
@@ -111,7 +111,7 @@ theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p
   rintro ⟨c, hc⟩
   rcases hp.2.2 a c (hc ▸ dvd_mul_right _ _) with (h | ⟨x, rfl⟩)
   · exact Or.inl h
-  · rw [mul_left_comm, mul_right_inj' hp.ne_zero] at hc
+  · rw [mul_left_comm, mul_right_inj' hp.ne_zero] at hc 
     exact Or.inr (hc.symm ▸ dvd_mul_right _ _)
 #align prime.left_dvd_or_dvd_right_of_dvd_mul Prime.left_dvd_or_dvd_right_of_dvd_mul
 
@@ -127,7 +127,7 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
 #align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_left
 
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
-    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h';
+    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h' ;
   exact hp.pow_dvd_of_dvd_mul_left n h h'
 #align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_right
 
@@ -160,9 +160,9 @@ theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x
   induction' i with i ih generalizing x
   · simp only [zero_add, pow_one] at *
     exact (h.dvd_or_dvd hxy).resolve_right hy
-  rw [pow_succ] at hxy⊢
+  rw [pow_succ] at hxy ⊢
   obtain ⟨x', rfl⟩ := (h.dvd_or_dvd (dvd_of_mul_right_dvd hxy)).resolve_right hy
-  rw [mul_assoc] at hxy
+  rw [mul_assoc] at hxy 
   exact mul_dvd_mul_left p (ih ((mul_dvd_mul_iff_left h.ne_zero).mp hxy))
 #align prime_pow_succ_dvd_mul prime_pow_succ_dvd_mul
 
@@ -227,7 +227,7 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
   · simp only [nat.lt_one_iff.mp hn, IsEmpty.forall_iff, not_irreducible_one, pow_zero]
   intro h
   obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_lt hn
-  rw [pow_succ, add_comm] at h
+  rw [pow_succ, add_comm] at h 
   exact (or_iff_left_of_imp is_unit_pow_succ_iff.mp).mp (of_irreducible_mul h)
 #align of_irreducible_pow of_irreducible_pow
 -/
@@ -237,9 +237,9 @@ theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
   by
   haveI := Classical.dec
   refine' or_iff_not_imp_right.2 fun H => _
-  simp [h, irreducible_iff] at H⊢
+  simp [h, irreducible_iff] at H ⊢
   refine' fun a b h => by_contradiction fun o => _
-  simp [not_or] at o
+  simp [not_or] at o 
   exact H _ o.1 _ o.2 h.symm
 #align irreducible_or_factor irreducible_or_factor
 
@@ -302,8 +302,8 @@ theorem irreducible_mul_iff {a b : α} :
   by
   constructor
   · refine' fun h => Or.imp (fun h' => ⟨_, h'⟩) (fun h' => ⟨_, h'⟩) (h.isUnit_or_isUnit rfl).symm
-    · rwa [irreducible_mul_isUnit h'] at h
-    · rwa [irreducible_isUnit_mul h'] at h
+    · rwa [irreducible_mul_isUnit h'] at h 
+    · rwa [irreducible_isUnit_mul h'] at h 
   · rintro (⟨ha, hb⟩ | ⟨hb, ha⟩)
     · rwa [irreducible_mul_isUnit hb]
     · rwa [irreducible_isUnit_mul ha]
@@ -316,7 +316,7 @@ section CommMonoid
 variable [CommMonoid α] {a : α}
 
 theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a := by rintro ⟨b, rfl⟩;
-  simp only [irreducible_mul_iff, or_self_iff] at ha; exact ha.1.not_unit ha.2
+  simp only [irreducible_mul_iff, or_self_iff] at ha ; exact ha.1.not_unit ha.2
 #align irreducible.not_square Irreducible.not_square
 
 theorem IsSquare.not_irreducible (ha : IsSquare a) : ¬Irreducible a := fun h => h.not_square ha
@@ -359,7 +359,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l
   have h : p ^ (k + l) * (x * y) = p ^ (k + l) * (p * z) := by
     simpa [mul_comm, pow_add, hx, hy, mul_assoc, mul_left_comm] using hz
   have hp0 : p ^ (k + l) ≠ 0 := pow_ne_zero _ hp.NeZero
-  have hpd : p ∣ x * y := ⟨z, by rwa [mul_right_inj' hp0] at h⟩
+  have hpd : p ∣ x * y := ⟨z, by rwa [mul_right_inj' hp0] at h ⟩
   (hp.dvd_or_dvd hpd).elim
     (fun ⟨d, hd⟩ => Or.inl ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩)
     fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩
@@ -578,7 +578,7 @@ theorem associated_of_dvd_dvd [CancelMonoidWithZero α] {a b : α} (hab : a ∣
   rcases hba with ⟨d, a_eq⟩
   by_cases ha0 : a = 0
   · simp_all
-  have hac0 : a * c ≠ 0 := by intro con; rw [Con, MulZeroClass.zero_mul] at a_eq; apply ha0 a_eq
+  have hac0 : a * c ≠ 0 := by intro con; rw [Con, MulZeroClass.zero_mul] at a_eq ; apply ha0 a_eq
   have : a * (c * d) = a * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
   have hcd : c * d = 1 := mul_left_cancel₀ ha0 this
   have : a * c * (d * c) = a * c * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
@@ -773,14 +773,14 @@ variable {R : Type _} [CancelCommMonoidWithZero R] [Unique Rˣ] {p₁ p₂ : R}
 
 #print eq_of_prime_pow_eq /-
 theorem eq_of_prime_pow_eq (hp₁ : Prime p₁) (hp₂ : Prime p₂) (hk₁ : 0 < k₁)
-    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h⊢;
+    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h ⊢;
   apply h.of_pow_associated_of_prime hp₁ hp₂ hk₁
 #align eq_of_prime_pow_eq eq_of_prime_pow_eq
 -/
 
 #print eq_of_prime_pow_eq' /-
 theorem eq_of_prime_pow_eq' (hp₁ : Prime p₁) (hp₂ : Prime p₂) (hk₁ : 0 < k₂)
-    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h⊢;
+    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h ⊢;
   apply h.of_pow_associated_of_prime' hp₁ hp₂ hk₁
 #align eq_of_prime_pow_eq' eq_of_prime_pow_eq'
 -/
@@ -932,7 +932,7 @@ theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
     (Quotient.induction_on₂ x y fun a b h =>
       have : a * b ~ᵤ 1 := Quotient.exact h
       ⟨Quotient.sound <| associated_one_of_associated_mul_one this,
-        Quotient.sound <| associated_one_of_associated_mul_one <| by rwa [mul_comm] at this⟩)
+        Quotient.sound <| associated_one_of_associated_mul_one <| by rwa [mul_comm] at this ⟩)
     (by simp (config := { contextual := true }))
 #align associates.mul_eq_one_iff Associates.mul_eq_one_iff
 
@@ -1100,7 +1100,7 @@ theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible
   · intro h x y
     refine' Quotient.induction_on₂ x y fun x y a_eq => _
     rcases Quotient.exact a_eq.symm with ⟨u, a_eq⟩
-    rw [mul_assoc] at a_eq
+    rw [mul_assoc] at a_eq 
     show IsUnit (Associates.mk x) ∨ IsUnit (Associates.mk y)
     simpa [is_unit_mk] using h _ _ a_eq.symm
 #align associates.irreducible_mk Associates.irreducible_mk
@@ -1113,10 +1113,10 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
   constructor
   · contrapose!; rw [forall_associated]
     intro h x hx hbax
-    rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax
+    rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax 
     cases' hbax with u hu
     apply h (x * ↑u⁻¹)
-    · rw [is_unit_mk] at hx
+    · rw [is_unit_mk] at hx 
       rw [Associated.isUnit_iff]
       apply hx
       use u
@@ -1170,7 +1170,7 @@ instance : CancelCommMonoidWithZero (Associates α) :=
     mul_left_cancel_of_ne_zero := by
       rintro ⟨a⟩ ⟨b⟩ ⟨c⟩ ha h
       rcases Quotient.exact' h with ⟨u, hu⟩
-      rw [mul_assoc] at hu
+      rw [mul_assoc] at hu 
       exact Quotient.sound' ⟨u, mul_left_cancel₀ (mk_ne_zero.1 ha) hu⟩ }
 
 theorem le_of_mul_le_mul_left (a b c : Associates α) (ha : a ≠ 0) : a * b ≤ a * c → b ≤ c
@@ -1188,7 +1188,7 @@ theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p
         have : d = 1 := bot_unique this
         simp [this]
     | Or.inr h =>
-      by_cases (fun this : d = 0 => by simp [this] at hp0 <;> contradiction) fun this : d ≠ 0 =>
+      by_cases (fun this : d = 0 => by simp [this] at hp0  <;> contradiction) fun this : d ≠ 0 =>
         have : d * m ≤ d * 1 := by simpa [mul_comm] using h
         Or.inl <| bot_unique <| Associates.le_of_mul_le_mul_left d m 1 ‹d ≠ 0› this
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
@@ -1274,7 +1274,7 @@ theorem DvdNotUnit.ne [CancelCommMonoidWithZero α] {p q : α} (h : DvdNotUnit p
   by_contra hcontra
   obtain ⟨hp, x, hx', hx''⟩ := h
   conv_lhs at hx'' => rw [← hcontra, ← mul_one p]
-  rw [(mul_left_cancel₀ hp hx'').symm] at hx'
+  rw [(mul_left_cancel₀ hp hx'').symm] at hx' 
   exact hx' isUnit_one
 #align dvd_not_unit.ne DvdNotUnit.ne
 -/
@@ -1293,9 +1293,9 @@ theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n
   induction' n with n ih generalizing q
   · simp [← isUnit_iff_dvd_one, associated_one_iff_isUnit]
   refine' ⟨fun h => _, fun ⟨i, hi, hq⟩ => hq.dvd.trans (pow_dvd_pow p hi)⟩
-  rw [pow_succ] at h
+  rw [pow_succ] at h 
   rcases hp.left_dvd_or_dvd_right_of_dvd_mul h with (⟨q, rfl⟩ | hno)
-  · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h
+  · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h 
     rcases h with ⟨i, hi, hq⟩
     refine' ⟨i + 1, Nat.succ_le_succ hi, (hq.mul_left p).trans _⟩
     rw [pow_succ]

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

@@ -39,12 +39,6 @@ variable {p : α} (hp : Prime p)
 
 include hp
 
-/- warning: prime.ne_zero -> Prime.ne_zero is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : α}, (Prime.{u1} α _inst_1 p) -> (Ne.{succ u1} α p (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align prime.ne_zero Prime.ne_zeroₓ'. -/
 theorem ne_zero : p ≠ 0 :=
   hp.1
 #align prime.ne_zero Prime.ne_zero
@@ -55,31 +49,13 @@ theorem not_unit : ¬IsUnit p :=
 #align prime.not_unit Prime.not_unit
 -/
 
-/- warning: prime.not_dvd_one -> Prime.not_dvd_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align prime.not_dvd_one Prime.not_dvd_oneₓ'. -/
 theorem not_dvd_one : ¬p ∣ 1 :=
   mt (isUnit_of_dvd_one _) hp.not_unit
 #align prime.not_dvd_one Prime.not_dvd_one
 
-/- warning: prime.ne_one -> Prime.ne_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : α}, (Prime.{u1} α _inst_1 p) -> (Ne.{succ u1} α p (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 _inst_1))))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align prime.ne_one Prime.ne_oneₓ'. -/
 theorem ne_one : p ≠ 1 := fun h => hp.2.1 (h.symm ▸ isUnit_one)
 #align prime.ne_one Prime.ne_one
 
-/- warning: prime.dvd_or_dvd -> Prime.dvd_or_dvd is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : α}, (Prime.{u1} α _inst_1 p) -> (forall {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) p (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 _inst_1))))) a b)) -> (Or (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) p a) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) p b)))
-Case conversion may be inaccurate. Consider using '#align prime.dvd_or_dvd Prime.dvd_or_dvdₓ'. -/
 theorem dvd_or_dvd (hp : Prime p) {a b : α} (h : p ∣ a * b) : p ∣ a ∨ p ∣ b :=
   hp.2.2 a b h
 #align prime.dvd_or_dvd Prime.dvd_or_dvd
@@ -101,22 +77,10 @@ theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p 
 
 end Prime
 
-/- warning: not_prime_zero -> not_prime_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α], Not (Prime.{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 _inst_1))))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align not_prime_zero not_prime_zeroₓ'. -/
 @[simp]
 theorem not_prime_zero : ¬Prime (0 : α) := fun h => h.NeZero rfl
 #align not_prime_zero not_prime_zero
 
-/- warning: not_prime_one -> not_prime_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α], Not (Prime.{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 _inst_1))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α], Not (Prime.{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 _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align not_prime_one not_prime_oneₓ'. -/
 @[simp]
 theorem not_prime_one : ¬Prime (1 : α) := fun h => h.not_unit isUnit_one
 #align not_prime_one not_prime_one
@@ -126,24 +90,12 @@ section Map
 variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomClass F α β]
   [MulHomClass G β α] (f : F) (g : G) {p : α}
 
-/- warning: comap_prime -> comap_prime is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u1} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u4}} [_inst_3 : MonoidWithZeroHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u1} α (coeFn.{succ u4, max (succ u2) (succ u1)} G (fun (_x : G) => β -> α) (FunLike.hasCoeToFun.{succ u4, succ u2, succ u1} G β (fun (_x : β) => α) (MulHomClass.toFunLike.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) _inst_4)) g (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f a)) a) -> (Prime.{u2} β _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f p)) -> (Prime.{u1} α _inst_1 p)
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-  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
-Case conversion may be inaccurate. Consider using '#align comap_prime comap_primeₓ'. -/
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
     refine' (hp.2.2 (f a) (f b) <| by convert map_dvd f h; simp).imp _ _ <;>
       · intro h; convert← map_dvd g h <;> apply hinv⟩
 #align comap_prime comap_prime
 
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-Case conversion may be inaccurate. Consider using '#align mul_equiv.prime_iff MulEquiv.prime_iffₓ'. -/
 theorem MulEquiv.prime_iff (e : α ≃* β) : Prime p ↔ Prime (e p) :=
   ⟨fun h => (comap_prime e.symm e fun a => by simp) <| (e.symm_apply_apply p).substr h,
     comap_prime e e.symm fun a => by simp⟩
@@ -153,12 +105,6 @@ end Map
 
 end Prime
 
-/- warning: prime.left_dvd_or_dvd_right_of_dvd_mul -> Prime.left_dvd_or_dvd_right_of_dvd_mul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align prime.left_dvd_or_dvd_right_of_dvd_mul Prime.left_dvd_or_dvd_right_of_dvd_mulₓ'. -/
 theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p : α} (hp : Prime p)
     {a b : α} : a ∣ p * b → p ∣ a ∨ a ∣ b :=
   by
@@ -169,12 +115,6 @@ theorem Prime.left_dvd_or_dvd_right_of_dvd_mul [CancelCommMonoidWithZero α] {p
     exact Or.inr (hc.symm ▸ dvd_mul_right _ _)
 #align prime.left_dvd_or_dvd_right_of_dvd_mul Prime.left_dvd_or_dvd_right_of_dvd_mul
 
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-Case conversion may be inaccurate. Consider using '#align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_leftₓ'. -/
 theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
     (n : ℕ) (h : ¬p ∣ a) (h' : p ^ n ∣ a * b) : p ^ n ∣ b :=
   by
@@ -186,23 +126,11 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
     rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ', mul_left_comm]
 #align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_left
 
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-Case conversion may be inaccurate. Consider using '#align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_rightₓ'. -/
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
     (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h';
   exact hp.pow_dvd_of_dvd_mul_left n h h'
 #align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_right
 
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-Case conversion may be inaccurate. Consider using '#align prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvdₓ'. -/
 theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWithZero α] {p a b : α}
     {n : ℕ} (hp : Prime p) (hpow : p ^ n.succ ∣ a ^ n.succ * b ^ n) (hb : ¬p ^ 2 ∣ b) : p ∣ a :=
   by
@@ -224,12 +152,6 @@ theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWith
   exact dvd_mul_right _ _
 #align prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd
 
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-Case conversion may be inaccurate. Consider using '#align prime_pow_succ_dvd_mul prime_pow_succ_dvd_mulₓ'. -/
 theorem prime_pow_succ_dvd_mul {α : Type _} [CancelCommMonoidWithZero α] {p x y : α} (h : Prime p)
     {i : ℕ} (hxy : p ^ (i + 1) ∣ x * y) : p ^ (i + 1) ∣ x ∨ p ∣ y :=
   by
@@ -258,22 +180,10 @@ structure Irreducible [Monoid α] (p : α) : Prop where
 
 namespace Irreducible
 
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 theorem not_dvd_one [CommMonoid α] {p : α} (hp : Irreducible p) : ¬p ∣ 1 :=
   mt (isUnit_of_dvd_one _) hp.not_unit
 #align irreducible.not_dvd_one Irreducible.not_dvd_one
 
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 theorem isUnit_or_isUnit [Monoid α] {p : α} (hp : Irreducible p) {a b : α} (h : p = a * b) :
     IsUnit a ∨ IsUnit b :=
   hp.isUnit_or_is_unit' a b h
@@ -281,43 +191,19 @@ theorem isUnit_or_isUnit [Monoid α] {p : α} (hp : Irreducible p) {a b : α} (h
 
 end Irreducible
 
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 theorem irreducible_iff [Monoid α] {p : α} :
     Irreducible p ↔ ¬IsUnit p ∧ ∀ a b, p = a * b → IsUnit a ∨ IsUnit b :=
   ⟨fun h => ⟨h.1, h.2⟩, fun h => ⟨h.1, h.2⟩⟩
 #align irreducible_iff irreducible_iff
 
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 @[simp]
 theorem not_irreducible_one [Monoid α] : ¬Irreducible (1 : α) := by simp [irreducible_iff]
 #align not_irreducible_one not_irreducible_one
 
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 theorem Irreducible.ne_one [Monoid α] : ∀ {p : α}, Irreducible p → p ≠ 1
   | _, hp, rfl => not_irreducible_one hp
 #align irreducible.ne_one Irreducible.ne_one
 
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 @[simp]
 theorem not_irreducible_zero [MonoidWithZero α] : ¬Irreducible (0 : α)
   | ⟨hn0, h⟩ =>
@@ -325,22 +211,10 @@ theorem not_irreducible_zero [MonoidWithZero α] : ¬Irreducible (0 : α)
     this.elim hn0 hn0
 #align not_irreducible_zero not_irreducible_zero
 
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 theorem Irreducible.ne_zero [MonoidWithZero α] : ∀ {p : α}, Irreducible p → p ≠ 0
   | _, hp, rfl => not_irreducible_zero hp
 #align irreducible.ne_zero Irreducible.ne_zero
 
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 theorem of_irreducible_mul {α} [Monoid α] {x y : α} : Irreducible (x * y) → IsUnit x ∨ IsUnit y
   | ⟨_, h⟩ => h _ _ rfl
 #align of_irreducible_mul of_irreducible_mul
@@ -358,12 +232,6 @@ theorem of_irreducible_pow {α} [Monoid α] {x : α} {n : ℕ} (hn : n ≠ 1) :
 #align of_irreducible_pow of_irreducible_pow
 -/
 
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 theorem irreducible_or_factor {α} [Monoid α] (x : α) (h : ¬IsUnit x) :
     Irreducible x ∨ ∃ a b, ¬IsUnit a ∧ ¬IsUnit b ∧ a * b = x :=
   by
@@ -395,12 +263,6 @@ section
 
 variable [Monoid α]
 
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 theorem irreducible_units_mul (a : αˣ) (b : α) : Irreducible (↑a * b) ↔ Irreducible b :=
   by
   simp only [irreducible_iff, Units.isUnit_units_mul, and_congr_right_iff]
@@ -413,23 +275,11 @@ theorem irreducible_units_mul (a : αˣ) (b : α) : Irreducible (↑a * b) ↔ I
     rw [mul_assoc, ← HAB, Units.inv_mul_cancel_left]
 #align irreducible_units_mul irreducible_units_mul
 
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 theorem irreducible_isUnit_mul {a b : α} (h : IsUnit a) : Irreducible (a * b) ↔ Irreducible b :=
   let ⟨a, ha⟩ := h
   ha ▸ irreducible_units_mul a b
 #align irreducible_is_unit_mul irreducible_isUnit_mul
 
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 theorem irreducible_mul_units (a : αˣ) (b : α) : Irreducible (b * ↑a) ↔ Irreducible b :=
   by
   simp only [irreducible_iff, Units.isUnit_mul_units, and_congr_right_iff]
@@ -442,23 +292,11 @@ theorem irreducible_mul_units (a : αˣ) (b : α) : Irreducible (b * ↑a) ↔ I
     rw [← mul_assoc, ← HAB, Units.mul_inv_cancel_right]
 #align irreducible_mul_units irreducible_mul_units
 
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 theorem irreducible_mul_isUnit {a b : α} (h : IsUnit a) : Irreducible (b * a) ↔ Irreducible b :=
   let ⟨a, ha⟩ := h
   ha ▸ irreducible_mul_units a b
 #align irreducible_mul_is_unit irreducible_mul_isUnit
 
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 theorem irreducible_mul_iff {a b : α} :
     Irreducible (a * b) ↔ Irreducible a ∧ IsUnit b ∨ Irreducible b ∧ IsUnit a :=
   by
@@ -477,22 +315,10 @@ section CommMonoid
 
 variable [CommMonoid α] {a : α}
 
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 theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a := by rintro ⟨b, rfl⟩;
   simp only [irreducible_mul_iff, or_self_iff] at ha; exact ha.1.not_unit ha.2
 #align irreducible.not_square Irreducible.not_square
 
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 theorem IsSquare.not_irreducible (ha : IsSquare a) : ¬Irreducible a := fun h => h.not_square ha
 #align is_square.not_irreducible IsSquare.not_irreducible
 
@@ -527,12 +353,6 @@ protected theorem Prime.irreducible (hp : Prime p) : Irreducible p :=
 #align prime.irreducible Prime.irreducible
 -/
 
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 theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l : ℕ} :
     p ^ k ∣ a → p ^ l ∣ b → p ^ (k + l + 1) ∣ a * b → p ^ (k + 1) ∣ a ∨ p ^ (l + 1) ∣ b :=
   fun ⟨x, hx⟩ ⟨y, hy⟩ ⟨z, hz⟩ =>
@@ -545,22 +365,10 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul (hp : Prime p) {a b : α} {k l
     fun ⟨d, hd⟩ => Or.inr ⟨d, by simp [*, pow_succ, mul_comm, mul_left_comm, mul_assoc]⟩
 #align succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
 
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 theorem Prime.not_square (hp : Prime p) : ¬IsSquare p :=
   hp.Irreducible.not_square
 #align prime.not_square Prime.not_square
 
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 theorem IsSquare.not_prime (ha : IsSquare a) : ¬Prime a := fun h => h.not_square ha
 #align is_square.not_prime IsSquare.not_prime
 
@@ -634,22 +442,10 @@ end Associated
 
 attribute [local instance] Associated.setoid
 
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 theorem unit_associated_one [Monoid α] {u : αˣ} : (u : α) ~ᵤ 1 :=
   ⟨u⁻¹, Units.mul_inv u⟩
 #align unit_associated_one unit_associated_one
 
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 theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsUnit a :=
   Iff.intro
     (fun h =>
@@ -658,12 +454,6 @@ theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsU
     fun ⟨c, h⟩ => Associated.symm ⟨c, by simp [h]⟩
 #align associated_one_iff_is_unit associated_one_iff_isUnit
 
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 theorem associated_zero_iff_eq_zero [MonoidWithZero α] (a : α) : a ~ᵤ 0 ↔ a = 0 :=
   Iff.intro
     (fun h => by
@@ -672,89 +462,41 @@ theorem associated_zero_iff_eq_zero [MonoidWithZero α] (a : α) : a ~ᵤ 0 ↔
     fun h => h ▸ Associated.refl a
 #align associated_zero_iff_eq_zero associated_zero_iff_eq_zero
 
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 theorem associated_one_of_mul_eq_one [CommMonoid α] {a : α} (b : α) (hab : a * b = 1) : a ~ᵤ 1 :=
   show (Units.mkOfMulEqOne a b hab : α) ~ᵤ 1 from unit_associated_one
 #align associated_one_of_mul_eq_one associated_one_of_mul_eq_one
 
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 theorem associated_one_of_associated_mul_one [CommMonoid α] {a b : α} : a * b ~ᵤ 1 → a ~ᵤ 1
   | ⟨u, h⟩ => associated_one_of_mul_eq_one (b * u) <| by simpa [mul_assoc] using h
 #align associated_one_of_associated_mul_one associated_one_of_associated_mul_one
 
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 theorem associated_mul_unit_left {β : Type _} [Monoid β] (a u : β) (hu : IsUnit u) :
     Associated (a * u) a :=
   let ⟨u', hu⟩ := hu
   ⟨u'⁻¹, hu ▸ Units.mul_inv_cancel_right _ _⟩
 #align associated_mul_unit_left associated_mul_unit_left
 
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-Case conversion may be inaccurate. Consider using '#align associated_unit_mul_left associated_unit_mul_leftₓ'. -/
 theorem associated_unit_mul_left {β : Type _} [CommMonoid β] (a u : β) (hu : IsUnit u) :
     Associated (u * a) a := by
   rw [mul_comm]
   exact associated_mul_unit_left _ _ hu
 #align associated_unit_mul_left associated_unit_mul_left
 
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 theorem associated_mul_unit_right {β : Type _} [Monoid β] (a u : β) (hu : IsUnit u) :
     Associated a (a * u) :=
   (associated_mul_unit_left a u hu).symm
 #align associated_mul_unit_right associated_mul_unit_right
 
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-Case conversion may be inaccurate. Consider using '#align associated_unit_mul_right associated_unit_mul_rightₓ'. -/
 theorem associated_unit_mul_right {β : Type _} [CommMonoid β] (a u : β) (hu : IsUnit u) :
     Associated a (u * a) :=
   (associated_unit_mul_left a u hu).symm
 #align associated_unit_mul_right associated_unit_mul_right
 
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 theorem associated_mul_isUnit_left_iff {β : Type _} [Monoid β] {a u b : β} (hu : IsUnit u) :
     Associated (a * u) b ↔ Associated a b :=
   ⟨trans (associated_mul_unit_right _ _ hu), trans (associated_mul_unit_left _ _ hu)⟩
 #align associated_mul_is_unit_left_iff associated_mul_isUnit_left_iff
 
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 theorem associated_isUnit_mul_left_iff {β : Type _} [CommMonoid β] {u a b : β} (hu : IsUnit u) :
     Associated (u * a) b ↔ Associated a b :=
   by
@@ -762,103 +504,49 @@ theorem associated_isUnit_mul_left_iff {β : Type _} [CommMonoid β] {u a b : β
   exact associated_mul_isUnit_left_iff hu
 #align associated_is_unit_mul_left_iff associated_isUnit_mul_left_iff
 
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 theorem associated_mul_isUnit_right_iff {β : Type _} [Monoid β] {a b u : β} (hu : IsUnit u) :
     Associated a (b * u) ↔ Associated a b :=
   Associated.comm.trans <| (associated_mul_isUnit_left_iff hu).trans Associated.comm
 #align associated_mul_is_unit_right_iff associated_mul_isUnit_right_iff
 
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 theorem associated_isUnit_mul_right_iff {β : Type _} [CommMonoid β] {a u b : β} (hu : IsUnit u) :
     Associated a (u * b) ↔ Associated a b :=
   Associated.comm.trans <| (associated_isUnit_mul_left_iff hu).trans Associated.comm
 #align associated_is_unit_mul_right_iff associated_isUnit_mul_right_iff
 
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 @[simp]
 theorem associated_mul_unit_left_iff {β : Type _} [Monoid β] {a b : β} {u : Units β} :
     Associated (a * u) b ↔ Associated a b :=
   associated_mul_isUnit_left_iff u.IsUnit
 #align associated_mul_unit_left_iff associated_mul_unit_left_iff
 
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 @[simp]
 theorem associated_unit_mul_left_iff {β : Type _} [CommMonoid β] {a b : β} {u : Units β} :
     Associated (↑u * a) b ↔ Associated a b :=
   associated_isUnit_mul_left_iff u.IsUnit
 #align associated_unit_mul_left_iff associated_unit_mul_left_iff
 
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 @[simp]
 theorem associated_mul_unit_right_iff {β : Type _} [Monoid β] {a b : β} {u : Units β} :
     Associated a (b * u) ↔ Associated a b :=
   associated_mul_isUnit_right_iff u.IsUnit
 #align associated_mul_unit_right_iff associated_mul_unit_right_iff
 
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 @[simp]
 theorem associated_unit_mul_right_iff {β : Type _} [CommMonoid β] {a b : β} {u : Units β} :
     Associated a (↑u * b) ↔ Associated a b :=
   associated_isUnit_mul_right_iff u.IsUnit
 #align associated_unit_mul_right_iff associated_unit_mul_right_iff
 
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 theorem Associated.mul_mul [CommMonoid α] {a₁ a₂ b₁ b₂ : α} :
     a₁ ~ᵤ b₁ → a₂ ~ᵤ b₂ → a₁ * a₂ ~ᵤ b₁ * b₂
   | ⟨c₁, h₁⟩, ⟨c₂, h₂⟩ => ⟨c₁ * c₂, by simp [h₁.symm, h₂.symm, mul_assoc, mul_comm, mul_left_comm]⟩
 #align associated.mul_mul Associated.mul_mul
 
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 theorem Associated.mul_left [CommMonoid α] (a : α) {b c : α} (h : b ~ᵤ c) : a * b ~ᵤ a * c :=
   (Associated.refl a).mul_mul h
 #align associated.mul_left Associated.mul_left
 
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 theorem Associated.mul_right [CommMonoid α] {a b : α} (h : a ~ᵤ b) (c : α) : a * c ~ᵤ b * c :=
   h.mul_mul (Associated.refl c)
 #align associated.mul_right Associated.mul_right
@@ -922,12 +610,6 @@ theorem Associated.dvd_iff_dvd_right [Monoid α] {a b c : α} (h : b ~ᵤ c) : a
 #align associated.dvd_iff_dvd_right Associated.dvd_iff_dvd_right
 -/
 
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 theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a = 0 ↔ b = 0 :=
   ⟨fun ha => by
     let ⟨u, hu⟩ := h
@@ -936,12 +618,6 @@ theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a
     simp [hu.symm, hb]⟩
 #align associated.eq_zero_iff Associated.eq_zero_iff
 
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 theorem Associated.ne_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a ≠ 0 ↔ b ≠ 0 :=
   not_congr h.eq_zero_iff
 #align associated.ne_zero_iff Associated.ne_zero_iff
@@ -1025,12 +701,6 @@ protected theorem Associated.irreducible_iff [Monoid α] {p q : α} (h : p ~ᵤ
 #align associated.irreducible_iff Associated.irreducible_iff
 -/
 
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 theorem Associated.of_mul_left [CancelCommMonoidWithZero α] {a b c d : α} (h : a * b ~ᵤ c * d)
     (h₁ : a ~ᵤ c) (ha : a ≠ 0) : b ~ᵤ d :=
   let ⟨u, hu⟩ := h
@@ -1042,12 +712,6 @@ theorem Associated.of_mul_left [CancelCommMonoidWithZero α] {a b c d : α} (h :
         simp [hv.symm, mul_assoc, mul_comm, mul_left_comm])⟩
 #align associated.of_mul_left Associated.of_mul_left
 
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 theorem Associated.of_mul_right [CancelCommMonoidWithZero α] {a b c d : α} :
     a * b ~ᵤ c * d → b ~ᵤ d → b ≠ 0 → a ~ᵤ c := by
   rw [mul_comm a, mul_comm c] <;> exact Associated.of_mul_left
@@ -1076,12 +740,6 @@ section UniqueUnits
 
 variable [Monoid α] [Unique αˣ]
 
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 theorem units_eq_one (u : αˣ) : u = 1 :=
   Subsingleton.elim u 1
 #align units_eq_one units_eq_one
@@ -1186,23 +844,11 @@ theorem mk_surjective [Monoid α] : Function.Surjective (@Associates.mk α _) :=
 instance [Monoid α] : One (Associates α) :=
   ⟨⟦1⟧⟩
 
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 @[simp]
 theorem mk_one [Monoid α] : Associates.mk (1 : α) = 1 :=
   rfl
 #align associates.mk_one Associates.mk_one
 
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 theorem one_eq_mk_one [Monoid α] : (1 : Associates α) = Associates.mk 1 :=
   rfl
 #align associates.one_eq_mk_one Associates.one_eq_mk_one
@@ -1210,12 +856,6 @@ theorem one_eq_mk_one [Monoid α] : (1 : Associates α) = Associates.mk 1 :=
 instance [Monoid α] : Bot (Associates α) :=
   ⟨1⟩
 
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 theorem bot_eq_one [Monoid α] : (⊥ : Associates α) = 1 :=
   rfl
 #align associates.bot_eq_one Associates.bot_eq_one
@@ -1246,12 +886,6 @@ instance : Mul (Associates α) :=
     Quotient.liftOn₂ a' b' (fun a b => ⟦a * b⟧) fun a₁ a₂ b₁ b₂ ⟨c₁, h₁⟩ ⟨c₂, h₂⟩ =>
       Quotient.sound <| ⟨c₁ * c₂, by simp [h₁.symm, h₂.symm, mul_assoc, mul_comm, mul_left_comm]⟩⟩
 
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 theorem mk_mul_mk {x y : α} : Associates.mk x * Associates.mk y = Associates.mk (x * y) :=
   rfl
 #align associates.mk_mul_mk Associates.mk_mul_mk
@@ -1270,65 +904,29 @@ instance : Preorder (Associates α) where
   le_refl := dvd_refl
   le_trans a b c := dvd_trans
 
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 /-- `associates.mk` as a `monoid_hom`. -/
 protected def mkMonoidHom : α →* Associates α :=
   ⟨Associates.mk, mk_one, fun x y => mk_mul_mk⟩
 #align associates.mk_monoid_hom Associates.mkMonoidHom
 
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 @[simp]
 theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a :=
   rfl
 #align associates.mk_monoid_hom_apply Associates.mkMonoidHom_apply
 
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 theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInverse f Associates.mk)
     (a : α) : a ~ᵤ f (Associates.mk a) :=
   Associates.mk_eq_mk_iff_associated.1 (hinv (Associates.mk a)).symm
 #align associates.associated_map_mk Associates.associated_map_mk
 
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 theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n := by
   induction n <;> simp [*, pow_succ, associates.mk_mul_mk.symm]
 #align associates.mk_pow Associates.mk_pow
 
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 theorem dvd_eq_le : ((· ∣ ·) : Associates α → Associates α → Prop) = (· ≤ ·) :=
   rfl
 #align associates.dvd_eq_le Associates.dvd_eq_le
 
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 theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
   Iff.intro
     (Quotient.induction_on₂ x y fun a b h =>
@@ -1338,63 +936,27 @@ theorem mul_eq_one_iff {x y : Associates α} : x * y = 1 ↔ x = 1 ∧ y = 1 :=
     (by simp (config := { contextual := true }))
 #align associates.mul_eq_one_iff Associates.mul_eq_one_iff
 
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 theorem units_eq_one (u : (Associates α)ˣ) : u = 1 :=
   Units.ext (mul_eq_one_iff.1 u.val_inv).1
 #align associates.units_eq_one Associates.units_eq_one
 
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 instance uniqueUnits : Unique (Associates α)ˣ
     where
   default := 1
   uniq := Associates.units_eq_one
 #align associates.unique_units Associates.uniqueUnits
 
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 theorem coe_unit_eq_one (u : (Associates α)ˣ) : (u : Associates α) = 1 := by simp
 #align associates.coe_unit_eq_one Associates.coe_unit_eq_one
 
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 theorem isUnit_iff_eq_one (a : Associates α) : IsUnit a ↔ a = 1 :=
   Iff.intro (fun ⟨u, h⟩ => h ▸ coe_unit_eq_one _) fun h => h.symm ▸ isUnit_one
 #align associates.is_unit_iff_eq_one Associates.isUnit_iff_eq_one
 
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 theorem isUnit_iff_eq_bot {a : Associates α} : IsUnit a ↔ a = ⊥ := by
   rw [Associates.isUnit_iff_eq_one, bot_eq_one]
 #align associates.is_unit_iff_eq_bot Associates.isUnit_iff_eq_bot
 
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 theorem isUnit_mk {a : α} : IsUnit (Associates.mk a) ↔ IsUnit a :=
   calc
     IsUnit (Associates.mk a) ↔ a ~ᵤ 1 := by
@@ -1405,44 +967,20 @@ theorem isUnit_mk {a : α} : IsUnit (Associates.mk a) ↔ IsUnit a :=
 
 section Order
 
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 theorem mul_mono {a b c d : Associates α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a * c ≤ b * d :=
   let ⟨x, hx⟩ := h₁
   let ⟨y, hy⟩ := h₂
   ⟨x * y, by simp [hx, hy, mul_comm, mul_assoc, mul_left_comm]⟩
 #align associates.mul_mono Associates.mul_mono
 
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 theorem one_le {a : Associates α} : 1 ≤ a :=
   Dvd.intro _ (one_mul a)
 #align associates.one_le Associates.one_le
 
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 theorem le_mul_right {a b : Associates α} : a ≤ a * b :=
   ⟨b, rfl⟩
 #align associates.le_mul_right Associates.le_mul_right
 
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 theorem le_mul_left {a b : Associates α} : a ≤ b * a := by rw [mul_comm] <;> exact le_mul_right
 #align associates.le_mul_left Associates.le_mul_left
 
@@ -1452,12 +990,6 @@ instance : OrderBot (Associates α) where
 
 end Order
 
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 theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a ∣ b
   | ⟨c', hc'⟩ =>
     (Quotient.inductionOn c' fun c hc =>
@@ -1470,32 +1002,14 @@ theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a 
       hc'
 #align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mk
 
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 theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.mk b := fun ⟨c, hc⟩ =>
   ⟨Associates.mk c, by simp [hc] <;> rfl⟩
 #align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvd
 
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 theorem mk_le_mk_iff_dvd_iff {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=
   Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
 #align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd_iff
 
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 theorem mk_dvd_mk {a b : α} : Associates.mk a ∣ Associates.mk b ↔ a ∣ b :=
   Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
 #align associates.mk_dvd_mk Associates.mk_dvd_mk
@@ -1512,23 +1026,11 @@ section MonoidWithZero
 
 variable [MonoidWithZero α]
 
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 @[simp]
 theorem mk_eq_zero {a : α} : Associates.mk a = 0 ↔ a = 0 :=
   ⟨fun h => (associated_zero_iff_eq_zero a).1 <| Quotient.exact h, fun h => h.symm ▸ rfl⟩
 #align associates.mk_eq_zero Associates.mk_eq_zero
 
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 theorem mk_ne_zero {a : α} : Associates.mk a ≠ 0 ↔ a ≠ 0 :=
   not_congr mk_eq_zero
 #align associates.mk_ne_zero Associates.mk_ne_zero
@@ -1539,12 +1041,6 @@ instance [Nontrivial α] : Nontrivial (Associates α) :=
       have : (0 : α) = 1 := ((associated_zero_iff_eq_zero 1).1 this.symm).symm
       zero_ne_one this⟩⟩
 
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 theorem exists_non_zero_rep {a : Associates α} : a ≠ 0 → ∃ a0 : α, a0 ≠ 0 ∧ Associates.mk a0 = a :=
   Quotient.inductionOn a fun b nz => ⟨b, mt (congr_arg Quotient.mk') nz, rfl⟩
 #align associates.exists_non_zero_rep Associates.exists_non_zero_rep
@@ -1574,23 +1070,11 @@ instance [DecidableRel ((· ∣ ·) : α → α → Prop)] :
     DecidableRel ((· ∣ ·) : Associates α → Associates α → Prop) := fun a b =>
   Quotient.recOnSubsingleton₂ a b fun a b => decidable_of_iff' _ mk_dvd_mk
 
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 theorem Prime.le_or_le {p : Associates α} (hp : Prime p) {a b : Associates α} (h : p ≤ a * b) :
     p ≤ a ∨ p ≤ b :=
   hp.2.2 a b h
 #align associates.prime.le_or_le Associates.Prime.le_or_le
 
-/- warning: associates.prime_mk -> Associates.prime_mk is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align associates.prime_mk Associates.prime_mkₓ'. -/
 theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p :=
   by
   rw [Prime, _root_.prime, forall_associated]
@@ -1606,12 +1090,6 @@ theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p :=
   rw [mk_mul_mk, mk_dvd_mk, mk_dvd_mk, mk_dvd_mk]
 #align associates.prime_mk Associates.prime_mk
 
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-Case conversion may be inaccurate. Consider using '#align associates.irreducible_mk Associates.irreducible_mkₓ'. -/
 theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible a :=
   by
   simp only [irreducible_iff, is_unit_mk]
@@ -1627,12 +1105,6 @@ theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible
     simpa [is_unit_mk] using h _ _ a_eq.symm
 #align associates.irreducible_mk Associates.irreducible_mk
 
-/- warning: associates.mk_dvd_not_unit_mk_iff -> Associates.mk_dvdNotUnit_mk_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align associates.mk_dvd_not_unit_mk_iff Associates.mk_dvdNotUnit_mk_iffₓ'. -/
 theorem mk_dvdNotUnit_mk_iff {a b : α} :
     DvdNotUnit (Associates.mk a) (Associates.mk b) ↔ DvdNotUnit a b :=
   by
@@ -1655,12 +1127,6 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
     simp [is_unit_mk, mk_mul_mk, hx]
 #align associates.mk_dvd_not_unit_mk_iff Associates.mk_dvdNotUnit_mk_iff
 
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-Case conversion may be inaccurate. Consider using '#align associates.dvd_not_unit_of_lt Associates.dvdNotUnit_of_ltₓ'. -/
 theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b :=
   by
   constructor; · rintro rfl; apply not_lt_of_le _ hlt; apply dvd_zero
@@ -1671,12 +1137,6 @@ theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b :=
   simp
 #align associates.dvd_not_unit_of_lt Associates.dvdNotUnit_of_lt
 
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-Case conversion may be inaccurate. Consider using '#align associates.irreducible_iff_prime_iff Associates.irreducible_iff_prime_iffₓ'. -/
 theorem irreducible_iff_prime_iff :
     (∀ a : α, Irreducible a ↔ Prime a) ↔ ∀ a : Associates α, Irreducible a ↔ Prime a := by
   simp_rw [forall_associated, irreducible_mk, prime_mk]
@@ -1713,22 +1173,10 @@ instance : CancelCommMonoidWithZero (Associates α) :=
       rw [mul_assoc] at hu
       exact Quotient.sound' ⟨u, mul_left_cancel₀ (mk_ne_zero.1 ha) hu⟩ }
 
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-Case conversion may be inaccurate. Consider using '#align associates.le_of_mul_le_mul_left Associates.le_of_mul_le_mul_leftₓ'. -/
 theorem le_of_mul_le_mul_left (a b c : Associates α) (ha : a ≠ 0) : a * b ≤ a * c → b ≤ c
   | ⟨d, hd⟩ => ⟨d, mul_left_cancel₀ ha <| by rwa [← mul_assoc]⟩
 #align associates.le_of_mul_le_mul_left Associates.le_of_mul_le_mul_left
 
-/- warning: associates.one_or_eq_of_le_of_prime -> Associates.one_or_eq_of_le_of_prime is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_primeₓ'. -/
 theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p → m = 1 ∨ m = p
   | _, m, ⟨hp0, hp1, h⟩, ⟨d, rfl⟩ =>
     match h m d dvd_rfl with
@@ -1751,22 +1199,10 @@ instance : CanonicallyOrderedMonoid (Associates α) :=
     exists_mul_of_le := fun a b => id
     le_self_mul := fun a b => ⟨b, rfl⟩ }
 
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-Case conversion may be inaccurate. Consider using '#align associates.dvd_not_unit_iff_lt Associates.dvdNotUnit_iff_ltₓ'. -/
 theorem dvdNotUnit_iff_lt {a b : Associates α} : DvdNotUnit a b ↔ a < b :=
   dvd_and_not_dvd_iff.symm
 #align associates.dvd_not_unit_iff_lt Associates.dvdNotUnit_iff_lt
 
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-Case conversion may be inaccurate. Consider using '#align associates.le_one_iff Associates.le_one_iffₓ'. -/
 theorem le_one_iff {p : Associates α} : p ≤ 1 ↔ p = 1 := by rw [← Associates.bot_eq_one, le_bot_iff]
 #align associates.le_one_iff Associates.le_one_iff
 
@@ -1815,12 +1251,6 @@ end CommMonoidWithZero
 
 section CancelCommMonoidWithZero
 
-/- warning: is_unit_of_associated_mul -> isUnit_of_associated_mul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_unit_of_associated_mul isUnit_of_associated_mulₓ'. -/
 theorem isUnit_of_associated_mul [CancelCommMonoidWithZero α] {p b : α} (h : Associated (p * b) p)
     (hp : p ≠ 0) : IsUnit b := by
   cases' h with a ha
@@ -1849,12 +1279,6 @@ theorem DvdNotUnit.ne [CancelCommMonoidWithZero α] {p q : α} (h : DvdNotUnit p
 #align dvd_not_unit.ne DvdNotUnit.ne
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pow_injective_of_not_unit pow_injective_of_not_unitₓ'. -/
 theorem pow_injective_of_not_unit [CancelCommMonoidWithZero α] {q : α} (hq : ¬IsUnit q)
     (hq' : q ≠ 0) : Function.Injective fun n : ℕ => q ^ n :=
   by
@@ -1863,12 +1287,6 @@ theorem pow_injective_of_not_unit [CancelCommMonoidWithZero α] {q : α} (hq : 
   · exact (pow_mul_pow_sub q h.le).symm
 #align pow_injective_of_not_unit pow_injective_of_not_unit
 
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-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : α} {q : α}, (Prime.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1) p) -> (forall (n : Nat), 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))))) q (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))))) p n)) (Exists.{1} Nat (fun (i : Nat) => Exists.{0} (LE.le.{0} Nat Nat.hasLe i n) (fun (H : LE.le.{0} Nat Nat.hasLe i n) => Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) q (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))))) p i)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : α} {q : α}, (Prime.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1) p) -> (forall (n : Nat), 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))))) q (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))))) p n)) (Exists.{1} Nat (fun (i : Nat) => And (LE.le.{0} Nat instLENat i n) (Associated.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))) q (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))))) p i)))))
-Case conversion may be inaccurate. Consider using '#align dvd_prime_pow dvd_prime_powₓ'. -/
 theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n : ℕ) :
     q ∣ p ^ n ↔ ∃ i ≤ n, Associated q (p ^ i) :=
   by

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

@@ -134,13 +134,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align comap_prime comap_primeₓ'. -/
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
-    refine'
-        (hp.2.2 (f a) (f b) <| by
-              convert map_dvd f h
-              simp).imp
-          _ _ <;>
-      · intro h
-        convert← map_dvd g h <;> apply hinv⟩
+    refine' (hp.2.2 (f a) (f b) <| by convert map_dvd f h; simp).imp _ _ <;>
+      · intro h; convert← map_dvd g h <;> apply hinv⟩
 #align comap_prime comap_prime
 
 /- warning: mul_equiv.prime_iff -> MulEquiv.prime_iff is a dubious translation:
@@ -184,8 +179,7 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
     (n : ℕ) (h : ¬p ∣ a) (h' : p ^ n ∣ a * b) : p ^ n ∣ b :=
   by
   induction' n with n ih
-  · rw [pow_zero]
-    exact one_dvd b
+  · rw [pow_zero]; exact one_dvd b
   · obtain ⟨c, rfl⟩ := ih (dvd_trans (pow_dvd_pow p n.le_succ) h')
     rw [pow_succ']
     apply mul_dvd_mul_left _ ((hp.dvd_or_dvd _).resolve_left h)
@@ -199,9 +193,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : α} {a : α} {b : α}, (Prime.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1) p) -> (forall (n : Nat), (Not (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) p 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))))) (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))))) p 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)))))) 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))))) (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))))) p n) a))
 Case conversion may be inaccurate. Consider using '#align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_rightₓ'. -/
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
-    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a :=
-  by
-  rw [mul_comm] at h'
+    (n : ℕ) (h : ¬p ∣ b) (h' : p ^ n ∣ a * b) : p ^ n ∣ a := by rw [mul_comm] at h';
   exact hp.pow_dvd_of_dvd_mul_left n h h'
 #align prime.pow_dvd_of_dvd_mul_right Prime.pow_dvd_of_dvd_mul_right
 
@@ -491,11 +483,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α}, (Irreducible.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) -> (Not (IsSquare.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a))
 Case conversion may be inaccurate. Consider using '#align irreducible.not_square Irreducible.not_squareₓ'. -/
-theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a :=
-  by
-  rintro ⟨b, rfl⟩
-  simp only [irreducible_mul_iff, or_self_iff] at ha
-  exact ha.1.not_unit ha.2
+theorem Irreducible.not_square (ha : Irreducible a) : ¬IsSquare a := by rintro ⟨b, rfl⟩;
+  simp only [irreducible_mul_iff, or_self_iff] at ha; exact ha.1.not_unit ha.2
 #align irreducible.not_square Irreducible.not_square
 
 /- warning: is_square.not_irreducible -> IsSquare.not_irreducible is a dubious translation:
@@ -901,10 +890,7 @@ theorem associated_of_dvd_dvd [CancelMonoidWithZero α] {a b : α} (hab : a ∣
   rcases hba with ⟨d, a_eq⟩
   by_cases ha0 : a = 0
   · simp_all
-  have hac0 : a * c ≠ 0 := by
-    intro con
-    rw [Con, MulZeroClass.zero_mul] at a_eq
-    apply ha0 a_eq
+  have hac0 : a * c ≠ 0 := by intro con; rw [Con, MulZeroClass.zero_mul] at a_eq; apply ha0 a_eq
   have : a * (c * d) = a * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
   have hcd : c * d = 1 := mul_left_cancel₀ ha0 this
   have : a * c * (d * c) = a * c * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
@@ -966,10 +952,7 @@ protected theorem Associated.prime [CommMonoidWithZero α] {p q : α} (h : p ~
   ⟨h.neZero_iff.1 hp.NeZero,
     let ⟨u, hu⟩ := h
     ⟨fun ⟨v, hv⟩ => hp.not_unit ⟨v * u⁻¹, by simp [hv, hu.symm]⟩,
-      hu ▸ by
-        simp [Units.mul_right_dvd]
-        intro a b
-        exact hp.dvd_or_dvd⟩⟩
+      hu ▸ by simp [Units.mul_right_dvd]; intro a b; exact hp.dvd_or_dvd⟩⟩
 #align associated.prime Associated.prime
 -/
 
@@ -1107,18 +1090,13 @@ theorem units_eq_one (u : αˣ) : u = 1 :=
 theorem associated_iff_eq {x y : α} : x ~ᵤ y ↔ x = y :=
   by
   constructor
-  · rintro ⟨c, rfl⟩
-    rw [units_eq_one c, Units.val_one, mul_one]
-  · rintro rfl
-    rfl
+  · rintro ⟨c, rfl⟩; rw [units_eq_one c, Units.val_one, mul_one]
+  · rintro rfl; rfl
 #align associated_iff_eq associated_iff_eq
 -/
 
 #print associated_eq_eq /-
-theorem associated_eq_eq : (Associated : α → α → Prop) = Eq :=
-  by
-  ext
-  rw [associated_iff_eq]
+theorem associated_eq_eq : (Associated : α → α → Prop) = Eq := by ext; rw [associated_iff_eq]
 #align associated_eq_eq associated_eq_eq
 -/
 
@@ -1137,18 +1115,14 @@ variable {R : Type _} [CancelCommMonoidWithZero R] [Unique Rˣ] {p₁ p₂ : R}
 
 #print eq_of_prime_pow_eq /-
 theorem eq_of_prime_pow_eq (hp₁ : Prime p₁) (hp₂ : Prime p₂) (hk₁ : 0 < k₁)
-    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ :=
-  by
-  rw [← associated_iff_eq] at h⊢
+    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h⊢;
   apply h.of_pow_associated_of_prime hp₁ hp₂ hk₁
 #align eq_of_prime_pow_eq eq_of_prime_pow_eq
 -/
 
 #print eq_of_prime_pow_eq' /-
 theorem eq_of_prime_pow_eq' (hp₁ : Prime p₁) (hp₂ : Prime p₂) (hk₁ : 0 < k₂)
-    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ :=
-  by
-  rw [← associated_iff_eq] at h⊢
+    (h : p₁ ^ k₁ = p₂ ^ k₂) : p₁ = p₂ := by rw [← associated_iff_eq] at h⊢;
   apply h.of_pow_associated_of_prime' hp₁ hp₂ hk₁
 #align eq_of_prime_pow_eq' eq_of_prime_pow_eq'
 -/
@@ -1255,10 +1229,7 @@ theorem exists_rep [Monoid α] (a : Associates α) : ∃ a0 : α, Associates.mk
 instance [Monoid α] [Subsingleton α] : Unique (Associates α)
     where
   default := 1
-  uniq a := by
-    apply Quotient.recOnSubsingleton₂
-    intro a b
-    congr
+  uniq a := by apply Quotient.recOnSubsingleton₂; intro a b; congr
 
 #print Associates.mk_injective /-
 theorem mk_injective [Monoid α] [Unique (Units α)] : Function.Injective (@Associates.mk α _) :=
@@ -1587,13 +1558,9 @@ variable [CommMonoidWithZero α]
 instance : CommMonoidWithZero (Associates α) :=
   { Associates.commMonoid,
     Associates.hasZero with
-    zero_mul := by
-      rintro ⟨a⟩
-      show Associates.mk (0 * a) = Associates.mk 0
+    zero_mul := by rintro ⟨a⟩; show Associates.mk (0 * a) = Associates.mk 0;
       rw [MulZeroClass.zero_mul]
-    mul_zero := by
-      rintro ⟨a⟩
-      show Associates.mk (a * 0) = Associates.mk 0
+    mul_zero := by rintro ⟨a⟩; show Associates.mk (a * 0) = Associates.mk 0;
       rw [MulZeroClass.mul_zero] }
 
 instance : OrderTop (Associates α) where
@@ -1628,12 +1595,9 @@ theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p :=
   by
   rw [Prime, _root_.prime, forall_associated]
   trans
-  · apply and_congr
-    rfl
-    apply and_congr
-    rfl
-    apply forall_congr'
-    intro a
+  · apply and_congr; rfl
+    apply and_congr; rfl
+    apply forall_congr'; intro a
     exact forall_associated
   apply and_congr mk_ne_zero
   apply and_congr
@@ -1675,8 +1639,7 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
   rw [DvdNotUnit, DvdNotUnit, mk_ne_zero]
   apply and_congr_right; intro ane0
   constructor
-  · contrapose!
-    rw [forall_associated]
+  · contrapose!; rw [forall_associated]
     intro h x hx hbax
     rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax
     cases' hbax with u hu
@@ -1700,10 +1663,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align associates.dvd_not_unit_of_lt Associates.dvdNotUnit_of_ltₓ'. -/
 theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b :=
   by
-  constructor;
-  · rintro rfl
-    apply not_lt_of_le _ hlt
-    apply dvd_zero
+  constructor; · rintro rfl; apply not_lt_of_le _ hlt; apply dvd_zero
   rcases hlt with ⟨⟨x, rfl⟩, ndvd⟩
   refine' ⟨x, _, rfl⟩
   contrapose! ndvd

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

@@ -130,7 +130,7 @@ variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomCla
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u1} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u4}} [_inst_3 : MonoidWithZeroHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u1} α (coeFn.{succ u4, max (succ u2) (succ u1)} G (fun (_x : G) => β -> α) (FunLike.hasCoeToFun.{succ u4, succ u2, succ u1} G β (fun (_x : β) => α) (MulHomClass.toFunLike.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) _inst_4)) g (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f a)) a) -> (Prime.{u2} β _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f p)) -> (Prime.{u1} α _inst_1 p)
 but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
+  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align comap_prime comap_primeₓ'. -/
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
@@ -1314,7 +1314,7 @@ protected def mkMonoidHom : α →* Associates α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (fun (_x : MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) => α -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHom.hasCoeToFun.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align associates.mk_monoid_hom_apply Associates.mkMonoidHom_applyₓ'. -/
 @[simp]
 theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a :=
@@ -1325,7 +1325,7 @@ theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align associates.associated_map_mk Associates.associated_map_mkₓ'. -/
 theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInverse f Associates.mk)
     (a : α) : a ~ᵤ f (Associates.mk a) :=

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

@@ -1344,7 +1344,7 @@ theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n
 
 /- warning: associates.dvd_eq_le -> Associates.dvd_eq_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (Dvd.Dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))))) (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (Dvd.Dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))))) (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9649 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9651 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9649 x._@.Mathlib.Algebra.Associated._hyg.9651) (fun (x._@.Mathlib.Algebra.Associated._hyg.9664 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9666 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9664 x._@.Mathlib.Algebra.Associated._hyg.9666)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_eq_le Associates.dvd_eq_leₓ'. -/
@@ -1436,7 +1436,7 @@ section Order
 
 /- warning: associates.mul_mono -> Associates.mul_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {c : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {d : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) c d) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) a c) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) b d))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {c : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {d : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) c d) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) a c) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) b d))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {c : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {d : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) c d) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instMulAssociatesToMonoid.{u1} α _inst_1)) a c) (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instMulAssociatesToMonoid.{u1} α _inst_1)) b d))
 Case conversion may be inaccurate. Consider using '#align associates.mul_mono Associates.mul_monoₓ'. -/
@@ -1448,7 +1448,7 @@ theorem mul_mono {a b c d : Associates α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a
 
 /- warning: associates.one_le -> Associates.one_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (OfNat.ofNat.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) 1 (OfNat.mk.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) 1 (One.one.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) a
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (OfNat.ofNat.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) 1 (OfNat.mk.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) 1 (One.one.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) a
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) (OfNat.ofNat.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) 1 (One.toOfNat1.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instOneAssociates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)))) a
 Case conversion may be inaccurate. Consider using '#align associates.one_le Associates.one_leₓ'. -/
@@ -1458,7 +1458,7 @@ theorem one_le {a : Associates α} : 1 ≤ a :=
 
 /- warning: associates.le_mul_right -> Associates.le_mul_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) a b)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) a b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instMulAssociatesToMonoid.{u1} α _inst_1)) a b)
 Case conversion may be inaccurate. Consider using '#align associates.le_mul_right Associates.le_mul_rightₓ'. -/
@@ -1468,7 +1468,7 @@ theorem le_mul_right {a b : Associates α} : a ≤ a * b :=
 
 /- warning: associates.le_mul_left -> Associates.le_mul_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) b a)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.hasMul.{u1} α _inst_1)) b a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)} {b : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)}, LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) a (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (instHMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instMulAssociatesToMonoid.{u1} α _inst_1)) b a)
 Case conversion may be inaccurate. Consider using '#align associates.le_mul_left Associates.le_mul_leftₓ'. -/
@@ -1483,7 +1483,7 @@ end Order
 
 /- warning: associates.dvd_of_mk_le_mk -> Associates.dvd_of_mk_le_mk is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mkₓ'. -/
@@ -1501,7 +1501,7 @@ theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a 
 
 /- warning: associates.mk_le_mk_of_dvd -> Associates.mk_le_mk_of_dvd is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b) -> (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b))
 Case conversion may be inaccurate. Consider using '#align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvdₓ'. -/
@@ -1511,7 +1511,7 @@ theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.
 
 /- warning: associates.mk_le_mk_iff_dvd_iff -> Associates.mk_le_mk_iff_dvd_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, Iff (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, Iff (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {a : α} {b : α}, Iff (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) b)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (Monoid.toSemigroup.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) a b)
 Case conversion may be inaccurate. Consider using '#align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd_iffₓ'. -/
@@ -1609,7 +1609,7 @@ instance [DecidableRel ((· ∣ ·) : α → α → Prop)] :
 
 /- warning: associates.prime.le_or_le -> Associates.Prime.le_or_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (Prime.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.commMonoidWithZero.{u1} α _inst_1) p) -> (forall {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (instHMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.hasMul.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b)) -> (Or (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p b)))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (Prime.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.commMonoidWithZero.{u1} α _inst_1) p) -> (forall {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (instHMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.hasMul.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b)) -> (Or (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toHasLe.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (Prime.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α _inst_1) p) -> (forall {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p (HMul.hMul.{u1, u1, u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (instHMul.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instMulAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b)) -> (Or (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p a) (LE.le.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLE.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) p b)))
 Case conversion may be inaccurate. Consider using '#align associates.prime.le_or_le Associates.Prime.le_or_leₓ'. -/
@@ -1694,7 +1694,7 @@ theorem mk_dvdNotUnit_mk_iff {a b : α} :
 
 /- warning: associates.dvd_not_unit_of_lt -> Associates.dvdNotUnit_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLT.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b) -> (DvdNotUnit.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.commMonoidWithZero.{u1} α _inst_1) a b)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toHasLt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.preorder.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b) -> (DvdNotUnit.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.commMonoidWithZero.{u1} α _inst_1) a b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} α] {a : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))} {b : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))}, (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Preorder.toLT.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instPreorderAssociatesToMonoid.{u1} α (CommMonoidWithZero.toCommMonoid.{u1} α _inst_1))) a b) -> (DvdNotUnit.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (Associates.instCommMonoidWithZeroAssociatesToMonoidToMonoidWithZero.{u1} α _inst_1) a b)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_not_unit_of_lt Associates.dvdNotUnit_of_ltₓ'. -/
@@ -1755,7 +1755,7 @@ instance : CancelCommMonoidWithZero (Associates α) :=
 
 /- warning: associates.le_of_mul_le_mul_left -> Associates.le_of_mul_le_mul_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (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)))) (c : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Ne.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a (OfNat.ofNat.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 0 (OfNat.mk.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 0 (Zero.zero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.hasZero.{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)))))))) -> (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)))) (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} (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 c)) -> (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 c)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (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)))) (c : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Ne.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a (OfNat.ofNat.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 0 (OfNat.mk.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 0 (Zero.zero.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.hasZero.{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)))))))) -> (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)))) (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} (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 c)) -> (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 c)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (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)))) (c : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Ne.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) a (OfNat.ofNat.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) 0 (Zero.toOfNat0.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Associates.instZeroAssociates.{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))))))) -> (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)))) (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} (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 c)) -> (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 c)
 Case conversion may be inaccurate. Consider using '#align associates.le_of_mul_le_mul_left Associates.le_of_mul_le_mul_leftₓ'. -/
@@ -1765,7 +1765,7 @@ theorem le_of_mul_le_mul_left (a b c : Associates α) (ha : a ≠ 0) : a * b ≤
 
 /- warning: associates.one_or_eq_of_le_of_prime -> Associates.one_or_eq_of_le_of_prime is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (m : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Prime.{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)) p) -> (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)))) m p) -> (Or (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m (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)))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m p))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (m : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Prime.{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)) p) -> (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)))) m p) -> (Or (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m (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)))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m p))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] (p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (m : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))), (Prime.{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)) p) -> (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)))) m p) -> (Or (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m (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))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) m p))
 Case conversion may be inaccurate. Consider using '#align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_primeₓ'. -/
@@ -1793,7 +1793,7 @@ instance : CanonicallyOrderedMonoid (Associates α) :=
 
 /- warning: associates.dvd_not_unit_iff_lt -> Associates.dvdNotUnit_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {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)))}, Iff (DvdNotUnit.{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)) a b) (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLT.{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)))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {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)))}, Iff (DvdNotUnit.{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)) a b) (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toHasLt.{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)))) a b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {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)))}, Iff (DvdNotUnit.{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)) a b) (LT.lt.{u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) (Preorder.toLT.{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)))) a b)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_not_unit_iff_lt Associates.dvdNotUnit_iff_ltₓ'. -/
@@ -1803,7 +1803,7 @@ theorem dvdNotUnit_iff_lt {a b : Associates α} : DvdNotUnit a b ↔ a < b :=
 
 /- warning: associates.le_one_iff -> Associates.le_one_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))}, Iff (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)))) p (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)))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) p (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))))))))
+  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))}, Iff (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)))) p (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)))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) p (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))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {p : Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))}, Iff (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)))) p (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))))))) (Eq.{succ u1} (Associates.{u1} α (MonoidWithZero.toMonoid.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))) p (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)))))))
 Case conversion may be inaccurate. Consider using '#align associates.le_one_iff Associates.le_one_iffₓ'. -/

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

@@ -140,7 +140,7 @@ theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime
               simp).imp
           _ _ <;>
       · intro h
-        convert ← map_dvd g h <;> apply hinv⟩
+        convert← map_dvd g h <;> apply hinv⟩
 #align comap_prime comap_prime
 
 /- warning: mul_equiv.prime_iff -> MulEquiv.prime_iff is a dubious translation:
@@ -1346,7 +1346,7 @@ theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (Dvd.Dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))))) (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9347 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9349 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9347 x._@.Mathlib.Algebra.Associated._hyg.9349) (fun (x._@.Mathlib.Algebra.Associated._hyg.9362 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9364 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9362 x._@.Mathlib.Algebra.Associated._hyg.9364)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9649 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9651 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9649 x._@.Mathlib.Algebra.Associated._hyg.9651) (fun (x._@.Mathlib.Algebra.Associated._hyg.9664 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9666 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9664 x._@.Mathlib.Algebra.Associated._hyg.9666)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_eq_le Associates.dvd_eq_leₓ'. -/
 theorem dvd_eq_le : ((· ∣ ·) : Associates α → Associates α → Prop) = (· ≤ ·) :=
   rfl

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

@@ -130,7 +130,7 @@ variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomCla
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u1} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u4}} [_inst_3 : MonoidWithZeroHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u1} α (coeFn.{succ u4, max (succ u2) (succ u1)} G (fun (_x : G) => β -> α) (FunLike.hasCoeToFun.{succ u4, succ u2, succ u1} G β (fun (_x : β) => α) (MulHomClass.toFunLike.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) _inst_4)) g (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f a)) a) -> (Prime.{u2} β _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f p)) -> (Prime.{u1} α _inst_1 p)
 but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
+  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align comap_prime comap_primeₓ'. -/
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
@@ -1314,7 +1314,7 @@ protected def mkMonoidHom : α →* Associates α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (fun (_x : MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) => α -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHom.hasCoeToFun.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align associates.mk_monoid_hom_apply Associates.mkMonoidHom_applyₓ'. -/
 @[simp]
 theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a :=
@@ -1325,7 +1325,7 @@ theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align associates.associated_map_mk Associates.associated_map_mkₓ'. -/
 theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInverse f Associates.mk)
     (a : α) : a ~ᵤ f (Associates.mk a) :=
@@ -1346,7 +1346,7 @@ theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (Dvd.Dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))))) (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9338 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9340 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9338 x._@.Mathlib.Algebra.Associated._hyg.9340) (fun (x._@.Mathlib.Algebra.Associated._hyg.9353 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9355 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9353 x._@.Mathlib.Algebra.Associated._hyg.9355)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9347 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9349 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9347 x._@.Mathlib.Algebra.Associated._hyg.9349) (fun (x._@.Mathlib.Algebra.Associated._hyg.9362 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9364 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9362 x._@.Mathlib.Algebra.Associated._hyg.9364)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_eq_le Associates.dvd_eq_leₓ'. -/
 theorem dvd_eq_le : ((· ∣ ·) : Associates α → Associates α → Prop) = (· ≤ ·) :=
   rfl

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

@@ -329,7 +329,7 @@ Case conversion may be inaccurate. Consider using '#align not_irreducible_zero n
 @[simp]
 theorem not_irreducible_zero [MonoidWithZero α] : ¬Irreducible (0 : α)
   | ⟨hn0, h⟩ =>
-    have : IsUnit (0 : α) ∨ IsUnit (0 : α) := h 0 0 (mul_zero 0).symm
+    have : IsUnit (0 : α) ∨ IsUnit (0 : α) := h 0 0 (MulZeroClass.mul_zero 0).symm
     this.elim hn0 hn0
 #align not_irreducible_zero not_irreducible_zero
 
@@ -903,7 +903,7 @@ theorem associated_of_dvd_dvd [CancelMonoidWithZero α] {a b : α} (hab : a ∣
   · simp_all
   have hac0 : a * c ≠ 0 := by
     intro con
-    rw [Con, zero_mul] at a_eq
+    rw [Con, MulZeroClass.zero_mul] at a_eq
     apply ha0 a_eq
   have : a * (c * d) = a * 1 := by rw [← mul_assoc, ← a_eq, mul_one]
   have hcd : c * d = 1 := mul_left_cancel₀ ha0 this
@@ -1590,15 +1590,15 @@ instance : CommMonoidWithZero (Associates α) :=
     zero_mul := by
       rintro ⟨a⟩
       show Associates.mk (0 * a) = Associates.mk 0
-      rw [zero_mul]
+      rw [MulZeroClass.zero_mul]
     mul_zero := by
       rintro ⟨a⟩
       show Associates.mk (a * 0) = Associates.mk 0
-      rw [mul_zero] }
+      rw [MulZeroClass.mul_zero] }
 
 instance : OrderTop (Associates α) where
   top := 0
-  le_top a := ⟨0, (mul_zero a).symm⟩
+  le_top a := ⟨0, (MulZeroClass.mul_zero a).symm⟩
 
 instance : BoundedOrder (Associates α) :=
   { Associates.orderTop, Associates.orderBot with }

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

@@ -130,7 +130,7 @@ variable [CommMonoidWithZero β] {F : Type _} {G : Type _} [MonoidWithZeroHomCla
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u1} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u4}} [_inst_3 : MonoidWithZeroHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u1} α (coeFn.{succ u4, max (succ u2) (succ u1)} G (fun (_x : G) => β -> α) (FunLike.hasCoeToFun.{succ u4, succ u2, succ u1} G β (fun (_x : β) => α) (MulHomClass.toFunLike.{u4, u2, u1} G β α (MulZeroClass.toHasMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) _inst_4)) g (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f a)) a) -> (Prime.{u2} β _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F α (fun (_x : α) => β) (MulHomClass.toFunLike.{u3, u1, u2} F α β (MulOneClass.toHasMul.{u1} α (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (MulOneClass.toHasMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u1, u2} F α β (MulZeroOneClass.toMulOneClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u1, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3)))) f p)) -> (Prime.{u1} α _inst_1 p)
 but is expected to have type
-  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
+  forall {α : Type.{u4}} {β : Type.{u2}} [_inst_1 : CommMonoidWithZero.{u4} α] [_inst_2 : CommMonoidWithZero.{u2} β] {F : Type.{u3}} {G : Type.{u1}} [_inst_3 : MonoidWithZeroHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))] [_inst_4 : MulHomClass.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))))] (f : F) (g : G) {p : α}, (forall (a : α), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : β) => α) (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (a : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) a) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) (FunLike.coe.{succ u1, succ u2, succ u4} G β (fun (_x : β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : β) => α) _x) (MulHomClass.toFunLike.{u1, u2, u4} G β α (MulZeroClass.toMul.{u2} β (MulZeroOneClass.toMulZeroClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MulZeroClass.toMul.{u4} α (MulZeroOneClass.toMulZeroClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) _inst_4) g (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f a)) a) -> (Prime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) p) _inst_2 (FunLike.coe.{succ u3, succ u4, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => β) _x) (MulHomClass.toFunLike.{u3, u4, u2} F α β (MulOneClass.toMul.{u4} α (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)))) (MulOneClass.toMul.{u2} β (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)))) (MonoidHomClass.toMulHomClass.{u3, u4, u2} F α β (MulZeroOneClass.toMulOneClass.{u4} α (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1))) (MulZeroOneClass.toMulOneClass.{u2} β (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2))) (MonoidWithZeroHomClass.toMonoidHomClass.{u3, u4, u2} F α β (MonoidWithZero.toMulZeroOneClass.{u4} α (CommMonoidWithZero.toMonoidWithZero.{u4} α _inst_1)) (MonoidWithZero.toMulZeroOneClass.{u2} β (CommMonoidWithZero.toMonoidWithZero.{u2} β _inst_2)) _inst_3))) f p)) -> (Prime.{u4} α _inst_1 p)
 Case conversion may be inaccurate. Consider using '#align comap_prime comap_primeₓ'. -/
 theorem comap_prime (hinv : ∀ a, g (f a : β) = a) (hp : Prime (f p)) : Prime p :=
   ⟨fun h => hp.1 <| by simp [h], fun h => hp.2.1 <| h.map f, fun a b h => by
@@ -1314,7 +1314,7 @@ protected def mkMonoidHom : α →* Associates α :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (fun (_x : MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) => α -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHom.hasCoeToFun.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1)))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) a) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (fun (_x : α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : α) => Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))))) (Associates.mkMonoidHom.{u1} α _inst_1) a) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align associates.mk_monoid_hom_apply Associates.mkMonoidHom_applyₓ'. -/
 @[simp]
 theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a :=
@@ -1325,7 +1325,7 @@ theorem mkMonoidHom_apply (a : α) : Associates.mkMonoidHom a = Associates.mk a
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (fun (_x : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) => (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> α) (MonoidHom.hasCoeToFun.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α] {f : MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))}, (Function.RightInverse.{succ u1, succ u1} α (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f) (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) -> (forall (a : α), Associated.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (fun (_x : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (MulOneClass.toMul.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))) (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (MonoidHom.monoidHomClass.{u1, u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) α (Monoid.toMulOneClass.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1))) (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1))))) f (Associates.mk.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align associates.associated_map_mk Associates.associated_map_mkₓ'. -/
 theorem associated_map_mk {f : Associates α →* α} (hinv : Function.RightInverse f Associates.mk)
     (a : α) : a ~ᵤ f (Associates.mk a) :=

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

@@ -1346,7 +1346,7 @@ theorem mk_pow (a : α) (n : ℕ) : Associates.mk (a ^ n) = Associates.mk a ^ n
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (Dvd.Dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.commMonoid.{u1} α _inst_1))))) (LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.preorder.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9342 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9344 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9342 x._@.Mathlib.Algebra.Associated._hyg.9344) (fun (x._@.Mathlib.Algebra.Associated._hyg.9357 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9359 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9357 x._@.Mathlib.Algebra.Associated._hyg.9359)
+  forall {α : Type.{u1}} [_inst_1 : CommMonoid.{u1} α], Eq.{succ u1} ((Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) -> Prop) (fun (x._@.Mathlib.Algebra.Associated._hyg.9338 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9340 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => Dvd.dvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (semigroupDvd.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Monoid.toSemigroup.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (CommMonoid.toMonoid.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instCommMonoidAssociatesToMonoid.{u1} α _inst_1)))) x._@.Mathlib.Algebra.Associated._hyg.9338 x._@.Mathlib.Algebra.Associated._hyg.9340) (fun (x._@.Mathlib.Algebra.Associated._hyg.9353 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (x._@.Mathlib.Algebra.Associated._hyg.9355 : Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) => LE.le.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Preorder.toLE.{u1} (Associates.{u1} α (CommMonoid.toMonoid.{u1} α _inst_1)) (Associates.instPreorderAssociatesToMonoid.{u1} α _inst_1)) x._@.Mathlib.Algebra.Associated._hyg.9353 x._@.Mathlib.Algebra.Associated._hyg.9355)
 Case conversion may be inaccurate. Consider using '#align associates.dvd_eq_le Associates.dvd_eq_leₓ'. -/
 theorem dvd_eq_le : ((· ∣ ·) : Associates α → Associates α → Prop) = (· ≤ ·) :=
   rfl

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

• consistently use the YYYY-MM-DD format
• when easily possible, put the date on the same line as the deprecated attribute
• when easily possible, format the entire declaration on the same line

Why these changes?

• consistency makes it easier for tools to parse this information
• compactness: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
• putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

@@ -1026,7 +1026,7 @@ theorem isPrimal_mk {a : α} : IsPrimal (Associates.mk a) ↔ IsPrimal a := by
     exact ⟨a₁, a₂ * u, h₁, Units.mul_right_dvd.mpr h₂, mul_assoc _ _ _⟩
   · exact ⟨a₁, a₂, h₁, h₂, congr_arg _ eq⟩
 
-@[deprecated] alias isPrimal_iff := isPrimal_mk -- 2024/03/16
+@[deprecated] alias isPrimal_iff := isPrimal_mk -- 2024-03-16
 
 @[simp]
 theorem decompositionMonoid_iff : DecompositionMonoid (Associates α) ↔ DecompositionMonoid α := by

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

@@ -9,8 +9,20 @@ import Mathlib.Algebra.Parity
 
 /-!
 # Associated, prime, and irreducible elements.
--/
 
+In this file we define the predicate `Prime p`
+saying that an element of a commutative monoid with zero is prime.
+Namely, `Prime p` means that `p` isn't zero, it isn't a unit,
+and `p ∣ a * b → p ∣ a ∨ p ∣ b` for all `a`, `b`;
+
+In decomposition monoids (e.g., `ℕ`, `ℤ`), this predicate is equivalent to `Irreducible`,
+however this is not true in general.
+
+We also define an equivalence relation `Associated`
+saying that two elements of a monoid differ by a multiplication by a unit.
+Then we show that the quotient type `Associates` is a monoid
+and prove basic properties of this quotient.
+-/
 
 variable {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
 
@@ -18,7 +30,8 @@ section Prime
 
 variable [CommMonoidWithZero α]
 
-/-- prime element of a `CommMonoidWithZero` -/
+/-- An element `p` of a commutative monoid with zero (e.g., a ring) is called *prime*,
+if it's not zero, not a unit, and `p ∣ a * b → p ∣ a ∨ p ∣ b` for all `a`, `b`. -/
 def Prime (p : α) : Prop :=
   p ≠ 0 ∧ ¬IsUnit p ∧ ∀ a b, p ∣ a * b → p ∣ a ∨ p ∣ b
 #align prime Prime
@@ -433,6 +446,7 @@ theorem unit_associated_one [Monoid α] {u : αˣ} : (u : α) ~ᵤ 1 :=
   ⟨u⁻¹, Units.mul_inv u⟩
 #align unit_associated_one unit_associated_one
 
+@[simp]
 theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsUnit a :=
   Iff.intro
     (fun h =>
@@ -441,6 +455,7 @@ theorem associated_one_iff_isUnit [Monoid α] {a : α} : (a : α) ~ᵤ 1 ↔ IsU
     fun ⟨c, h⟩ => Associated.symm ⟨c, by simp [h]⟩
 #align associated_one_iff_is_unit associated_one_iff_isUnit
 
+@[simp]
 theorem associated_zero_iff_eq_zero [MonoidWithZero α] (a : α) : a ~ᵤ 0 ↔ a = 0 :=
   Iff.intro
     (fun h => by
@@ -555,7 +570,7 @@ theorem associated_of_dvd_dvd [CancelMonoidWithZero α] {a b : α} (hab : a ∣
   rcases hab with ⟨c, rfl⟩
   rcases hba with ⟨d, a_eq⟩
   by_cases ha0 : a = 0
-  · simp_all; rfl
+  · simp_all
   have hac0 : a * c ≠ 0 := by
     intro con
     rw [con, zero_mul] at a_eq
@@ -584,12 +599,9 @@ theorem Associated.dvd_iff_dvd_right [Monoid α] {a b c : α} (h : b ~ᵤ c) : a
   hu ▸ Units.dvd_mul_right.symm
 #align associated.dvd_iff_dvd_right Associated.dvd_iff_dvd_right
 
-theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a = 0 ↔ b = 0 :=
-  ⟨fun ha => by
-    let ⟨u, hu⟩ := h
-    simp [hu.symm, ha], fun hb => by
-    let ⟨u, hu⟩ := h.symm
-    simp [hu.symm, hb]⟩
+theorem Associated.eq_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a = 0 ↔ b = 0 := by
+  obtain ⟨u, rfl⟩ := h
+  rw [← Units.eq_mul_inv_iff_mul_eq, zero_mul]
 #align associated.eq_zero_iff Associated.eq_zero_iff
 
 theorem Associated.ne_zero_iff [MonoidWithZero α] {a b : α} (h : a ~ᵤ b) : a ≠ 0 ↔ b ≠ 0 :=
@@ -843,6 +855,10 @@ theorem one_eq_mk_one [Monoid α] : (1 : Associates α) = Associates.mk 1 :=
   rfl
 #align associates.one_eq_mk_one Associates.one_eq_mk_one
 
+@[simp]
+theorem mk_eq_one [Monoid α] {a : α} : Associates.mk a = 1 ↔ IsUnit a := by
+  rw [← mk_one, mk_eq_mk_iff_associated, associated_one_iff_isUnit]
+
 instance [Monoid α] : Bot (Associates α) :=
   ⟨1⟩
 
@@ -857,11 +873,7 @@ theorem exists_rep [Monoid α] (a : Associates α) : ∃ a0 : α, Associates.mk
 instance [Monoid α] [Subsingleton α] :
     Unique (Associates α) where
   default := 1
-  uniq a := by
-    apply Quotient.recOnSubsingleton₂
-    intro a b
-    congr
-    simp [eq_iff_true_of_subsingleton]
+  uniq := forall_associated.2 fun _ ↦ mk_eq_one.2 <| isUnit_of_subsingleton _
 
 theorem mk_injective [Monoid α] [Unique (Units α)] : Function.Injective (@Associates.mk α _) :=
   fun _ _ h => associated_iff_eq.mp (Associates.mk_eq_mk_iff_associated.mp h)
@@ -872,11 +884,7 @@ section CommMonoid
 variable [CommMonoid α]
 
 instance instMul : Mul (Associates α) :=
-  ⟨fun a' b' =>
-    (Quotient.liftOn₂ a' b' fun a b => ⟦a * b⟧) fun a₁ a₂ b₁ b₂ ⟨c₁, h₁⟩ ⟨c₂, h₂⟩ =>
-      Quotient.sound <| ⟨c₁ * c₂, by
-        rw [← h₁, ← h₂]
-        simp only [Units.val_mul, mul_left_comm, mul_comm]⟩⟩
+  ⟨Quotient.map₂ (· * ·) fun _ _ h₁ _ _ h₂ ↦ h₁.mul_mul h₂⟩
 
 theorem mk_mul_mk {x y : α} : Associates.mk x * Associates.mk y = Associates.mk (x * y) :=
   rfl
@@ -986,45 +994,48 @@ instance instOrderBot : OrderBot (Associates α) where
 
 end Order
 
-theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a ∣ b
-  | ⟨c', hc'⟩ =>
-    let step : ∀ (c : α),
-      Associates.mk b = Associates.mk a * Quotient.mk (Associated.setoid α) c → a ∣ b := by
-      intro c hc
-      let ⟨d, hd⟩ := (Quotient.exact hc).symm
-      exact ⟨↑d * c,
-          calc
-            b = a * c * ↑d := hd.symm
-            _ = a * (↑d * c) := by ac_rfl
-            ⟩
-    Quotient.inductionOn c' step hc'
+@[simp]
+theorem mk_dvd_mk {a b : α} : Associates.mk a ∣ Associates.mk b ↔ a ∣ b := by
+  simp only [dvd_def, mk_surjective.exists, mk_mul_mk, mk_eq_mk_iff_associated,
+    Associated.comm (x := b)]
+  constructor
+  · rintro ⟨x, u, rfl⟩
+    exact ⟨_, mul_assoc ..⟩
+  · rintro ⟨c, rfl⟩
+    use c
+#align associates.mk_dvd_mk Associates.mk_dvd_mk
+
+theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a ∣ b :=
+  mk_dvd_mk.mp
 #align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mk
 
-theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.mk b := fun ⟨c, hc⟩ =>
-  ⟨Associates.mk c, by simp only [hc, mk_mul_mk]⟩
+theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.mk b :=
+  mk_dvd_mk.mpr
 #align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvd
 
-theorem mk_le_mk_iff_dvd_iff {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=
-  Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
-#align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd_iff
+theorem mk_le_mk_iff_dvd {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b := mk_dvd_mk
+#align associates.mk_le_mk_iff_dvd_iff Associates.mk_le_mk_iff_dvd
 
-theorem mk_dvd_mk {a b : α} : Associates.mk a ∣ Associates.mk b ↔ a ∣ b :=
-  Iff.intro dvd_of_mk_le_mk mk_le_mk_of_dvd
-#align associates.mk_dvd_mk Associates.mk_dvd_mk
+@[deprecated] alias mk_le_mk_iff_dvd_iff := mk_le_mk_iff_dvd
 
-theorem isPrimal_iff {a : α} : IsPrimal (Associates.mk a) ↔ IsPrimal a := by
+@[simp]
+theorem isPrimal_mk {a : α} : IsPrimal (Associates.mk a) ↔ IsPrimal a := by
   simp_rw [IsPrimal, forall_associated, mk_surjective.exists, mk_mul_mk, mk_dvd_mk]
   constructor <;> intro h b c dvd <;> obtain ⟨a₁, a₂, h₁, h₂, eq⟩ := @h b c dvd
   · obtain ⟨u, rfl⟩ := mk_eq_mk_iff_associated.mp eq.symm
     exact ⟨a₁, a₂ * u, h₁, Units.mul_right_dvd.mpr h₂, mul_assoc _ _ _⟩
   · exact ⟨a₁, a₂, h₁, h₂, congr_arg _ eq⟩
 
+@[deprecated] alias isPrimal_iff := isPrimal_mk -- 2024/03/16
+
+@[simp]
 theorem decompositionMonoid_iff : DecompositionMonoid (Associates α) ↔ DecompositionMonoid α := by
-  simp_rw [_root_.decompositionMonoid_iff, forall_associated, isPrimal_iff]
+  simp_rw [_root_.decompositionMonoid_iff, forall_associated, isPrimal_mk]
 
 instance instDecompositionMonoid [DecompositionMonoid α] : DecompositionMonoid (Associates α) :=
   decompositionMonoid_iff.mpr ‹_›
 
+@[simp]
 theorem mk_isRelPrime_iff {a b : α} :
     IsRelPrime (Associates.mk a) (Associates.mk b) ↔ IsRelPrime a b := by
   simp_rw [IsRelPrime, forall_associated, mk_dvd_mk, isUnit_mk]
@@ -1037,6 +1048,8 @@ instance [Zero α] [Monoid α] : Zero (Associates α) :=
 instance [Zero α] [Monoid α] : Top (Associates α) :=
   ⟨0⟩
 
+@[simp] theorem mk_zero [Zero α] [Monoid α] : Associates.mk (0 : α) = 0 := rfl
+
 section MonoidWithZero
 
 variable [MonoidWithZero α]
@@ -1046,15 +1059,15 @@ theorem mk_eq_zero {a : α} : Associates.mk a = 0 ↔ a = 0 :=
   ⟨fun h => (associated_zero_iff_eq_zero a).1 <| Quotient.exact h, fun h => h.symm ▸ rfl⟩
 #align associates.mk_eq_zero Associates.mk_eq_zero
 
+@[simp]
+theorem quot_out_zero : Quot.out (0 : Associates α) = 0 := by rw [← mk_eq_zero, quot_out]
+
 theorem mk_ne_zero {a : α} : Associates.mk a ≠ 0 ↔ a ≠ 0 :=
   not_congr mk_eq_zero
 #align associates.mk_ne_zero Associates.mk_ne_zero
 
 instance [Nontrivial α] : Nontrivial (Associates α) :=
-  ⟨⟨0, 1, fun h =>
-      have : (0 : α) ~ᵤ 1 := Quotient.exact h
-      have : (0 : α) = 1 := ((associated_zero_iff_eq_zero 1).1 this.symm).symm
-      zero_ne_one this⟩⟩
+  ⟨⟨1, 0, mk_ne_zero.2 one_ne_zero⟩⟩
 
 theorem exists_non_zero_rep {a : Associates α} : a ≠ 0 → ∃ a0 : α, a0 ≠ 0 ∧ Associates.mk a0 = a :=
   Quotient.inductionOn a fun b nz => ⟨b, mt (congr_arg Quotient.mk'') nz, rfl⟩
@@ -1067,18 +1080,14 @@ section CommMonoidWithZero
 variable [CommMonoidWithZero α]
 
 instance instCommMonoidWithZero : CommMonoidWithZero (Associates α) where
-    zero_mul := by
-      rintro ⟨a⟩
-      show Associates.mk (0 * a) = Associates.mk 0
-      rw [zero_mul]
-    mul_zero := by
-      rintro ⟨a⟩
-      show Associates.mk (a * 0) = Associates.mk 0
-      rw [mul_zero]
+    zero_mul := forall_associated.2 fun a ↦ by rw [← mk_zero, mk_mul_mk, zero_mul]
+    mul_zero := forall_associated.2 fun a ↦ by rw [← mk_zero, mk_mul_mk, mul_zero]
 
 instance instOrderTop : OrderTop (Associates α) where
   top := 0
-  le_top a := ⟨0, (mul_zero a).symm⟩
+  le_top := dvd_zero
+
+@[simp] protected theorem le_zero (a : Associates α) : a ≤ 0 := le_top
 
 instance instBoundedOrder : BoundedOrder (Associates α) where
 
@@ -1091,57 +1100,36 @@ theorem Prime.le_or_le {p : Associates α} (hp : Prime p) {a b : Associates α}
   hp.2.2 a b h
 #align associates.prime.le_or_le Associates.Prime.le_or_le
 
-theorem prime_mk (p : α) : Prime (Associates.mk p) ↔ Prime p := by
+@[simp]
+theorem prime_mk {p : α} : Prime (Associates.mk p) ↔ Prime p := by
   rw [Prime, _root_.Prime, forall_associated]
-  trans
-  · apply and_congr
-    rfl
-    apply and_congr
-    rfl
-    apply forall_congr'
-    intro a
-    exact forall_associated
-  apply and_congr mk_ne_zero
-  apply and_congr
-  · rw [isUnit_mk]
-  refine' forall₂_congr fun a b => _
-  rw [mk_mul_mk, mk_dvd_mk, mk_dvd_mk, mk_dvd_mk]
+  simp only [forall_associated, mk_ne_zero, isUnit_mk, mk_mul_mk, mk_dvd_mk]
 #align associates.prime_mk Associates.prime_mk
 
-theorem irreducible_mk (a : α) : Irreducible (Associates.mk a) ↔ Irreducible a := by
-  simp only [irreducible_iff, isUnit_mk]
-  apply and_congr Iff.rfl
+@[simp]
+theorem irreducible_mk {a : α} : Irreducible (Associates.mk a) ↔ Irreducible a := by
+  simp only [irreducible_iff, isUnit_mk, forall_associated, isUnit_mk, mk_mul_mk,
+    mk_eq_mk_iff_associated, Associated.comm (x := a)]
+  apply Iff.rfl.and
   constructor
   · rintro h x y rfl
-    simpa [isUnit_mk] using h (Associates.mk x) (Associates.mk y) rfl
-  · intro h x y
-    refine' Quotient.inductionOn₂ x y fun x y a_eq => _
-    rcases Quotient.exact a_eq.symm with ⟨u, a_eq⟩
-    rw [mul_assoc] at a_eq
-    show IsUnit (Associates.mk x) ∨ IsUnit (Associates.mk y)
-    simpa [isUnit_mk] using h _ _ a_eq.symm
+    exact h _ _ <| .refl _
+  · rintro h x y ⟨u, rfl⟩
+    simpa using h x (y * u) (mul_assoc _ _ _)
 #align associates.irreducible_mk Associates.irreducible_mk
 
+@[simp]
 theorem mk_dvdNotUnit_mk_iff {a b : α} :
     DvdNotUnit (Associates.mk a) (Associates.mk b) ↔ DvdNotUnit a b := by
-  rw [DvdNotUnit, DvdNotUnit, mk_ne_zero]
-  apply and_congr_right; intro
+  simp only [DvdNotUnit, mk_ne_zero, mk_surjective.exists, isUnit_mk, mk_mul_mk,
+    mk_eq_mk_iff_associated, Associated.comm (x := b)]
+  refine Iff.rfl.and ?_
   constructor
-  · contrapose!
-    rw [forall_associated]
-    intro h x hx hbax
-    rw [mk_mul_mk, mk_eq_mk_iff_associated] at hbax
-    cases' hbax with u hu
-    apply h (x * ↑u⁻¹)
-    · rw [isUnit_mk] at hx
-      rw [Associated.isUnit_iff]
-      apply hx
-      use u
-      simp
-    simp [← mul_assoc, ← hu]
+  · rintro ⟨x, hx, u, rfl⟩
+    refine ⟨x * u, ?_, mul_assoc ..⟩
+    simpa
   · rintro ⟨x, ⟨hx, rfl⟩⟩
-    use Associates.mk x
-    simp [isUnit_mk, mk_mul_mk, hx]
+    use x
 #align associates.mk_dvd_not_unit_mk_iff Associates.mk_dvdNotUnit_mk_iff
 
 theorem dvdNotUnit_of_lt {a b : Associates α} (hlt : a < b) : DvdNotUnit a b := by
@@ -1168,9 +1156,8 @@ section CancelCommMonoidWithZero
 variable [CancelCommMonoidWithZero α]
 
 instance instPartialOrder : PartialOrder (Associates α) where
-    le_antisymm := fun a' b' =>
-      Quotient.inductionOn₂ a' b' fun _ _ hab hba =>
-        Quot.sound <| associated_of_dvd_dvd (dvd_of_mk_le_mk hab) (dvd_of_mk_le_mk hba)
+    le_antisymm := mk_surjective.forall₂.2 fun _a _b hab hba => mk_eq_mk_iff_associated.2 <|
+      associated_of_dvd_dvd (dvd_of_mk_le_mk hab) (dvd_of_mk_le_mk hba)
 
 instance instOrderedCommMonoid : OrderedCommMonoid (Associates α) where
     mul_le_mul_left := fun a _ ⟨d, hd⟩ c => hd.symm ▸ mul_assoc c a d ▸ le_mul_right
@@ -1192,29 +1179,12 @@ theorem le_of_mul_le_mul_left (a b c : Associates α) (ha : a ≠ 0) : a * b ≤
   | ⟨d, hd⟩ => ⟨d, mul_left_cancel₀ ha <| by rwa [← mul_assoc]⟩
 #align associates.le_of_mul_le_mul_left Associates.le_of_mul_le_mul_left
 
-theorem one_or_eq_of_le_of_prime : ∀ p m : Associates α, Prime p → m ≤ p → m = 1 ∨ m = p
-  | p, m, ⟨hp0, _, h⟩, ⟨d, r⟩ => by
-    have dvd_rfl' : p ∣ m * d := by rw [r]
-    rw [r]
-    match h m d dvd_rfl' with
-    | Or.inl h' =>
-      if h : m = 0 then
-        simp [h, zero_mul]
-      else
-        rw [r] at h'
-        have : m * d ≤ m * 1 := by simpa using h'
-        have : d ≤ 1 := Associates.le_of_mul_le_mul_left m d 1 ‹m ≠ 0› this
-        have : d = 1 := bot_unique this
-        simp [this]
-    | Or.inr h' =>
-      if h : d = 0 then
-        rw [r] at hp0
-        have : m * d = 0 := by rw [h]; simp
-        contradiction
-      else
-        rw [r] at h'
-        have : d * m ≤ d * 1 := by simpa [mul_comm] using h'
-        exact Or.inl <| bot_unique <| Associates.le_of_mul_le_mul_left d m 1 ‹d ≠ 0› this
+theorem one_or_eq_of_le_of_prime {p m : Associates α} (hp : Prime p) (hle : m ≤ p) :
+    m = 1 ∨ m = p := by
+  rcases mk_surjective p with ⟨p, rfl⟩
+  rcases mk_surjective m with ⟨m, rfl⟩
+  simpa [mk_eq_mk_iff_associated, Associated.comm, -Quotient.eq]
+    using (prime_mk.1 hp).irreducible.dvd_iff.mp (mk_le_mk_iff_dvd.1 hle)
 #align associates.one_or_eq_of_le_of_prime Associates.one_or_eq_of_le_of_prime
 
 instance : CanonicallyOrderedCommMonoid (Associates α) where

@@ -538,7 +538,7 @@ theorem Associated.mul_mul [CommMonoid α] {a₁ a₂ b₁ b₂ : α}
 
 theorem Associated.pow_pow [CommMonoid α] {a b : α} {n : ℕ} (h : a ~ᵤ b) : a ^ n ~ᵤ b ^ n := by
   induction' n with n ih
-  · simp only [Nat.zero_eq, pow_zero]; rfl
+  · simp [Associated.refl]
   convert h.mul_mul ih <;> rw [pow_succ']
 #align associated.pow_pow Associated.pow_pow
 
@@ -1001,7 +1001,7 @@ theorem dvd_of_mk_le_mk {a b : α} : Associates.mk a ≤ Associates.mk b → a 
 #align associates.dvd_of_mk_le_mk Associates.dvd_of_mk_le_mk
 
 theorem mk_le_mk_of_dvd {a b : α} : a ∣ b → Associates.mk a ≤ Associates.mk b := fun ⟨c, hc⟩ =>
-  ⟨Associates.mk c, by simp only [hc]; rfl⟩
+  ⟨Associates.mk c, by simp only [hc, mk_mul_mk]⟩
 #align associates.mk_le_mk_of_dvd Associates.mk_le_mk_of_dvd
 
 theorem mk_le_mk_iff_dvd_iff {a b : α} : Associates.mk a ≤ Associates.mk b ↔ a ∣ b :=

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

@@ -380,7 +380,7 @@ def Associated [Monoid α] (x y : α) : Prop :=
 #align associated Associated
 
 /-- Notation for two elements of a monoid are associated, i.e.
-if one of them is another one multiplied by a unit on the right.-/
+if one of them is another one multiplied by a unit on the right. -/
 local infixl:50 " ~ᵤ " => Associated
 
 namespace Associated

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

@@ -819,6 +819,9 @@ theorem quot_out [Monoid α] (a : Associates α) : Associates.mk (Quot.out a) =
   rw [← quot_mk_eq_mk, Quot.out_eq]
 #align associates.quot_out Associates.quot_outₓ
 
+theorem mk_quot_out [Monoid α] (a : α) : Quot.out (Associates.mk a) ~ᵤ a := by
+  rw [← Associates.mk_eq_mk_iff_associated, Associates.quot_out]
+
 theorem forall_associated [Monoid α] {p : Associates α → Prop} :
     (∀ a, p a) ↔ ∀ a, p (Associates.mk a) :=
   Iff.intro (fun h _ => h _) fun h a => Quotient.inductionOn a h

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.

@@ -61,7 +61,7 @@ theorem dvd_of_dvd_pow (hp : Prime p) {a : α} {n : ℕ} (h : p ∣ a ^ n) : p 
     have := isUnit_of_dvd_one h
     have := not_unit hp
     contradiction
-  rw [pow_succ] at h
+  rw [pow_succ'] at h
   cases' dvd_or_dvd hp h with dvd_a dvd_pow
   · assumption
   exact ih dvd_pow
@@ -121,9 +121,9 @@ theorem Prime.pow_dvd_of_dvd_mul_left [CancelCommMonoidWithZero α] {p a b : α}
   · rw [pow_zero]
     exact one_dvd b
   · obtain ⟨c, rfl⟩ := ih (dvd_trans (pow_dvd_pow p n.le_succ) h')
-    rw [pow_succ']
+    rw [pow_succ]
     apply mul_dvd_mul_left _ ((hp.dvd_or_dvd _).resolve_left h)
-    rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ', mul_left_comm]
+    rwa [← mul_dvd_mul_iff_left (pow_ne_zero n hp.ne_zero), ← pow_succ, mul_left_comm]
 #align prime.pow_dvd_of_dvd_mul_left Prime.pow_dvd_of_dvd_mul_left
 
 theorem Prime.pow_dvd_of_dvd_mul_right [CancelCommMonoidWithZero α] {p a b : α} (hp : Prime p)
@@ -142,7 +142,7 @@ theorem Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd [CancelCommMonoidWith
   -- Then we can divide out a common factor of `p ^ n` from the equation `hy`.
   have : a ^ n.succ * x ^ n = p * y := by
     refine' mul_left_cancel₀ (pow_ne_zero n hp.ne_zero) _
-    rw [← mul_assoc _ p, ← pow_succ', ← hy, mul_pow, ← mul_assoc (a ^ n.succ), mul_comm _ (p ^ n),
+    rw [← mul_assoc _ p, ← pow_succ, ← hy, mul_pow, ← mul_assoc (a ^ n.succ), mul_comm _ (p ^ n),
       mul_assoc]
   -- So `p ∣ a` (and we're done) or `p ∣ x`, which can't be the case since it implies `p^2 ∣ b`.
   refine' hp.dvd_of_dvd_pow ((hp.dvd_or_dvd ⟨_, this⟩).resolve_right fun hdvdx => hb _)
@@ -158,7 +158,7 @@ theorem prime_pow_succ_dvd_mul {α : Type*} [CancelCommMonoidWithZero α] {p x y
   induction' i with i ih generalizing x
   · rw [pow_one] at hxy ⊢
     exact (h.dvd_or_dvd hxy).resolve_right hy
-  rw [pow_succ] at hxy ⊢
+  rw [pow_succ'] at hxy ⊢
   obtain ⟨x', rfl⟩ := (h.dvd_or_dvd (dvd_of_mul_right_dvd hxy)).resolve_right hy
   rw [mul_assoc] at hxy
   exact mul_dvd_mul_left p (ih ((mul_dvd_mul_iff_left h.ne_zero).mp hxy))
@@ -539,7 +539,7 @@ theorem Associated.mul_mul [CommMonoid α] {a₁ a₂ b₁ b₂ : α}
 theorem Associated.pow_pow [CommMonoid α] {a b : α} {n : ℕ} (h : a ~ᵤ b) : a ^ n ~ᵤ b ^ n := by
   induction' n with n ih
   · simp only [Nat.zero_eq, pow_zero]; rfl
-  convert h.mul_mul ih <;> rw [pow_succ]
+  convert h.mul_mul ih <;> rw [pow_succ']
 #align associated.pow_pow Associated.pow_pow
 
 protected theorem Associated.dvd [Monoid α] {a b : α} : a ~ᵤ b → a ∣ b := fun ⟨u, hu⟩ =>
@@ -625,7 +625,7 @@ lemma prime_pow_iff [CancelCommMonoidWithZero α] {p : α} {n : ℕ} :
   cases' n with n
   · simp at hp
   · rw [Nat.succ.injEq]
-    rw [pow_succ, prime_mul_iff] at hp
+    rw [pow_succ', prime_mul_iff] at hp
     rcases hp with ⟨hp, hpn⟩ | ⟨hp, hpn⟩
     · by_contra contra
       rw [isUnit_pow_iff contra] at hpn
@@ -1295,12 +1295,12 @@ theorem dvd_prime_pow [CancelCommMonoidWithZero α] {p q : α} (hp : Prime p) (n
   induction' n with n ih generalizing q
   · simp [← isUnit_iff_dvd_one, associated_one_iff_isUnit]
   refine' ⟨fun h => _, fun ⟨i, hi, hq⟩ => hq.dvd.trans (pow_dvd_pow p hi)⟩
-  rw [pow_succ] at h
+  rw [pow_succ'] at h
   rcases hp.left_dvd_or_dvd_right_of_dvd_mul h with (⟨q, rfl⟩ | hno)
   · rw [mul_dvd_mul_iff_left hp.ne_zero, ih] at h
     rcases h with ⟨i, hi, hq⟩
     refine' ⟨i + 1, Nat.succ_le_succ hi, (hq.mul_left p).trans _⟩
-    rw [pow_succ]
+    rw [pow_succ']
   · obtain ⟨i, hi, hq⟩ := ih.mp hno
     exact ⟨i, hi.trans n.le_succ, hq⟩
 #align dvd_prime_pow dvd_prime_pow