ring_theory.int.basic ⟷ Mathlib.RingTheory.Int.Basic

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

@@ -257,13 +257,11 @@ theorem gcd_eq_one_of_gcd_mul_right_eq_one_left {a : ℤ} {m n : ℕ} (h : a.gcd
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_left Int.gcd_eq_one_of_gcd_mul_right_eq_one_left
 -/
 
-#print Int.gcd_eq_one_of_gcd_mul_right_eq_one_right /-
 /-- If `gcd a (m * n) = 1`, then `gcd a n = 1`. -/
-theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
+theorem gcd_eq_one_of_gcd_hMul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
     a.gcd n = 1 :=
   Nat.dvd_one.mp <| trans_rel_left _ (gcd_dvd_gcd_mul_left_right a n m) h
-#align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
--/
+#align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_hMul_right_eq_one_right
 
 #print Int.sq_of_gcd_eq_one /-
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :

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

@@ -164,8 +164,8 @@ instance : GCDMonoid ℤ where
     by
     rw [← Int.ofNat_mul, gcd_mul_lcm, coe_nat_abs, abs_eq_normalize]
     exact normalize_associated (a * b)
-  lcm_zero_left a := coe_nat_eq_zero.2 <| Nat.lcm_zero_left _
-  lcm_zero_right a := coe_nat_eq_zero.2 <| Nat.lcm_zero_right _
+  lcm_zero_left a := natCast_eq_zero.2 <| Nat.lcm_zero_left _
+  lcm_zero_right a := natCast_eq_zero.2 <| Nat.lcm_zero_right _
 
 instance : NormalizedGCDMonoid ℤ :=
   { Int.normalizationMonoid,
@@ -287,7 +287,7 @@ theorem sq_of_coprime {a b c : ℤ} (h : IsCoprime a b) (heq : a * b = c ^ 2) :
 #print Int.natAbs_euclideanDomain_gcd /-
 theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd a b) = Int.gcd a b :=
   by
-  apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]
+  apply Nat.dvd_antisymm <;> rw [← Int.natCast_dvd_natCast]
   · rw [Int.natAbs_dvd]
     exact Int.dvd_gcd (EuclideanDomain.gcd_dvd_left _ _) (EuclideanDomain.gcd_dvd_right _ _)
   · rw [Int.dvd_natAbs]
@@ -306,7 +306,7 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
       Quotient.inductionOn' a fun a =>
         Associates.mk_eq_mk_iff_associated.2 <| Associated.symm <| ⟨norm_unit a, _⟩
     show normalize a = Int.natAbs (normalize a)
-    rw [Int.coe_natAbs, Int.abs_eq_normalize, normalize_idem]
+    rw [Int.natCast_natAbs, Int.abs_eq_normalize, normalize_idem]
   · intro n
     dsimp
     rw [← normalize_apply, ← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
@@ -327,7 +327,7 @@ theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     (p : ℤ) ∣ m ∨ (p : ℤ) ∣ n :=
   by
-  rw [Int.coe_nat_dvd_left, Int.coe_nat_dvd_left]
+  rw [Int.natCast_dvd, Int.natCast_dvd]
   exact Int.Prime.dvd_mul hp h
 #align int.prime.dvd_mul' Int.Prime.dvd_mul'
 -/
@@ -344,7 +344,7 @@ theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
 #print Int.Prime.dvd_pow' /-
 theorem Int.Prime.dvd_pow' {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     (p : ℤ) ∣ n := by
-  rw [Int.coe_nat_dvd_left]
+  rw [Int.natCast_dvd]
   exact Int.Prime.dvd_pow hp h
 #align int.prime.dvd_pow' Int.Prime.dvd_pow'
 -/
@@ -445,7 +445,7 @@ theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
 
 #print Int.associated_natAbs /-
 theorem Int.associated_natAbs (k : ℤ) : Associated k k.natAbs :=
-  associated_of_dvd_dvd (Int.coe_nat_dvd_right.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
+  associated_of_dvd_dvd (Int.dvd_natCast.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
 #align int.associated_nat_abs Int.associated_natAbs
 -/
 

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

@@ -357,7 +357,7 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
   · apply Or.intro_left
     exact le_antisymm (Nat.le_of_dvd zero_lt_two hp2) (Nat.Prime.two_le hp)
   · apply Or.intro_right
-    rw [sq, Int.natAbs_mul] at hpp 
+    rw [sq, Int.natAbs_mul] at hpp
     exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
 -/
@@ -378,7 +378,7 @@ theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
   cases n; · simp
   rw [← Multiset.rel_eq, ← associated_eq_eq]
   apply factors_unique irreducible_of_normalized_factor _
-  · rw [Multiset.coe_prod, Nat.prod_factors n.succ_ne_zero]
+  · rw [Multiset.prod_coe, Nat.prod_factors n.succ_ne_zero]
     apply normalized_factors_prod (Nat.succ_ne_zero _)
   · infer_instance
   · intro x hx
@@ -495,7 +495,7 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
   by
   obtain ⟨d, hd⟩ := exists_associated_pow_of_mul_eq_pow' hab h
   replace hd := hd.symm
-  rw [associated_iff_nat_abs, nat_abs_eq_nat_abs_iff, ← neg_pow_bit1] at hd 
+  rw [associated_iff_nat_abs, nat_abs_eq_nat_abs_iff, ← neg_pow_bit1] at hd
   obtain rfl | rfl := hd <;> exact ⟨_, rfl⟩
 #align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_left
 -/
@@ -503,7 +503,7 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
 #print Int.eq_pow_of_mul_eq_pow_bit1_right /-
 theorem eq_pow_of_mul_eq_pow_bit1_right {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, b = d ^ bit1 k :=
-  eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h )
+  eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h)
 #align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_right
 -/
 

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

@@ -41,7 +41,7 @@ instance : WfDvdMonoid ℕ :=
     refine'
       RelHomClass.wellFounded
         (⟨fun x : ℕ => if x = 0 then (⊤ : ℕ∞) else x, _⟩ : DvdNotUnit →r (· < ·))
-        (WithTop.wellFounded_lt Nat.lt_wfRel)
+        (WithTop.instWellFoundedLT Nat.lt_wfRel)
     intro a b h
     cases a
     · exfalso; revert h; simp [DvdNotUnit]

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

@@ -3,10 +3,10 @@ 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, Aaron Anderson
 -/
-import Mathbin.Algebra.EuclideanDomain.Basic
-import Mathbin.Data.Nat.Factors
-import Mathbin.RingTheory.Coprime.Basic
-import Mathbin.RingTheory.PrincipalIdealDomain
+import Algebra.EuclideanDomain.Basic
+import Data.Nat.Factors
+import RingTheory.Coprime.Basic
+import RingTheory.PrincipalIdealDomain
 
 #align_import ring_theory.int.basic from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"
 

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

@@ -236,7 +236,7 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
 -/
 
 #print Int.coprime_iff_nat_coprime /-
-theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
+theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.Coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_nat_abs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
 -/

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

@@ -96,7 +96,7 @@ instance : NormalizationMonoid ℤ
     where
   normUnit := fun a : ℤ => if 0 ≤ a then 1 else -1
   normUnit_zero := if_pos le_rfl
-  normUnit_mul a b hna hnb := by
+  normUnit_hMul a b hna hnb := by
     cases' hna.lt_or_lt with ha ha <;> cases' hnb.lt_or_lt with hb hb <;>
       simp [mul_nonneg_iff, ha.le, ha.not_le, hb.le, hb.not_le]
   normUnit_coe_units u :=
@@ -231,7 +231,7 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     obtain ⟨p, ⟨hp, ha, hb⟩⟩ := nat.prime.not_coprime_iff_dvd.mp hg
     apply Nat.Prime.not_dvd_one hp
     rw [← coe_nat_dvd, Int.ofNat_one, ← h]
-    exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
+    exact dvd_add ((coe_nat_dvd_left.mpr ha).hMul_left _) ((coe_nat_dvd_left.mpr hb).hMul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -205,7 +205,7 @@ theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ) (h : IsUnit u), (Int.natAbs
   by
   cases' nat_abs_eq a with h
   · use 1, isUnit_one; rw [← h, one_mul]
-  · use -1, is_unit_one.neg; rw [← neg_eq_iff_eq_neg.mpr h]
+  · use-1, is_unit_one.neg; rw [← neg_eq_iff_eq_neg.mpr h]
     simp only [neg_mul, one_mul]
 #align int.exists_unit_of_abs Int.exists_unit_of_abs
 -/

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

@@ -2,17 +2,14 @@
 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, Aaron Anderson
-
-! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.EuclideanDomain.Basic
 import Mathbin.Data.Nat.Factors
 import Mathbin.RingTheory.Coprime.Basic
 import Mathbin.RingTheory.PrincipalIdealDomain
 
+#align_import ring_theory.int.basic from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"
+
 /-!
 # Divisibility over ℕ and ℤ
 

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

@@ -79,13 +79,17 @@ instance : NormalizedGCDMonoid ℕ :=
     normalize_gcd := fun a b => normalize_eq _
     normalize_lcm := fun a b => normalize_eq _ }
 
+#print gcd_eq_nat_gcd /-
 theorem gcd_eq_nat_gcd (m n : ℕ) : gcd m n = Nat.gcd m n :=
   rfl
 #align gcd_eq_nat_gcd gcd_eq_nat_gcd
+-/
 
+#print lcm_eq_nat_lcm /-
 theorem lcm_eq_nat_lcm (m n : ℕ) : lcm m n = Nat.lcm m n :=
   rfl
 #align lcm_eq_nat_lcm lcm_eq_nat_lcm
+-/
 
 namespace Int
 
@@ -102,10 +106,13 @@ instance : NormalizationMonoid ℤ
     (units_eq_one_or u).elim (fun eq => Eq.symm ▸ if_pos zero_le_one) fun eq =>
       Eq.symm ▸ if_neg (not_le_of_gt <| show (-1 : ℤ) < 0 by decide)
 
+#print Int.normalize_of_nonneg /-
 theorem normalize_of_nonneg {z : ℤ} (h : 0 ≤ z) : normalize z = z :=
   show z * ↑(ite _ _ _) = z by rw [if_pos h, Units.val_one, mul_one]
 #align int.normalize_of_nonneg Int.normalize_of_nonneg
+-/
 
+#print Int.normalize_of_nonpos /-
 theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
   by
   obtain rfl | h := h.eq_or_lt
@@ -113,27 +120,38 @@ theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
   · change z * ↑(ite _ _ _) = -z
     rw [if_neg (not_le_of_gt h), Units.val_neg, Units.val_one, mul_neg_one]
 #align int.normalize_of_nonpos Int.normalize_of_nonpos
+-/
 
+#print Int.normalize_coe_nat /-
 theorem normalize_coe_nat (n : ℕ) : normalize (n : ℤ) = n :=
   normalize_of_nonneg (ofNat_le_ofNat_of_le <| Nat.zero_le n)
 #align int.normalize_coe_nat Int.normalize_coe_nat
+-/
 
+#print Int.abs_eq_normalize /-
 theorem abs_eq_normalize (z : ℤ) : |z| = normalize z := by
   cases le_total 0 z <;> simp [normalize_of_nonneg, normalize_of_nonpos, *]
 #align int.abs_eq_normalize Int.abs_eq_normalize
+-/
 
+#print Int.nonneg_of_normalize_eq_self /-
 theorem nonneg_of_normalize_eq_self {z : ℤ} (hz : normalize z = z) : 0 ≤ z :=
   abs_eq_self.1 <| by rw [abs_eq_normalize, hz]
 #align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_self
+-/
 
+#print Int.nonneg_iff_normalize_eq_self /-
 theorem nonneg_iff_normalize_eq_self (z : ℤ) : normalize z = z ↔ 0 ≤ z :=
   ⟨nonneg_of_normalize_eq_self, normalize_of_nonneg⟩
 #align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_self
+-/
 
+#print Int.eq_of_associated_of_nonneg /-
 theorem eq_of_associated_of_nonneg {a b : ℤ} (h : Associated a b) (ha : 0 ≤ a) (hb : 0 ≤ b) :
     a = b :=
   dvd_antisymm_of_normalize_eq (normalize_of_nonneg ha) (normalize_of_nonneg hb) h.Dvd h.symm.Dvd
 #align int.eq_of_associated_of_nonneg Int.eq_of_associated_of_nonneg
+-/
 
 end NormalizationMonoid
 
@@ -185,6 +203,7 @@ theorem natAbs_lcm (i j : ℤ) : natAbs (GCDMonoid.lcm i j) = Int.lcm i j :=
 
 end GCDMonoid
 
+#print Int.exists_unit_of_abs /-
 theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ) (h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
   by
   cases' nat_abs_eq a with h
@@ -192,6 +211,7 @@ theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ) (h : IsUnit u), (Int.natAbs
   · use -1, is_unit_one.neg; rw [← neg_eq_iff_eq_neg.mpr h]
     simp only [neg_mul, one_mul]
 #align int.exists_unit_of_abs Int.exists_unit_of_abs
+-/
 
 #print Int.gcd_eq_natAbs /-
 theorem gcd_eq_natAbs {a b : ℤ} : Int.gcd a b = Nat.gcd a.natAbs b.natAbs :=
@@ -199,6 +219,7 @@ theorem gcd_eq_natAbs {a b : ℤ} : Int.gcd a b = Nat.gcd a.natAbs b.natAbs :=
 #align int.gcd_eq_nat_abs Int.gcd_eq_natAbs
 -/
 
+#print Int.gcd_eq_one_iff_coprime /-
 theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :=
   by
   constructor
@@ -215,10 +236,13 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     rw [← coe_nat_dvd, Int.ofNat_one, ← h]
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
+-/
 
+#print Int.coprime_iff_nat_coprime /-
 theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_nat_abs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
+-/
 
 #print Int.gcd_ne_one_iff_gcd_mul_right_ne_one /-
 /-- If `gcd a (m * n) ≠ 1`, then `gcd a m ≠ 1` or `gcd a n ≠ 1`. -/
@@ -244,6 +268,7 @@ theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gc
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
 -/
 
+#print Int.sq_of_gcd_eq_one /-
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   by
@@ -253,12 +278,16 @@ theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^
   rw [← hu]
   cases' Int.units_eq_one_or u with hu' hu' <;> · rw [hu']; simp
 #align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_one
+-/
 
+#print Int.sq_of_coprime /-
 theorem sq_of_coprime {a b c : ℤ} (h : IsCoprime a b) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   sq_of_gcd_eq_one (gcd_eq_one_iff_coprime.mpr h) HEq
 #align int.sq_of_coprime Int.sq_of_coprime
+-/
 
+#print Int.natAbs_euclideanDomain_gcd /-
 theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd a b) = Int.gcd a b :=
   by
   apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]
@@ -267,9 +296,11 @@ theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd
   · rw [Int.dvd_natAbs]
     exact EuclideanDomain.dvd_gcd (Int.gcd_dvd_left _ _) (Int.gcd_dvd_right _ _)
 #align int.nat_abs_euclidean_domain_gcd Int.natAbs_euclideanDomain_gcd
+-/
 
 end Int
 
+#print associatesIntEquivNat /-
 /-- Maps an associate class of integers consisting of `-n, n` to `n : ℕ` -/
 def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
   by
@@ -283,7 +314,9 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
     dsimp
     rw [← normalize_apply, ← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
 #align associates_int_equiv_nat associatesIntEquivNat
+-/
 
+#print Int.Prime.dvd_mul /-
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     p ∣ m.natAbs ∨ p ∣ n.natAbs :=
   by
@@ -291,27 +324,35 @@ theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
   rw [← Int.natAbs_mul]
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_mul Int.Prime.dvd_mul
+-/
 
+#print Int.Prime.dvd_mul' /-
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     (p : ℤ) ∣ m ∨ (p : ℤ) ∣ n :=
   by
   rw [Int.coe_nat_dvd_left, Int.coe_nat_dvd_left]
   exact Int.Prime.dvd_mul hp h
 #align int.prime.dvd_mul' Int.Prime.dvd_mul'
+-/
 
+#print Int.Prime.dvd_pow /-
 theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     p ∣ n.natAbs := by
   apply @Nat.Prime.dvd_of_dvd_pow _ _ k hp
   rw [← Int.natAbs_pow]
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_pow Int.Prime.dvd_pow
+-/
 
+#print Int.Prime.dvd_pow' /-
 theorem Int.Prime.dvd_pow' {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     (p : ℤ) ∣ n := by
   rw [Int.coe_nat_dvd_left]
   exact Int.Prime.dvd_pow hp h
 #align int.prime.dvd_pow' Int.Prime.dvd_pow'
+-/
 
+#print prime_two_or_dvd_of_dvd_two_mul_pow_self_two /-
 theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : Nat.Prime p)
     (h : (p : ℤ) ∣ 2 * m ^ 2) : p = 2 ∨ p ∣ Int.natAbs m :=
   by
@@ -322,15 +363,19 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
     rw [sq, Int.natAbs_mul] at hpp 
     exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
+-/
 
+#print Int.exists_prime_and_dvd /-
 theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime p ∧ p ∣ n :=
   by
   obtain ⟨p, pp, pd⟩ := Nat.exists_prime_and_dvd hn
   exact ⟨p, nat.prime_iff_prime_int.mp pp, int.coe_nat_dvd_left.mpr pd⟩
 #align int.exists_prime_and_dvd Int.exists_prime_and_dvd
+-/
 
 open UniqueFactorizationMonoid
 
+#print Nat.factors_eq /-
 theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
   by
   cases n; · simp
@@ -343,7 +388,9 @@ theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
     rw [Nat.irreducible_iff_prime, ← Nat.prime_iff]
     exact Nat.prime_of_mem_factors hx
 #align nat.factors_eq Nat.factors_eq
+-/
 
+#print Nat.factors_multiset_prod_of_irreducible /-
 theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
     (h : ∀ x : ℕ, x ∈ s → Irreducible x) : normalizedFactors s.Prod = s :=
   by
@@ -355,16 +402,21 @@ theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
   intro con
   exact not_irreducible_zero (h 0 Con)
 #align nat.factors_multiset_prod_of_irreducible Nat.factors_multiset_prod_of_irreducible
+-/
 
 namespace multiplicity
 
+#print multiplicity.finite_int_iff_natAbs_finite /-
 theorem finite_int_iff_natAbs_finite {a b : ℤ} : Finite a b ↔ Finite a.natAbs b.natAbs := by
   simp only [finite_def, ← Int.natAbs_dvd_natAbs, Int.natAbs_pow]
 #align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finite
+-/
 
+#print multiplicity.finite_int_iff /-
 theorem finite_int_iff {a b : ℤ} : Finite a b ↔ a.natAbs ≠ 1 ∧ b ≠ 0 := by
   rw [finite_int_iff_nat_abs_finite, finite_nat_iff, pos_iff_ne_zero, Int.natAbs_ne_zero]
 #align multiplicity.finite_int_iff multiplicity.finite_int_iff
+-/
 
 #print multiplicity.decidableNat /-
 instance decidableNat : DecidableRel fun a b : ℕ => (multiplicity a b).Dom := fun a b =>
@@ -372,9 +424,11 @@ instance decidableNat : DecidableRel fun a b : ℕ => (multiplicity a b).Dom :=
 #align multiplicity.decidable_nat multiplicity.decidableNat
 -/
 
+#print multiplicity.decidableInt /-
 instance decidableInt : DecidableRel fun a b : ℤ => (multiplicity a b).Dom := fun a b =>
   decidable_of_iff _ finite_int_iff.symm
 #align multiplicity.decidable_int multiplicity.decidableInt
+-/
 
 end multiplicity
 
@@ -392,40 +446,53 @@ theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
 #align induction_on_primes induction_on_primes
 -/
 
+#print Int.associated_natAbs /-
 theorem Int.associated_natAbs (k : ℤ) : Associated k k.natAbs :=
   associated_of_dvd_dvd (Int.coe_nat_dvd_right.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
 #align int.associated_nat_abs Int.associated_natAbs
+-/
 
+#print Int.prime_iff_natAbs_prime /-
 theorem Int.prime_iff_natAbs_prime {k : ℤ} : Prime k ↔ Nat.Prime k.natAbs :=
   (Int.associated_natAbs k).prime_iff.trans Nat.prime_iff_prime_int.symm
 #align int.prime_iff_nat_abs_prime Int.prime_iff_natAbs_prime
+-/
 
+#print Int.associated_iff_natAbs /-
 theorem Int.associated_iff_natAbs {a b : ℤ} : Associated a b ↔ a.natAbs = b.natAbs :=
   by
   rw [← dvd_dvd_iff_associated, ← Int.natAbs_dvd_natAbs, ← Int.natAbs_dvd_natAbs,
     dvd_dvd_iff_associated]
   exact associated_iff_eq
 #align int.associated_iff_nat_abs Int.associated_iff_natAbs
+-/
 
+#print Int.associated_iff /-
 theorem Int.associated_iff {a b : ℤ} : Associated a b ↔ a = b ∨ a = -b :=
   by
   rw [Int.associated_iff_natAbs]
   exact Int.natAbs_eq_natAbs_iff
 #align int.associated_iff Int.associated_iff
+-/
 
 namespace Int
 
+#print Int.zmultiples_natAbs /-
 theorem zmultiples_natAbs (a : ℤ) :
     AddSubgroup.zmultiples (a.natAbs : ℤ) = AddSubgroup.zmultiples a :=
   le_antisymm
     (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (dvd_natAbs.mpr (dvd_refl a))))
     (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
 #align int.zmultiples_nat_abs Int.zmultiples_natAbs
+-/
 
+#print Int.span_natAbs /-
 theorem span_natAbs (a : ℤ) : Ideal.span ({a.natAbs} : Set ℤ) = Ideal.span {a} := by
   rw [Ideal.span_singleton_eq_span_singleton]; exact (associated_nat_abs _).symm
 #align int.span_nat_abs Int.span_natAbs
+-/
 
+#print Int.eq_pow_of_mul_eq_pow_bit1_left /-
 theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, a = d ^ bit1 k :=
   by
@@ -434,16 +501,21 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
   rw [associated_iff_nat_abs, nat_abs_eq_nat_abs_iff, ← neg_pow_bit1] at hd 
   obtain rfl | rfl := hd <;> exact ⟨_, rfl⟩
 #align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_left
+-/
 
+#print Int.eq_pow_of_mul_eq_pow_bit1_right /-
 theorem eq_pow_of_mul_eq_pow_bit1_right {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, b = d ^ bit1 k :=
   eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h )
 #align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_right
+-/
 
+#print Int.eq_pow_of_mul_eq_pow_bit1 /-
 theorem eq_pow_of_mul_eq_pow_bit1 {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : (∃ d, a = d ^ bit1 k) ∧ ∃ e, b = e ^ bit1 k :=
   ⟨eq_pow_of_mul_eq_pow_bit1_left hab h, eq_pow_of_mul_eq_pow_bit1_right hab h⟩
 #align int.eq_pow_of_mul_eq_pow_bit1 Int.eq_pow_of_mul_eq_pow_bit1
+-/
 
 end Int
 

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

@@ -185,7 +185,7 @@ theorem natAbs_lcm (i j : ℤ) : natAbs (GCDMonoid.lcm i j) = Int.lcm i j :=
 
 end GCDMonoid
 
-theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
+theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ) (h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
   by
   cases' nat_abs_eq a with h
   · use 1, isUnit_one; rw [← h, one_mul]
@@ -319,7 +319,7 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
   · apply Or.intro_left
     exact le_antisymm (Nat.le_of_dvd zero_lt_two hp2) (Nat.Prime.two_le hp)
   · apply Or.intro_right
-    rw [sq, Int.natAbs_mul] at hpp
+    rw [sq, Int.natAbs_mul] at hpp 
     exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
 
@@ -431,13 +431,13 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
   by
   obtain ⟨d, hd⟩ := exists_associated_pow_of_mul_eq_pow' hab h
   replace hd := hd.symm
-  rw [associated_iff_nat_abs, nat_abs_eq_nat_abs_iff, ← neg_pow_bit1] at hd
+  rw [associated_iff_nat_abs, nat_abs_eq_nat_abs_iff, ← neg_pow_bit1] at hd 
   obtain rfl | rfl := hd <;> exact ⟨_, rfl⟩
 #align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_left
 
 theorem eq_pow_of_mul_eq_pow_bit1_right {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, b = d ^ bit1 k :=
-  eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h)
+  eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h )
 #align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_right
 
 theorem eq_pow_of_mul_eq_pow_bit1 {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}

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

@@ -79,22 +79,10 @@ instance : NormalizedGCDMonoid ℕ :=
     normalize_gcd := fun a b => normalize_eq _
     normalize_lcm := fun a b => normalize_eq _ }
 
-/- warning: gcd_eq_nat_gcd -> gcd_eq_nat_gcd is a dubious translation:
-lean 3 declaration is
-  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.gcd.{0} Nat Nat.cancelCommMonoidWithZero Nat.gcdMonoid m n) (Nat.gcd m n)
-but is expected to have type
-  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.gcd.{0} Nat Nat.cancelCommMonoidWithZero instGCDMonoidNatCancelCommMonoidWithZero m n) (Nat.gcd m n)
-Case conversion may be inaccurate. Consider using '#align gcd_eq_nat_gcd gcd_eq_nat_gcdₓ'. -/
 theorem gcd_eq_nat_gcd (m n : ℕ) : gcd m n = Nat.gcd m n :=
   rfl
 #align gcd_eq_nat_gcd gcd_eq_nat_gcd
 
-/- warning: lcm_eq_nat_lcm -> lcm_eq_nat_lcm is a dubious translation:
-lean 3 declaration is
-  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.lcm.{0} Nat Nat.cancelCommMonoidWithZero Nat.gcdMonoid m n) (Nat.lcm m n)
-but is expected to have type
-  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.lcm.{0} Nat Nat.cancelCommMonoidWithZero instGCDMonoidNatCancelCommMonoidWithZero m n) (Nat.lcm m n)
-Case conversion may be inaccurate. Consider using '#align lcm_eq_nat_lcm lcm_eq_nat_lcmₓ'. -/
 theorem lcm_eq_nat_lcm (m n : ℕ) : lcm m n = Nat.lcm m n :=
   rfl
 #align lcm_eq_nat_lcm lcm_eq_nat_lcm
@@ -114,22 +102,10 @@ instance : NormalizationMonoid ℤ
     (units_eq_one_or u).elim (fun eq => Eq.symm ▸ if_pos zero_le_one) fun eq =>
       Eq.symm ▸ if_neg (not_le_of_gt <| show (-1 : ℤ) < 0 by decide)
 
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Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int 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Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
-Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonneg Int.normalize_of_nonnegₓ'. -/
 theorem normalize_of_nonneg {z : ℤ} (h : 0 ≤ z) : normalize z = z :=
   show z * ↑(ite _ _ _) = z by rw [if_pos h, Units.val_one, mul_one]
 #align int.normalize_of_nonneg Int.normalize_of_nonneg
 
-/- warning: int.normalize_of_nonpos -> Int.normalize_of_nonpos is a dubious translation:
-lean 3 declaration is
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Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.instNegInt z))
-Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonpos Int.normalize_of_nonposₓ'. -/
 theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
   by
   obtain rfl | h := h.eq_or_lt
@@ -138,52 +114,22 @@ theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
     rw [if_neg (not_le_of_gt h), Units.val_neg, Units.val_one, mul_neg_one]
 #align int.normalize_of_nonpos Int.normalize_of_nonpos
 
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-Case conversion may be inaccurate. Consider using '#align int.normalize_coe_nat Int.normalize_coe_natₓ'. -/
 theorem normalize_coe_nat (n : ℕ) : normalize (n : ℤ) = n :=
   normalize_of_nonneg (ofNat_le_ofNat_of_le <| Nat.zero_le n)
 #align int.normalize_coe_nat Int.normalize_coe_nat
 
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
-Case conversion may be inaccurate. Consider using '#align int.abs_eq_normalize Int.abs_eq_normalizeₓ'. -/
 theorem abs_eq_normalize (z : ℤ) : |z| = normalize z := by
   cases le_total 0 z <;> simp [normalize_of_nonneg, normalize_of_nonpos, *]
 #align int.abs_eq_normalize Int.abs_eq_normalize
 
-/- warning: int.nonneg_of_normalize_eq_self -> Int.nonneg_of_normalize_eq_self is a dubious translation:
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(MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int 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(CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
-Case conversion may be inaccurate. Consider using '#align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_selfₓ'. -/
 theorem nonneg_of_normalize_eq_self {z : ℤ} (hz : normalize z = z) : 0 ≤ z :=
   abs_eq_self.1 <| by rw [abs_eq_normalize, hz]
 #align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_self
 
-/- warning: int.nonneg_iff_normalize_eq_self -> Int.nonneg_iff_normalize_eq_self is a dubious translation:
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-  forall (z : Int), Iff (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z)
-but is expected to have type
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(MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
-Case conversion may be inaccurate. Consider using '#align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_selfₓ'. -/
 theorem nonneg_iff_normalize_eq_self (z : ℤ) : normalize z = z ↔ 0 ≤ z :=
   ⟨nonneg_of_normalize_eq_self, normalize_of_nonneg⟩
 #align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_self
 
-/- warning: int.eq_of_associated_of_nonneg -> Int.eq_of_associated_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, (Associated.{0} Int Int.monoid a b) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) a) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) b) -> (Eq.{1} Int a b)
-but is expected to have type
-  forall {a : Int} {b : Int}, (Associated.{0} Int Int.instMonoidInt a b) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) a) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) b) -> (Eq.{1} Int a b)
-Case conversion may be inaccurate. Consider using '#align int.eq_of_associated_of_nonneg Int.eq_of_associated_of_nonnegₓ'. -/
 theorem eq_of_associated_of_nonneg {a b : ℤ} (h : Associated a b) (ha : 0 ≤ a) (hb : 0 ≤ b) :
     a = b :=
   dvd_antisymm_of_normalize_eq (normalize_of_nonneg ha) (normalize_of_nonneg hb) h.Dvd h.symm.Dvd
@@ -239,12 +185,6 @@ theorem natAbs_lcm (i j : ℤ) : natAbs (GCDMonoid.lcm i j) = Int.lcm i j :=
 
 end GCDMonoid
 
-/- warning: int.exists_unit_of_abs -> Int.exists_unit_of_abs is a dubious translation:
-lean 3 declaration is
-  forall (a : Int), Exists.{1} Int (fun (u : Int) => Exists.{0} (IsUnit.{0} Int Int.monoid u) (fun (h : IsUnit.{0} Int Int.monoid u) => Eq.{1} Int ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) u a)))
-but is expected to have type
-  forall (a : Int), Exists.{1} Int (fun (u : Int) => Exists.{0} (IsUnit.{0} Int Int.instMonoidInt u) (fun (h : IsUnit.{0} Int Int.instMonoidInt u) => Eq.{1} Int (Nat.cast.{0} Int instNatCastInt (Int.natAbs a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) u a)))
-Case conversion may be inaccurate. Consider using '#align int.exists_unit_of_abs Int.exists_unit_of_absₓ'. -/
 theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
   by
   cases' nat_abs_eq a with h
@@ -259,12 +199,6 @@ theorem gcd_eq_natAbs {a b : ℤ} : Int.gcd a b = Nat.gcd a.natAbs b.natAbs :=
 #align int.gcd_eq_nat_abs Int.gcd_eq_natAbs
 -/
 
-/- warning: int.gcd_eq_one_iff_coprime -> Int.gcd_eq_one_iff_coprime is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (IsCoprime.{0} Int Int.commSemiring a b)
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (IsCoprime.{0} Int Int.instCommSemiringInt a b)
-Case conversion may be inaccurate. Consider using '#align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprimeₓ'. -/
 theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :=
   by
   constructor
@@ -282,12 +216,6 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
-/- warning: int.coprime_iff_nat_coprime -> Int.coprime_iff_nat_coprime is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (IsCoprime.{0} Int Int.commSemiring a b) (Nat.coprime (Int.natAbs a) (Int.natAbs b))
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (IsCoprime.{0} Int Int.instCommSemiringInt a b) (Nat.coprime (Int.natAbs a) (Int.natAbs b))
-Case conversion may be inaccurate. Consider using '#align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprimeₓ'. -/
 theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_nat_abs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
@@ -316,12 +244,6 @@ theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gc
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
 -/
 
-/- warning: int.sq_of_gcd_eq_one -> Int.sq_of_gcd_eq_one is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
-Case conversion may be inaccurate. Consider using '#align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_oneₓ'. -/
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   by
@@ -332,23 +254,11 @@ theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^
   cases' Int.units_eq_one_or u with hu' hu' <;> · rw [hu']; simp
 #align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_one
 
-/- warning: int.sq_of_coprime -> Int.sq_of_coprime is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
-Case conversion may be inaccurate. Consider using '#align int.sq_of_coprime Int.sq_of_coprimeₓ'. -/
 theorem sq_of_coprime {a b c : ℤ} (h : IsCoprime a b) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   sq_of_gcd_eq_one (gcd_eq_one_iff_coprime.mpr h) HEq
 #align int.sq_of_coprime Int.sq_of_coprime
 
-/- warning: int.nat_abs_euclidean_domain_gcd -> Int.natAbs_euclideanDomain_gcd is a dubious translation:
-lean 3 declaration is
-  forall (a : Int) (b : Int), Eq.{1} Nat (Int.natAbs (EuclideanDomain.gcd.{0} Int Int.euclideanDomain (fun (a : Int) (b : Int) => Int.decidableEq a b) a b)) (Int.gcd a b)
-but is expected to have type
-  forall (a : Int) (b : Int), Eq.{1} Nat (Int.natAbs (EuclideanDomain.gcd.{0} ([mdata borrowed:1 Int]) Int.euclideanDomain (fun (a : [mdata borrowed:1 Int]) (b : [mdata borrowed:1 Int]) => Int.instDecidableEqInt a b) a b)) (Int.gcd a b)
-Case conversion may be inaccurate. Consider using '#align int.nat_abs_euclidean_domain_gcd Int.natAbs_euclideanDomain_gcdₓ'. -/
 theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd a b) = Int.gcd a b :=
   by
   apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]
@@ -360,12 +270,6 @@ theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd
 
 end Int
 
-/- warning: associates_int_equiv_nat -> associatesIntEquivNat is a dubious translation:
-lean 3 declaration is
-  Equiv.{1, 1} (Associates.{0} Int Int.monoid) Nat
-but is expected to have type
-  Equiv.{1, 1} (Associates.{0} Int Int.instMonoidInt) Nat
-Case conversion may be inaccurate. Consider using '#align associates_int_equiv_nat associatesIntEquivNatₓ'. -/
 /-- Maps an associate class of integers consisting of `-n, n` to `n : ℕ` -/
 def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
   by
@@ -380,12 +284,6 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
     rw [← normalize_apply, ← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
 #align associates_int_equiv_nat associatesIntEquivNat
 
-/- warning: int.prime.dvd_mul -> Int.Prime.dvd_mul is a dubious translation:
-lean 3 declaration is
-  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) -> (Or (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs m)) (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs n)))
-but is expected to have type
-  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) -> (Or (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs m)) (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs n)))
-Case conversion may be inaccurate. Consider using '#align int.prime.dvd_mul Int.Prime.dvd_mulₓ'. -/
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     p ∣ m.natAbs ∨ p ∣ n.natAbs :=
   by
@@ -394,12 +292,6 @@ theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_mul Int.Prime.dvd_mul
 
-/- warning: int.prime.dvd_mul' -> Int.Prime.dvd_mul' is a dubious translation:
-lean 3 declaration is
-  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) -> (Or (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) m) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) n))
-but is expected to have type
-  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) -> (Or (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) m) (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) n))
-Case conversion may be inaccurate. Consider using '#align int.prime.dvd_mul' Int.Prime.dvd_mul'ₓ'. -/
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     (p : ℤ) ∣ m ∨ (p : ℤ) ∣ n :=
   by
@@ -407,12 +299,6 @@ theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : 
   exact Int.Prime.dvd_mul hp h
 #align int.prime.dvd_mul' Int.Prime.dvd_mul'
 
-/- warning: int.prime.dvd_pow -> Int.Prime.dvd_pow is a dubious translation:
-lean 3 declaration is
-  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n k)) -> (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs n))
-but is expected to have type
-  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat n k)) -> (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs n))
-Case conversion may be inaccurate. Consider using '#align int.prime.dvd_pow Int.Prime.dvd_powₓ'. -/
 theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     p ∣ n.natAbs := by
   apply @Nat.Prime.dvd_of_dvd_pow _ _ k hp
@@ -420,24 +306,12 @@ theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_pow Int.Prime.dvd_pow
 
-/- warning: int.prime.dvd_pow' -> Int.Prime.dvd_pow' is a dubious translation:
-lean 3 declaration is
-  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n k)) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) n)
-but is expected to have type
-  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat n k)) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) n)
-Case conversion may be inaccurate. Consider using '#align int.prime.dvd_pow' Int.Prime.dvd_pow'ₓ'. -/
 theorem Int.Prime.dvd_pow' {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     (p : ℤ) ∣ n := by
   rw [Int.coe_nat_dvd_left]
   exact Int.Prime.dvd_pow hp h
 #align int.prime.dvd_pow' Int.Prime.dvd_pow'
 
-/- warning: prime_two_or_dvd_of_dvd_two_mul_pow_self_two -> prime_two_or_dvd_of_dvd_two_mul_pow_self_two is a dubious translation:
-lean 3 declaration is
-  forall {m : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> (Or (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs m)))
-but is expected to have type
-  forall {m : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) -> (Or (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs m)))
-Case conversion may be inaccurate. Consider using '#align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_twoₓ'. -/
 theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : Nat.Prime p)
     (h : (p : ℤ) ∣ 2 * m ^ 2) : p = 2 ∨ p ∣ Int.natAbs m :=
   by
@@ -449,12 +323,6 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
     exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
 
-/- warning: int.exists_prime_and_dvd -> Int.exists_prime_and_dvd is a dubious translation:
-lean 3 declaration is
-  forall {n : Int}, (Ne.{1} Nat (Int.natAbs n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Exists.{1} Int (fun (p : Int) => And (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) p) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) p n)))
-but is expected to have type
-  forall {n : Int}, (Ne.{1} Nat (Int.natAbs n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Exists.{1} Int (fun (p : Int) => And (Prime.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) p) (Dvd.dvd.{0} Int Int.instDvdInt p n)))
-Case conversion may be inaccurate. Consider using '#align int.exists_prime_and_dvd Int.exists_prime_and_dvdₓ'. -/
 theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime p ∧ p ∣ n :=
   by
   obtain ⟨p, pp, pd⟩ := Nat.exists_prime_and_dvd hn
@@ -463,12 +331,6 @@ theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime
 
 open UniqueFactorizationMonoid
 
-/- warning: nat.factors_eq -> Nat.factors_eq is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) (normalizationMonoidOfUniqueUnits.{0} Nat Nat.cancelCommMonoidWithZero Nat.unique_units) Nat.uniqueFactorizationMonoid n) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (List.{0} Nat) (Multiset.{0} Nat) (HasLiftT.mk.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (CoeTCₓ.coe.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (coeBase.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (Multiset.hasCoe.{0} Nat)))) (Nat.factors n))
-but is expected to have type
-  forall {n : Nat}, Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (NormalizedGCDMonoid.toNormalizationMonoid.{0} Nat Nat.cancelCommMonoidWithZero instNormalizedGCDMonoidNatCancelCommMonoidWithZero) Nat.instUniqueFactorizationMonoidNatCancelCommMonoidWithZero n) (Multiset.ofList.{0} Nat (Nat.factors n))
-Case conversion may be inaccurate. Consider using '#align nat.factors_eq Nat.factors_eqₓ'. -/
 theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
   by
   cases n; · simp
@@ -482,12 +344,6 @@ theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
     exact Nat.prime_of_mem_factors hx
 #align nat.factors_eq Nat.factors_eq
 
-/- warning: nat.factors_multiset_prod_of_irreducible -> Nat.factors_multiset_prod_of_irreducible is a dubious translation:
-lean 3 declaration is
-  forall {s : Multiset.{0} Nat}, (forall (x : Nat), (Membership.Mem.{0, 0} Nat (Multiset.{0} Nat) (Multiset.hasMem.{0} Nat) x s) -> (Irreducible.{0} Nat Nat.monoid x)) -> (Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) (normalizationMonoidOfUniqueUnits.{0} Nat Nat.cancelCommMonoidWithZero Nat.unique_units) Nat.uniqueFactorizationMonoid (Multiset.prod.{0} Nat Nat.commMonoid s)) s)
-but is expected to have type
-  forall {s : Multiset.{0} Nat}, (forall (x : Nat), (Membership.mem.{0, 0} Nat (Multiset.{0} Nat) (Multiset.instMembershipMultiset.{0} Nat) x s) -> (Irreducible.{0} Nat Nat.monoid x)) -> (Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (NormalizedGCDMonoid.toNormalizationMonoid.{0} Nat Nat.cancelCommMonoidWithZero instNormalizedGCDMonoidNatCancelCommMonoidWithZero) Nat.instUniqueFactorizationMonoidNatCancelCommMonoidWithZero (Multiset.prod.{0} Nat Nat.commMonoid s)) s)
-Case conversion may be inaccurate. Consider using '#align nat.factors_multiset_prod_of_irreducible Nat.factors_multiset_prod_of_irreducibleₓ'. -/
 theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
     (h : ∀ x : ℕ, x ∈ s → Irreducible x) : normalizedFactors s.Prod = s :=
   by
@@ -502,22 +358,10 @@ theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
 
 namespace multiplicity
 
-/- warning: multiplicity.finite_int_iff_nat_abs_finite -> multiplicity.finite_int_iff_natAbs_finite is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.monoid a b) (multiplicity.Finite.{0} Nat Nat.monoid (Int.natAbs a) (Int.natAbs b))
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.instMonoidInt a b) (multiplicity.Finite.{0} Nat Nat.monoid (Int.natAbs a) (Int.natAbs b))
-Case conversion may be inaccurate. Consider using '#align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finiteₓ'. -/
 theorem finite_int_iff_natAbs_finite {a b : ℤ} : Finite a b ↔ Finite a.natAbs b.natAbs := by
   simp only [finite_def, ← Int.natAbs_dvd_natAbs, Int.natAbs_pow]
 #align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finite
 
-/- warning: multiplicity.finite_int_iff -> multiplicity.finite_int_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.monoid a b) (And (Ne.{1} Nat (Int.natAbs a) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.instMonoidInt a b) (And (Ne.{1} Nat (Int.natAbs a) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))
-Case conversion may be inaccurate. Consider using '#align multiplicity.finite_int_iff multiplicity.finite_int_iffₓ'. -/
 theorem finite_int_iff {a b : ℤ} : Finite a b ↔ a.natAbs ≠ 1 ∧ b ≠ 0 := by
   rw [finite_int_iff_nat_abs_finite, finite_nat_iff, pos_iff_ne_zero, Int.natAbs_ne_zero]
 #align multiplicity.finite_int_iff multiplicity.finite_int_iff
@@ -528,12 +372,6 @@ instance decidableNat : DecidableRel fun a b : ℕ => (multiplicity a b).Dom :=
 #align multiplicity.decidable_nat multiplicity.decidableNat
 -/
 
-/- warning: multiplicity.decidable_int -> multiplicity.decidableInt is a dubious translation:
-lean 3 declaration is
-  DecidableRel.{1} Int (fun (a : Int) (b : Int) => Part.Dom.{0} Nat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) a b))
-but is expected to have type
-  DecidableRel.{1} Int (fun (a : Int) (b : Int) => Part.Dom.{0} Nat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) a b))
-Case conversion may be inaccurate. Consider using '#align multiplicity.decidable_int multiplicity.decidableIntₓ'. -/
 instance decidableInt : DecidableRel fun a b : ℤ => (multiplicity a b).Dom := fun a b =>
   decidable_of_iff _ finite_int_iff.symm
 #align multiplicity.decidable_int multiplicity.decidableInt
@@ -554,32 +392,14 @@ theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
 #align induction_on_primes induction_on_primes
 -/
 
-/- warning: int.associated_nat_abs -> Int.associated_natAbs is a dubious translation:
-lean 3 declaration is
-  forall (k : Int), Associated.{0} Int Int.monoid k ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs k))
-but is expected to have type
-  forall (k : Int), Associated.{0} Int Int.instMonoidInt k (Nat.cast.{0} Int instNatCastInt (Int.natAbs k))
-Case conversion may be inaccurate. Consider using '#align int.associated_nat_abs Int.associated_natAbsₓ'. -/
 theorem Int.associated_natAbs (k : ℤ) : Associated k k.natAbs :=
   associated_of_dvd_dvd (Int.coe_nat_dvd_right.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
 #align int.associated_nat_abs Int.associated_natAbs
 
-/- warning: int.prime_iff_nat_abs_prime -> Int.prime_iff_natAbs_prime is a dubious translation:
-lean 3 declaration is
-  forall {k : Int}, Iff (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) k) (Nat.Prime (Int.natAbs k))
-but is expected to have type
-  forall {k : Int}, Iff (Prime.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) k) (Nat.Prime (Int.natAbs k))
-Case conversion may be inaccurate. Consider using '#align int.prime_iff_nat_abs_prime Int.prime_iff_natAbs_primeₓ'. -/
 theorem Int.prime_iff_natAbs_prime {k : ℤ} : Prime k ↔ Nat.Prime k.natAbs :=
   (Int.associated_natAbs k).prime_iff.trans Nat.prime_iff_prime_int.symm
 #align int.prime_iff_nat_abs_prime Int.prime_iff_natAbs_prime
 
-/- warning: int.associated_iff_nat_abs -> Int.associated_iff_natAbs is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.monoid a b) (Eq.{1} Nat (Int.natAbs a) (Int.natAbs b))
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.instMonoidInt a b) (Eq.{1} Nat (Int.natAbs a) (Int.natAbs b))
-Case conversion may be inaccurate. Consider using '#align int.associated_iff_nat_abs Int.associated_iff_natAbsₓ'. -/
 theorem Int.associated_iff_natAbs {a b : ℤ} : Associated a b ↔ a.natAbs = b.natAbs :=
   by
   rw [← dvd_dvd_iff_associated, ← Int.natAbs_dvd_natAbs, ← Int.natAbs_dvd_natAbs,
@@ -587,12 +407,6 @@ theorem Int.associated_iff_natAbs {a b : ℤ} : Associated a b ↔ a.natAbs = b.
   exact associated_iff_eq
 #align int.associated_iff_nat_abs Int.associated_iff_natAbs
 
-/- warning: int.associated_iff -> Int.associated_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.monoid a b) (Or (Eq.{1} Int a b) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg b)))
-but is expected to have type
-  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.instMonoidInt a b) (Or (Eq.{1} Int a b) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt b)))
-Case conversion may be inaccurate. Consider using '#align int.associated_iff Int.associated_iffₓ'. -/
 theorem Int.associated_iff {a b : ℤ} : Associated a b ↔ a = b ∨ a = -b :=
   by
   rw [Int.associated_iff_natAbs]
@@ -601,12 +415,6 @@ theorem Int.associated_iff {a b : ℤ} : Associated a b ↔ a = b ∨ a = -b :=
 
 namespace Int
 
-/- warning: int.zmultiples_nat_abs -> Int.zmultiples_natAbs is a dubious translation:
-lean 3 declaration is
-  forall (a : Int), Eq.{1} (AddSubgroup.{0} Int Int.addGroup) (AddSubgroup.zmultiples.{0} Int Int.addGroup ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a))) (AddSubgroup.zmultiples.{0} Int Int.addGroup a)
-but is expected to have type
-  forall (a : Int), Eq.{1} (AddSubgroup.{0} Int Int.instAddGroupInt) (AddSubgroup.zmultiples.{0} Int Int.instAddGroupInt (Nat.cast.{0} Int instNatCastInt (Int.natAbs a))) (AddSubgroup.zmultiples.{0} Int Int.instAddGroupInt a)
-Case conversion may be inaccurate. Consider using '#align int.zmultiples_nat_abs Int.zmultiples_natAbsₓ'. -/
 theorem zmultiples_natAbs (a : ℤ) :
     AddSubgroup.zmultiples (a.natAbs : ℤ) = AddSubgroup.zmultiples a :=
   le_antisymm
@@ -614,22 +422,10 @@ theorem zmultiples_natAbs (a : ℤ) :
     (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
 #align int.zmultiples_nat_abs Int.zmultiples_natAbs
 
-/- warning: int.span_nat_abs -> Int.span_natAbs is a dubious translation:
-lean 3 declaration is
-  forall (a : Int), Eq.{1} (Ideal.{0} Int Int.semiring) (Ideal.span.{0} Int Int.semiring (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a)))) (Ideal.span.{0} Int Int.semiring (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) a))
-but is expected to have type
-  forall (a : Int), Eq.{1} (Ideal.{0} Int Int.instSemiringInt) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) (Nat.cast.{0} Int instNatCastInt (Int.natAbs a)))) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) a))
-Case conversion may be inaccurate. Consider using '#align int.span_nat_abs Int.span_natAbsₓ'. -/
 theorem span_natAbs (a : ℤ) : Ideal.span ({a.natAbs} : Set ℤ) = Ideal.span {a} := by
   rw [Ideal.span_singleton_eq_span_singleton]; exact (associated_nat_abs _).symm
 #align int.span_nat_abs Int.span_natAbs
 
-/- warning: int.eq_pow_of_mul_eq_pow_bit1_left -> Int.eq_pow_of_mul_eq_pow_bit1_left is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))))
-Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_leftₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, a = d ^ bit1 k :=
   by
@@ -639,23 +435,11 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
   obtain rfl | rfl := hd <;> exact ⟨_, rfl⟩
 #align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_left
 
-/- warning: int.eq_pow_of_mul_eq_pow_bit1_right -> Int.eq_pow_of_mul_eq_pow_bit1_right is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))))
-Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_rightₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1_right {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, b = d ^ bit1 k :=
   eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h)
 #align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_right
 
-/- warning: int.eq_pow_of_mul_eq_pow_bit1 -> Int.eq_pow_of_mul_eq_pow_bit1 is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (And (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))) (Exists.{1} Int (fun (e : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) e (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (And (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))) (Exists.{1} Int (fun (e : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) e (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))))))
-Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1 Int.eq_pow_of_mul_eq_pow_bit1ₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1 {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : (∃ d, a = d ^ bit1 k) ∧ ∃ e, b = e ^ bit1 k :=
   ⟨eq_pow_of_mul_eq_pow_bit1_left hab h, eq_pow_of_mul_eq_pow_bit1_right hab h⟩

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

@@ -47,9 +47,7 @@ instance : WfDvdMonoid ℕ :=
         (WithTop.wellFounded_lt Nat.lt_wfRel)
     intro a b h
     cases a
-    · exfalso
-      revert h
-      simp [DvdNotUnit]
+    · exfalso; revert h; simp [DvdNotUnit]
     cases b
     · simpa [succ_ne_zero] using WithTop.coe_lt_top (a + 1)
     cases' dvd_and_not_dvd_iff.2 h with h1 h2
@@ -250,10 +248,8 @@ Case conversion may be inaccurate. Consider using '#align int.exists_unit_of_abs
 theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
   by
   cases' nat_abs_eq a with h
-  · use 1, isUnit_one
-    rw [← h, one_mul]
-  · use -1, is_unit_one.neg
-    rw [← neg_eq_iff_eq_neg.mpr h]
+  · use 1, isUnit_one; rw [← h, one_mul]
+  · use -1, is_unit_one.neg; rw [← neg_eq_iff_eq_neg.mpr h]
     simp only [neg_mul, one_mul]
 #align int.exists_unit_of_abs Int.exists_unit_of_abs
 
@@ -329,16 +325,11 @@ Case conversion may be inaccurate. Consider using '#align int.sq_of_gcd_eq_one I
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   by
-  have h' : IsUnit (GCDMonoid.gcd a b) :=
-    by
-    rw [← coe_gcd, h, Int.ofNat_one]
-    exact isUnit_one
+  have h' : IsUnit (GCDMonoid.gcd a b) := by rw [← coe_gcd, h, Int.ofNat_one]; exact isUnit_one
   obtain ⟨d, ⟨u, hu⟩⟩ := exists_associated_pow_of_mul_eq_pow h' HEq
   use d
   rw [← hu]
-  cases' Int.units_eq_one_or u with hu' hu' <;>
-    · rw [hu']
-      simp
+  cases' Int.units_eq_one_or u with hu' hu' <;> · rw [hu']; simp
 #align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_one
 
 /- warning: int.sq_of_coprime -> Int.sq_of_coprime is a dubious translation:
@@ -629,10 +620,8 @@ lean 3 declaration is
 but is expected to have type
   forall (a : Int), Eq.{1} (Ideal.{0} Int Int.instSemiringInt) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) (Nat.cast.{0} Int instNatCastInt (Int.natAbs a)))) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) a))
 Case conversion may be inaccurate. Consider using '#align int.span_nat_abs Int.span_natAbsₓ'. -/
-theorem span_natAbs (a : ℤ) : Ideal.span ({a.natAbs} : Set ℤ) = Ideal.span {a} :=
-  by
-  rw [Ideal.span_singleton_eq_span_singleton]
-  exact (associated_nat_abs _).symm
+theorem span_natAbs (a : ℤ) : Ideal.span ({a.natAbs} : Set ℤ) = Ideal.span {a} := by
+  rw [Ideal.span_singleton_eq_span_singleton]; exact (associated_nat_abs _).symm
 #align int.span_nat_abs Int.span_natAbs
 
 /- warning: int.eq_pow_of_mul_eq_pow_bit1_left -> Int.eq_pow_of_mul_eq_pow_bit1_left is a dubious translation:

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

@@ -120,7 +120,7 @@ instance : NormalizationMonoid ℤ
 lean 3 declaration is
   forall {z : Int}, (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z) -> (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
 but is expected to have type
-  forall {z : Int}, (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
+  forall {z : Int}, (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
 Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonneg Int.normalize_of_nonnegₓ'. -/
 theorem normalize_of_nonneg {z : ℤ} (h : 0 ≤ z) : normalize z = z :=
   show z * ↑(ite _ _ _) = z by rw [if_pos h, Units.val_one, mul_one]
@@ -130,7 +130,7 @@ theorem normalize_of_nonneg {z : ℤ} (h : 0 ≤ z) : normalize z = z :=
 lean 3 declaration is
   forall {z : Int}, (LE.le.{0} Int Int.hasLe z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.hasNeg z))
 but is expected to have type
-  forall {z : Int}, (LE.le.{0} Int Int.instLEInt z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.instNegInt z))
+  forall {z : Int}, (LE.le.{0} Int Int.instLEInt z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.instNegInt z))
 Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonpos Int.normalize_of_nonposₓ'. -/
 theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
   by
@@ -144,7 +144,7 @@ theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) (Nat.cast.{0} Int instNatCastInt n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) instNatCastInt n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) (Nat.cast.{0} Int instNatCastInt n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) instNatCastInt n)
 Case conversion may be inaccurate. Consider using '#align int.normalize_coe_nat Int.normalize_coe_natₓ'. -/
 theorem normalize_coe_nat (n : ℕ) : normalize (n : ℤ) = n :=
   normalize_of_nonneg (ofNat_le_ofNat_of_le <| Nat.zero_le n)
@@ -154,7 +154,7 @@ theorem normalize_coe_nat (n : ℕ) : normalize (n : ℤ) = n :=
 lean 3 declaration is
   forall (z : Int), Eq.{1} Int (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
 but is expected to have type
-  forall (z : Int), Eq.{1} Int (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.instNegInt (SemilatticeSup.toSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (DistribLattice.toLattice.{0} Int (instDistribLattice.{0} Int Int.instLinearOrderInt))))) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
+  forall (z : Int), Eq.{1} Int (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.instNegInt (SemilatticeSup.toSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (DistribLattice.toLattice.{0} Int (instDistribLattice.{0} Int Int.instLinearOrderInt))))) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
 Case conversion may be inaccurate. Consider using '#align int.abs_eq_normalize Int.abs_eq_normalizeₓ'. -/
 theorem abs_eq_normalize (z : ℤ) : |z| = normalize z := by
   cases le_total 0 z <;> simp [normalize_of_nonneg, normalize_of_nonpos, *]
@@ -164,7 +164,7 @@ theorem abs_eq_normalize (z : ℤ) : |z| = normalize z := by
 lean 3 declaration is
   forall {z : Int}, (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z)
 but is expected to have type
-  forall {z : Int}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
+  forall {z : Int}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
 Case conversion may be inaccurate. Consider using '#align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_selfₓ'. -/
 theorem nonneg_of_normalize_eq_self {z : ℤ} (hz : normalize z = z) : 0 ≤ z :=
   abs_eq_self.1 <| by rw [abs_eq_normalize, hz]
@@ -174,7 +174,7 @@ theorem nonneg_of_normalize_eq_self {z : ℤ} (hz : normalize z = z) : 0 ≤ z :
 lean 3 declaration is
   forall (z : Int), Iff (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z)
 but is expected to have type
-  forall (z : Int), Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
+  forall (z : Int), Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
 Case conversion may be inaccurate. Consider using '#align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_selfₓ'. -/
 theorem nonneg_iff_normalize_eq_self (z : ℤ) : normalize z = z ↔ 0 ≤ z :=
   ⟨nonneg_of_normalize_eq_self, normalize_of_nonneg⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
 
 ! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit c085f3044fe585c575e322bfab45b3633c48d820
+! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -618,8 +618,9 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align int.zmultiples_nat_abs Int.zmultiples_natAbsₓ'. -/
 theorem zmultiples_natAbs (a : ℤ) :
     AddSubgroup.zmultiples (a.natAbs : ℤ) = AddSubgroup.zmultiples a :=
-  le_antisymm (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (dvd_natAbs.mpr (dvd_refl a))))
-    (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
+  le_antisymm
+    (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (dvd_natAbs.mpr (dvd_refl a))))
+    (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
 #align int.zmultiples_nat_abs Int.zmultiples_natAbs
 
 /- warning: int.span_nat_abs -> Int.span_natAbs is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
 
 ! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit c085f3044fe585c575e322bfab45b3633c48d820
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.PrincipalIdealDomain
 /-!
 # Divisibility over ℕ and ℤ
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file collects results for the integers and natural numbers that use abstract algebra in
 their proofs or cases of ℕ and ℤ being examples of structures in abstract algebra.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -78,10 +78,22 @@ instance : NormalizedGCDMonoid ℕ :=
     normalize_gcd := fun a b => normalize_eq _
     normalize_lcm := fun a b => normalize_eq _ }
 
+/- warning: gcd_eq_nat_gcd -> gcd_eq_nat_gcd is a dubious translation:
+lean 3 declaration is
+  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.gcd.{0} Nat Nat.cancelCommMonoidWithZero Nat.gcdMonoid m n) (Nat.gcd m n)
+but is expected to have type
+  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.gcd.{0} Nat Nat.cancelCommMonoidWithZero instGCDMonoidNatCancelCommMonoidWithZero m n) (Nat.gcd m n)
+Case conversion may be inaccurate. Consider using '#align gcd_eq_nat_gcd gcd_eq_nat_gcdₓ'. -/
 theorem gcd_eq_nat_gcd (m n : ℕ) : gcd m n = Nat.gcd m n :=
   rfl
 #align gcd_eq_nat_gcd gcd_eq_nat_gcd
 
+/- warning: lcm_eq_nat_lcm -> lcm_eq_nat_lcm is a dubious translation:
+lean 3 declaration is
+  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.lcm.{0} Nat Nat.cancelCommMonoidWithZero Nat.gcdMonoid m n) (Nat.lcm m n)
+but is expected to have type
+  forall (m : Nat) (n : Nat), Eq.{1} Nat (GCDMonoid.lcm.{0} Nat Nat.cancelCommMonoidWithZero instGCDMonoidNatCancelCommMonoidWithZero m n) (Nat.lcm m n)
+Case conversion may be inaccurate. Consider using '#align lcm_eq_nat_lcm lcm_eq_nat_lcmₓ'. -/
 theorem lcm_eq_nat_lcm (m n : ℕ) : lcm m n = Nat.lcm m n :=
   rfl
 #align lcm_eq_nat_lcm lcm_eq_nat_lcm
@@ -101,10 +113,22 @@ instance : NormalizationMonoid ℤ
     (units_eq_one_or u).elim (fun eq => Eq.symm ▸ if_pos zero_le_one) fun eq =>
       Eq.symm ▸ if_neg (not_le_of_gt <| show (-1 : ℤ) < 0 by decide)
 
+/- warning: int.normalize_of_nonneg -> Int.normalize_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {z : Int}, (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z) -> (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
+but is expected to have type
+  forall {z : Int}, (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z)
+Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonneg Int.normalize_of_nonnegₓ'. -/
 theorem normalize_of_nonneg {z : ℤ} (h : 0 ≤ z) : normalize z = z :=
   show z * ↑(ite _ _ _) = z by rw [if_pos h, Units.val_one, mul_one]
 #align int.normalize_of_nonneg Int.normalize_of_nonneg
 
+/- warning: int.normalize_of_nonpos -> Int.normalize_of_nonpos is a dubious translation:
+lean 3 declaration is
+  forall {z : Int}, (LE.le.{0} Int Int.hasLe z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.hasNeg z))
+but is expected to have type
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(CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) (Neg.neg.{0} Int Int.instNegInt z))
+Case conversion may be inaccurate. Consider using '#align int.normalize_of_nonpos Int.normalize_of_nonposₓ'. -/
 theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
   by
   obtain rfl | h := h.eq_or_lt
@@ -113,22 +137,52 @@ theorem normalize_of_nonpos {z : ℤ} (h : z ≤ 0) : normalize z = -z :=
     rw [if_neg (not_le_of_gt h), Units.val_neg, Units.val_one, mul_neg_one]
 #align int.normalize_of_nonpos Int.normalize_of_nonpos
 
+/- warning: int.normalize_coe_nat -> Int.normalize_coe_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) (Nat.cast.{0} Int instNatCastInt n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) (Nat.cast.{0} Int instNatCastInt n)) instNatCastInt n)
+Case conversion may be inaccurate. Consider using '#align int.normalize_coe_nat Int.normalize_coe_natₓ'. -/
 theorem normalize_coe_nat (n : ℕ) : normalize (n : ℤ) = n :=
   normalize_of_nonneg (ofNat_le_ofNat_of_le <| Nat.zero_le n)
 #align int.normalize_coe_nat Int.normalize_coe_nat
 
+/- warning: int.abs_eq_normalize -> Int.abs_eq_normalize is a dubious translation:
+lean 3 declaration is
+  forall (z : Int), Eq.{1} Int (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
+but is expected to have type
+  forall (z : Int), Eq.{1} Int (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.instNegInt (SemilatticeSup.toSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (DistribLattice.toLattice.{0} Int (instDistribLattice.{0} Int Int.instLinearOrderInt))))) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z)
+Case conversion may be inaccurate. Consider using '#align int.abs_eq_normalize Int.abs_eq_normalizeₓ'. -/
 theorem abs_eq_normalize (z : ℤ) : |z| = normalize z := by
   cases le_total 0 z <;> simp [normalize_of_nonneg, normalize_of_nonpos, *]
 #align int.abs_eq_normalize Int.abs_eq_normalize
 
+/- warning: int.nonneg_of_normalize_eq_self -> Int.nonneg_of_normalize_eq_self is a dubious translation:
+lean 3 declaration is
+  forall {z : Int}, (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z)
+but is expected to have type
+  forall {z : Int}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
+Case conversion may be inaccurate. Consider using '#align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_selfₓ'. -/
 theorem nonneg_of_normalize_eq_self {z : ℤ} (hz : normalize z = z) : 0 ≤ z :=
   abs_eq_self.1 <| by rw [abs_eq_normalize, hz]
 #align int.nonneg_of_normalize_eq_self Int.nonneg_of_normalize_eq_self
 
+/- warning: int.nonneg_iff_normalize_eq_self -> Int.nonneg_iff_normalize_eq_self is a dubious translation:
+lean 3 declaration is
+  forall (z : Int), Iff (Eq.{1} Int (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (fun (_x : MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) => Int -> Int) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.commSemiring (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) z)
+but is expected to have type
+  forall (z : Int), Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int (fun (_x : Int) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Int) => Int) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MulOneClass.toMul.{0} Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MulZeroOneClass.toMulOneClass.{0} Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))))) Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Int Int (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))) (MonoidWithZero.toMulZeroOneClass.{0} Int (CommMonoidWithZero.toMonoidWithZero.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))))))))) (normalize.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))) Int.normalizationMonoid) z) z) (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) z)
+Case conversion may be inaccurate. Consider using '#align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_selfₓ'. -/
 theorem nonneg_iff_normalize_eq_self (z : ℤ) : normalize z = z ↔ 0 ≤ z :=
   ⟨nonneg_of_normalize_eq_self, normalize_of_nonneg⟩
 #align int.nonneg_iff_normalize_eq_self Int.nonneg_iff_normalize_eq_self
 
+/- warning: int.eq_of_associated_of_nonneg -> Int.eq_of_associated_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, (Associated.{0} Int Int.monoid a b) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) a) -> (LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) b) -> (Eq.{1} Int a b)
+but is expected to have type
+  forall {a : Int} {b : Int}, (Associated.{0} Int Int.instMonoidInt a b) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) a) -> (LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) b) -> (Eq.{1} Int a b)
+Case conversion may be inaccurate. Consider using '#align int.eq_of_associated_of_nonneg Int.eq_of_associated_of_nonnegₓ'. -/
 theorem eq_of_associated_of_nonneg {a b : ℤ} (h : Associated a b) (ha : 0 ≤ a) (hb : 0 ≤ b) :
     a = b :=
   dvd_antisymm_of_normalize_eq (normalize_of_nonneg ha) (normalize_of_nonneg hb) h.Dvd h.symm.Dvd
@@ -158,24 +212,38 @@ instance : NormalizedGCDMonoid ℤ :=
     normalize_gcd := fun a b => normalize_coe_nat _
     normalize_lcm := fun a b => normalize_coe_nat _ }
 
+#print Int.coe_gcd /-
 theorem coe_gcd (i j : ℤ) : ↑(Int.gcd i j) = GCDMonoid.gcd i j :=
   rfl
 #align int.coe_gcd Int.coe_gcd
+-/
 
+#print Int.coe_lcm /-
 theorem coe_lcm (i j : ℤ) : ↑(Int.lcm i j) = GCDMonoid.lcm i j :=
   rfl
 #align int.coe_lcm Int.coe_lcm
+-/
 
+#print Int.natAbs_gcd /-
 theorem natAbs_gcd (i j : ℤ) : natAbs (GCDMonoid.gcd i j) = Int.gcd i j :=
   rfl
 #align int.nat_abs_gcd Int.natAbs_gcd
+-/
 
+#print Int.natAbs_lcm /-
 theorem natAbs_lcm (i j : ℤ) : natAbs (GCDMonoid.lcm i j) = Int.lcm i j :=
   rfl
 #align int.nat_abs_lcm Int.natAbs_lcm
+-/
 
 end GCDMonoid
 
+/- warning: int.exists_unit_of_abs -> Int.exists_unit_of_abs is a dubious translation:
+lean 3 declaration is
+  forall (a : Int), Exists.{1} Int (fun (u : Int) => Exists.{0} (IsUnit.{0} Int Int.monoid u) (fun (h : IsUnit.{0} Int Int.monoid u) => Eq.{1} Int ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) u a)))
+but is expected to have type
+  forall (a : Int), Exists.{1} Int (fun (u : Int) => Exists.{0} (IsUnit.{0} Int Int.instMonoidInt u) (fun (h : IsUnit.{0} Int Int.instMonoidInt u) => Eq.{1} Int (Nat.cast.{0} Int instNatCastInt (Int.natAbs a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) u a)))
+Case conversion may be inaccurate. Consider using '#align int.exists_unit_of_abs Int.exists_unit_of_absₓ'. -/
 theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs a : ℤ) = u * a :=
   by
   cases' nat_abs_eq a with h
@@ -186,10 +254,18 @@ theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs
     simp only [neg_mul, one_mul]
 #align int.exists_unit_of_abs Int.exists_unit_of_abs
 
+#print Int.gcd_eq_natAbs /-
 theorem gcd_eq_natAbs {a b : ℤ} : Int.gcd a b = Nat.gcd a.natAbs b.natAbs :=
   rfl
 #align int.gcd_eq_nat_abs Int.gcd_eq_natAbs
+-/
 
+/- warning: int.gcd_eq_one_iff_coprime -> Int.gcd_eq_one_iff_coprime is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (IsCoprime.{0} Int Int.commSemiring a b)
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (IsCoprime.{0} Int Int.instCommSemiringInt a b)
+Case conversion may be inaccurate. Consider using '#align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprimeₓ'. -/
 theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :=
   by
   constructor
@@ -207,28 +283,46 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
+/- warning: int.coprime_iff_nat_coprime -> Int.coprime_iff_nat_coprime is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (IsCoprime.{0} Int Int.commSemiring a b) (Nat.coprime (Int.natAbs a) (Int.natAbs b))
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (IsCoprime.{0} Int Int.instCommSemiringInt a b) (Nat.coprime (Int.natAbs a) (Int.natAbs b))
+Case conversion may be inaccurate. Consider using '#align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprimeₓ'. -/
 theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_nat_abs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
 
+#print Int.gcd_ne_one_iff_gcd_mul_right_ne_one /-
 /-- If `gcd a (m * n) ≠ 1`, then `gcd a m ≠ 1` or `gcd a n ≠ 1`. -/
 theorem gcd_ne_one_iff_gcd_mul_right_ne_one {a : ℤ} {m n : ℕ} :
     a.gcd (m * n) ≠ 1 ↔ a.gcd m ≠ 1 ∨ a.gcd n ≠ 1 := by
   simp only [gcd_eq_one_iff_coprime, ← not_and_or, not_iff_not, IsCoprime.mul_right_iff]
 #align int.gcd_ne_one_iff_gcd_mul_right_ne_one Int.gcd_ne_one_iff_gcd_mul_right_ne_one
+-/
 
+#print Int.gcd_eq_one_of_gcd_mul_right_eq_one_left /-
 /-- If `gcd a (m * n) = 1`, then `gcd a m = 1`. -/
 theorem gcd_eq_one_of_gcd_mul_right_eq_one_left {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
     a.gcd m = 1 :=
   Nat.dvd_one.mp <| trans_rel_left _ (gcd_dvd_gcd_mul_right_right a m n) h
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_left Int.gcd_eq_one_of_gcd_mul_right_eq_one_left
+-/
 
+#print Int.gcd_eq_one_of_gcd_mul_right_eq_one_right /-
 /-- If `gcd a (m * n) = 1`, then `gcd a n = 1`. -/
 theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
     a.gcd n = 1 :=
   Nat.dvd_one.mp <| trans_rel_left _ (gcd_dvd_gcd_mul_left_right a n m) h
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
+-/
 
+/- warning: int.sq_of_gcd_eq_one -> Int.sq_of_gcd_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (Eq.{1} Nat (Int.gcd a b) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_oneₓ'. -/
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   by
@@ -244,11 +338,23 @@ theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^
       simp
 #align int.sq_of_gcd_eq_one Int.sq_of_gcd_eq_one
 
+/- warning: int.sq_of_coprime -> Int.sq_of_coprime is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a0 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) -> (Exists.{1} Int (fun (a0 : Int) => Or (Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a0 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align int.sq_of_coprime Int.sq_of_coprimeₓ'. -/
 theorem sq_of_coprime {a b c : ℤ} (h : IsCoprime a b) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 :=
   sq_of_gcd_eq_one (gcd_eq_one_iff_coprime.mpr h) HEq
 #align int.sq_of_coprime Int.sq_of_coprime
 
+/- warning: int.nat_abs_euclidean_domain_gcd -> Int.natAbs_euclideanDomain_gcd is a dubious translation:
+lean 3 declaration is
+  forall (a : Int) (b : Int), Eq.{1} Nat (Int.natAbs (EuclideanDomain.gcd.{0} Int Int.euclideanDomain (fun (a : Int) (b : Int) => Int.decidableEq a b) a b)) (Int.gcd a b)
+but is expected to have type
+  forall (a : Int) (b : Int), Eq.{1} Nat (Int.natAbs (EuclideanDomain.gcd.{0} ([mdata borrowed:1 Int]) Int.euclideanDomain (fun (a : [mdata borrowed:1 Int]) (b : [mdata borrowed:1 Int]) => Int.instDecidableEqInt a b) a b)) (Int.gcd a b)
+Case conversion may be inaccurate. Consider using '#align int.nat_abs_euclidean_domain_gcd Int.natAbs_euclideanDomain_gcdₓ'. -/
 theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd a b) = Int.gcd a b :=
   by
   apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]
@@ -260,6 +366,12 @@ theorem natAbs_euclideanDomain_gcd (a b : ℤ) : Int.natAbs (EuclideanDomain.gcd
 
 end Int
 
+/- warning: associates_int_equiv_nat -> associatesIntEquivNat is a dubious translation:
+lean 3 declaration is
+  Equiv.{1, 1} (Associates.{0} Int Int.monoid) Nat
+but is expected to have type
+  Equiv.{1, 1} (Associates.{0} Int Int.instMonoidInt) Nat
+Case conversion may be inaccurate. Consider using '#align associates_int_equiv_nat associatesIntEquivNatₓ'. -/
 /-- Maps an associate class of integers consisting of `-n, n` to `n : ℕ` -/
 def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
   by
@@ -274,6 +386,12 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ :=
     rw [← normalize_apply, ← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
 #align associates_int_equiv_nat associatesIntEquivNat
 
+/- warning: int.prime.dvd_mul -> Int.Prime.dvd_mul is a dubious translation:
+lean 3 declaration is
+  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) -> (Or (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs m)) (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs n)))
+but is expected to have type
+  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) -> (Or (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs m)) (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs n)))
+Case conversion may be inaccurate. Consider using '#align int.prime.dvd_mul Int.Prime.dvd_mulₓ'. -/
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     p ∣ m.natAbs ∨ p ∣ n.natAbs :=
   by
@@ -282,6 +400,12 @@ theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_mul Int.Prime.dvd_mul
 
+/- warning: int.prime.dvd_mul' -> Int.Prime.dvd_mul' is a dubious translation:
+lean 3 declaration is
+  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) -> (Or (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) m) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) n))
+but is expected to have type
+  forall {m : Int} {n : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) -> (Or (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) m) (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) n))
+Case conversion may be inaccurate. Consider using '#align int.prime.dvd_mul' Int.Prime.dvd_mul'ₓ'. -/
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     (p : ℤ) ∣ m ∨ (p : ℤ) ∣ n :=
   by
@@ -289,6 +413,12 @@ theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : 
   exact Int.Prime.dvd_mul hp h
 #align int.prime.dvd_mul' Int.Prime.dvd_mul'
 
+/- warning: int.prime.dvd_pow -> Int.Prime.dvd_pow is a dubious translation:
+lean 3 declaration is
+  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n k)) -> (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs n))
+but is expected to have type
+  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat n k)) -> (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs n))
+Case conversion may be inaccurate. Consider using '#align int.prime.dvd_pow Int.Prime.dvd_powₓ'. -/
 theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     p ∣ n.natAbs := by
   apply @Nat.Prime.dvd_of_dvd_pow _ _ k hp
@@ -296,12 +426,24 @@ theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ
   exact int.coe_nat_dvd_left.mp h
 #align int.prime.dvd_pow Int.Prime.dvd_pow
 
+/- warning: int.prime.dvd_pow' -> Int.Prime.dvd_pow' is a dubious translation:
+lean 3 declaration is
+  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) n k)) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) n)
+but is expected to have type
+  forall {n : Int} {k : Nat} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat n k)) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) n)
+Case conversion may be inaccurate. Consider using '#align int.prime.dvd_pow' Int.Prime.dvd_pow'ₓ'. -/
 theorem Int.Prime.dvd_pow' {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     (p : ℤ) ∣ n := by
   rw [Int.coe_nat_dvd_left]
   exact Int.Prime.dvd_pow hp h
 #align int.prime.dvd_pow' Int.Prime.dvd_pow'
 
+/- warning: prime_two_or_dvd_of_dvd_two_mul_pow_self_two -> prime_two_or_dvd_of_dvd_two_mul_pow_self_two is a dubious translation:
+lean 3 declaration is
+  forall {m : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) m (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> (Or (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Dvd.Dvd.{0} Nat Nat.hasDvd p (Int.natAbs m)))
+but is expected to have type
+  forall {m : Int} {p : Nat}, (Nat.Prime p) -> (Dvd.dvd.{0} Int Int.instDvdInt (Nat.cast.{0} Int instNatCastInt p) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) m (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) -> (Or (Eq.{1} Nat p (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Dvd.dvd.{0} Nat Nat.instDvdNat p (Int.natAbs m)))
+Case conversion may be inaccurate. Consider using '#align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_twoₓ'. -/
 theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : Nat.Prime p)
     (h : (p : ℤ) ∣ 2 * m ^ 2) : p = 2 ∨ p ∣ Int.natAbs m :=
   by
@@ -313,6 +455,12 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
     exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
 
+/- warning: int.exists_prime_and_dvd -> Int.exists_prime_and_dvd is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, (Ne.{1} Nat (Int.natAbs n) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Exists.{1} Int (fun (p : Int) => And (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) p) (Dvd.Dvd.{0} Int (semigroupDvd.{0} Int Int.semigroup) p n)))
+but is expected to have type
+  forall {n : Int}, (Ne.{1} Nat (Int.natAbs n) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Exists.{1} Int (fun (p : Int) => And (Prime.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) p) (Dvd.dvd.{0} Int Int.instDvdInt p n)))
+Case conversion may be inaccurate. Consider using '#align int.exists_prime_and_dvd Int.exists_prime_and_dvdₓ'. -/
 theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime p ∧ p ∣ n :=
   by
   obtain ⟨p, pp, pd⟩ := Nat.exists_prime_and_dvd hn
@@ -321,6 +469,12 @@ theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime
 
 open UniqueFactorizationMonoid
 
+/- warning: nat.factors_eq -> Nat.factors_eq is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) (normalizationMonoidOfUniqueUnits.{0} Nat Nat.cancelCommMonoidWithZero Nat.unique_units) Nat.uniqueFactorizationMonoid n) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (List.{0} Nat) (Multiset.{0} Nat) (HasLiftT.mk.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (CoeTCₓ.coe.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (coeBase.{1, 1} (List.{0} Nat) (Multiset.{0} Nat) (Multiset.hasCoe.{0} Nat)))) (Nat.factors n))
+but is expected to have type
+  forall {n : Nat}, Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (NormalizedGCDMonoid.toNormalizationMonoid.{0} Nat Nat.cancelCommMonoidWithZero instNormalizedGCDMonoidNatCancelCommMonoidWithZero) Nat.instUniqueFactorizationMonoidNatCancelCommMonoidWithZero n) (Multiset.ofList.{0} Nat (Nat.factors n))
+Case conversion may be inaccurate. Consider using '#align nat.factors_eq Nat.factors_eqₓ'. -/
 theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
   by
   cases n; · simp
@@ -334,6 +488,12 @@ theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors :=
     exact Nat.prime_of_mem_factors hx
 #align nat.factors_eq Nat.factors_eq
 
+/- warning: nat.factors_multiset_prod_of_irreducible -> Nat.factors_multiset_prod_of_irreducible is a dubious translation:
+lean 3 declaration is
+  forall {s : Multiset.{0} Nat}, (forall (x : Nat), (Membership.Mem.{0, 0} Nat (Multiset.{0} Nat) (Multiset.hasMem.{0} Nat) x s) -> (Irreducible.{0} Nat Nat.monoid x)) -> (Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) (normalizationMonoidOfUniqueUnits.{0} Nat Nat.cancelCommMonoidWithZero Nat.unique_units) Nat.uniqueFactorizationMonoid (Multiset.prod.{0} Nat Nat.commMonoid s)) s)
+but is expected to have type
+  forall {s : Multiset.{0} Nat}, (forall (x : Nat), (Membership.mem.{0, 0} Nat (Multiset.{0} Nat) (Multiset.instMembershipMultiset.{0} Nat) x s) -> (Irreducible.{0} Nat Nat.monoid x)) -> (Eq.{1} (Multiset.{0} Nat) (UniqueFactorizationMonoid.normalizedFactors.{0} Nat Nat.cancelCommMonoidWithZero (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (NormalizedGCDMonoid.toNormalizationMonoid.{0} Nat Nat.cancelCommMonoidWithZero instNormalizedGCDMonoidNatCancelCommMonoidWithZero) Nat.instUniqueFactorizationMonoidNatCancelCommMonoidWithZero (Multiset.prod.{0} Nat Nat.commMonoid s)) s)
+Case conversion may be inaccurate. Consider using '#align nat.factors_multiset_prod_of_irreducible Nat.factors_multiset_prod_of_irreducibleₓ'. -/
 theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
     (h : ∀ x : ℕ, x ∈ s → Irreducible x) : normalizedFactors s.Prod = s :=
   by
@@ -348,24 +508,45 @@ theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
 
 namespace multiplicity
 
+/- warning: multiplicity.finite_int_iff_nat_abs_finite -> multiplicity.finite_int_iff_natAbs_finite is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.monoid a b) (multiplicity.Finite.{0} Nat Nat.monoid (Int.natAbs a) (Int.natAbs b))
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.instMonoidInt a b) (multiplicity.Finite.{0} Nat Nat.monoid (Int.natAbs a) (Int.natAbs b))
+Case conversion may be inaccurate. Consider using '#align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finiteₓ'. -/
 theorem finite_int_iff_natAbs_finite {a b : ℤ} : Finite a b ↔ Finite a.natAbs b.natAbs := by
   simp only [finite_def, ← Int.natAbs_dvd_natAbs, Int.natAbs_pow]
 #align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finite
 
+/- warning: multiplicity.finite_int_iff -> multiplicity.finite_int_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.monoid a b) (And (Ne.{1} Nat (Int.natAbs a) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (multiplicity.Finite.{0} Int Int.instMonoidInt a b) (And (Ne.{1} Nat (Int.natAbs a) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))
+Case conversion may be inaccurate. Consider using '#align multiplicity.finite_int_iff multiplicity.finite_int_iffₓ'. -/
 theorem finite_int_iff {a b : ℤ} : Finite a b ↔ a.natAbs ≠ 1 ∧ b ≠ 0 := by
   rw [finite_int_iff_nat_abs_finite, finite_nat_iff, pos_iff_ne_zero, Int.natAbs_ne_zero]
 #align multiplicity.finite_int_iff multiplicity.finite_int_iff
 
+#print multiplicity.decidableNat /-
 instance decidableNat : DecidableRel fun a b : ℕ => (multiplicity a b).Dom := fun a b =>
   decidable_of_iff _ finite_nat_iff.symm
 #align multiplicity.decidable_nat multiplicity.decidableNat
+-/
 
+/- warning: multiplicity.decidable_int -> multiplicity.decidableInt is a dubious translation:
+lean 3 declaration is
+  DecidableRel.{1} Int (fun (a : Int) (b : Int) => Part.Dom.{0} Nat (multiplicity.{0} Int Int.monoid (fun (a : Int) (b : Int) => Int.decidableDvd a b) a b))
+but is expected to have type
+  DecidableRel.{1} Int (fun (a : Int) (b : Int) => Part.Dom.{0} Nat (multiplicity.{0} Int Int.instMonoidInt (fun (a : Int) (b : Int) => Int.decidableDvd a b) a b))
+Case conversion may be inaccurate. Consider using '#align multiplicity.decidable_int multiplicity.decidableIntₓ'. -/
 instance decidableInt : DecidableRel fun a b : ℤ => (multiplicity a b).Dom := fun a b =>
   decidable_of_iff _ finite_int_iff.symm
 #align multiplicity.decidable_int multiplicity.decidableInt
 
 end multiplicity
 
+#print induction_on_primes /-
 theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
     (h : ∀ p a : ℕ, p.Prime → P a → P (p * a)) (n : ℕ) : P n :=
   by
@@ -377,15 +558,34 @@ theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
   · intro a p _ hp ha
     exact h p a hp.nat_prime ha
 #align induction_on_primes induction_on_primes
+-/
 
+/- warning: int.associated_nat_abs -> Int.associated_natAbs is a dubious translation:
+lean 3 declaration is
+  forall (k : Int), Associated.{0} Int Int.monoid k ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs k))
+but is expected to have type
+  forall (k : Int), Associated.{0} Int Int.instMonoidInt k (Nat.cast.{0} Int instNatCastInt (Int.natAbs k))
+Case conversion may be inaccurate. Consider using '#align int.associated_nat_abs Int.associated_natAbsₓ'. -/
 theorem Int.associated_natAbs (k : ℤ) : Associated k k.natAbs :=
   associated_of_dvd_dvd (Int.coe_nat_dvd_right.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
 #align int.associated_nat_abs Int.associated_natAbs
 
+/- warning: int.prime_iff_nat_abs_prime -> Int.prime_iff_natAbs_prime is a dubious translation:
+lean 3 declaration is
+  forall {k : Int}, Iff (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) k) (Nat.Prime (Int.natAbs k))
+but is expected to have type
+  forall {k : Int}, Iff (Prime.{0} Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) k) (Nat.Prime (Int.natAbs k))
+Case conversion may be inaccurate. Consider using '#align int.prime_iff_nat_abs_prime Int.prime_iff_natAbs_primeₓ'. -/
 theorem Int.prime_iff_natAbs_prime {k : ℤ} : Prime k ↔ Nat.Prime k.natAbs :=
   (Int.associated_natAbs k).prime_iff.trans Nat.prime_iff_prime_int.symm
 #align int.prime_iff_nat_abs_prime Int.prime_iff_natAbs_prime
 
+/- warning: int.associated_iff_nat_abs -> Int.associated_iff_natAbs is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.monoid a b) (Eq.{1} Nat (Int.natAbs a) (Int.natAbs b))
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.instMonoidInt a b) (Eq.{1} Nat (Int.natAbs a) (Int.natAbs b))
+Case conversion may be inaccurate. Consider using '#align int.associated_iff_nat_abs Int.associated_iff_natAbsₓ'. -/
 theorem Int.associated_iff_natAbs {a b : ℤ} : Associated a b ↔ a.natAbs = b.natAbs :=
   by
   rw [← dvd_dvd_iff_associated, ← Int.natAbs_dvd_natAbs, ← Int.natAbs_dvd_natAbs,
@@ -393,6 +593,12 @@ theorem Int.associated_iff_natAbs {a b : ℤ} : Associated a b ↔ a.natAbs = b.
   exact associated_iff_eq
 #align int.associated_iff_nat_abs Int.associated_iff_natAbs
 
+/- warning: int.associated_iff -> Int.associated_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.monoid a b) (Or (Eq.{1} Int a b) (Eq.{1} Int a (Neg.neg.{0} Int Int.hasNeg b)))
+but is expected to have type
+  forall {a : Int} {b : Int}, Iff (Associated.{0} Int Int.instMonoidInt a b) (Or (Eq.{1} Int a b) (Eq.{1} Int a (Neg.neg.{0} Int Int.instNegInt b)))
+Case conversion may be inaccurate. Consider using '#align int.associated_iff Int.associated_iffₓ'. -/
 theorem Int.associated_iff {a b : ℤ} : Associated a b ↔ a = b ∨ a = -b :=
   by
   rw [Int.associated_iff_natAbs]
@@ -401,18 +607,36 @@ theorem Int.associated_iff {a b : ℤ} : Associated a b ↔ a = b ∨ a = -b :=
 
 namespace Int
 
+/- warning: int.zmultiples_nat_abs -> Int.zmultiples_natAbs is a dubious translation:
+lean 3 declaration is
+  forall (a : Int), Eq.{1} (AddSubgroup.{0} Int Int.addGroup) (AddSubgroup.zmultiples.{0} Int Int.addGroup ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a))) (AddSubgroup.zmultiples.{0} Int Int.addGroup a)
+but is expected to have type
+  forall (a : Int), Eq.{1} (AddSubgroup.{0} Int Int.instAddGroupInt) (AddSubgroup.zmultiples.{0} Int Int.instAddGroupInt (Nat.cast.{0} Int instNatCastInt (Int.natAbs a))) (AddSubgroup.zmultiples.{0} Int Int.instAddGroupInt a)
+Case conversion may be inaccurate. Consider using '#align int.zmultiples_nat_abs Int.zmultiples_natAbsₓ'. -/
 theorem zmultiples_natAbs (a : ℤ) :
     AddSubgroup.zmultiples (a.natAbs : ℤ) = AddSubgroup.zmultiples a :=
   le_antisymm (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (dvd_natAbs.mpr (dvd_refl a))))
     (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
 #align int.zmultiples_nat_abs Int.zmultiples_natAbs
 
+/- warning: int.span_nat_abs -> Int.span_natAbs is a dubious translation:
+lean 3 declaration is
+  forall (a : Int), Eq.{1} (Ideal.{0} Int Int.semiring) (Ideal.span.{0} Int Int.semiring (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) (Int.natAbs a)))) (Ideal.span.{0} Int Int.semiring (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.hasSingleton.{0} Int) a))
+but is expected to have type
+  forall (a : Int), Eq.{1} (Ideal.{0} Int Int.instSemiringInt) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) (Nat.cast.{0} Int instNatCastInt (Int.natAbs a)))) (Ideal.span.{0} Int Int.instSemiringInt (Singleton.singleton.{0, 0} Int (Set.{0} Int) (Set.instSingletonSet.{0} Int) a))
+Case conversion may be inaccurate. Consider using '#align int.span_nat_abs Int.span_natAbsₓ'. -/
 theorem span_natAbs (a : ℤ) : Ideal.span ({a.natAbs} : Set ℤ) = Ideal.span {a} :=
   by
   rw [Ideal.span_singleton_eq_span_singleton]
   exact (associated_nat_abs _).symm
 #align int.span_nat_abs Int.span_natAbs
 
+/- warning: int.eq_pow_of_mul_eq_pow_bit1_left -> Int.eq_pow_of_mul_eq_pow_bit1_left is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))))
+Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_leftₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, a = d ^ bit1 k :=
   by
@@ -422,11 +646,23 @@ theorem eq_pow_of_mul_eq_pow_bit1_left {a b c : ℤ} (hab : IsCoprime a b) {k :
   obtain rfl | rfl := hd <;> exact ⟨_, rfl⟩
 #align int.eq_pow_of_mul_eq_pow_bit1_left Int.eq_pow_of_mul_eq_pow_bit1_left
 
+/- warning: int.eq_pow_of_mul_eq_pow_bit1_right -> Int.eq_pow_of_mul_eq_pow_bit1_right is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (Exists.{1} Int (fun (d : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))))
+Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_rightₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1_right {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : ∃ d, b = d ^ bit1 k :=
   eq_pow_of_mul_eq_pow_bit1_left hab.symm (by rwa [mul_comm] at h)
 #align int.eq_pow_of_mul_eq_pow_bit1_right Int.eq_pow_of_mul_eq_pow_bit1_right
 
+/- warning: int.eq_pow_of_mul_eq_pow_bit1 -> Int.eq_pow_of_mul_eq_pow_bit1 is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.commSemiring a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) a b) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))) -> (And (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) d (bit1.{0} Nat Nat.hasOne Nat.hasAdd k)))) (Exists.{1} Int (fun (e : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) e (bit1.{0} Nat Nat.hasOne Nat.hasAdd k))))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt a b) -> (forall {k : Nat}, (Eq.{1} Int (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) a b) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat c (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))) -> (And (Exists.{1} Int (fun (d : Int) => Eq.{1} Int a (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) d (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k)))) (Exists.{1} Int (fun (e : Int) => Eq.{1} Int b (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) e (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat k))))))
+Case conversion may be inaccurate. Consider using '#align int.eq_pow_of_mul_eq_pow_bit1 Int.eq_pow_of_mul_eq_pow_bit1ₓ'. -/
 theorem eq_pow_of_mul_eq_pow_bit1 {a b c : ℤ} (hab : IsCoprime a b) {k : ℕ}
     (h : a * b = c ^ bit1 k) : (∃ d, a = d ^ bit1 k) ∧ ∃ e, b = e ^ bit1 k :=
   ⟨eq_pow_of_mul_eq_pow_bit1_left hab h, eq_pow_of_mul_eq_pow_bit1_right hab h⟩

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
 
 ! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit e1bccd6e40ae78370f01659715d3c948716e3b7e
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -182,7 +182,7 @@ theorem exists_unit_of_abs (a : ℤ) : ∃ (u : ℤ)(h : IsUnit u), (Int.natAbs
   · use 1, isUnit_one
     rw [← h, one_mul]
   · use -1, is_unit_one.neg
-    rw [← neg_eq_iff_neg_eq.mp (Eq.symm h)]
+    rw [← neg_eq_iff_eq_neg.mpr h]
     simp only [neg_mul, one_mul]
 #align int.exists_unit_of_abs Int.exists_unit_of_abs
 

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

These don't use any abstract algebra.

@@ -182,18 +182,6 @@ theorem gcd_ne_one_iff_gcd_mul_right_ne_one {a : ℤ} {m n : ℕ} :
   simp only [gcd_eq_one_iff_coprime, ← not_and_or, not_iff_not, IsCoprime.mul_right_iff]
 #align int.gcd_ne_one_iff_gcd_mul_right_ne_one Int.gcd_ne_one_iff_gcd_mul_right_ne_one
 
-/-- If `gcd a (m * n) = 1`, then `gcd a m = 1`. -/
-theorem gcd_eq_one_of_gcd_mul_right_eq_one_left {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
-    a.gcd m = 1 :=
-  Nat.dvd_one.mp <| h ▸ (gcd_dvd_gcd_mul_right_right a m n)
-#align int.gcd_eq_one_of_gcd_mul_right_eq_one_left Int.gcd_eq_one_of_gcd_mul_right_eq_one_left
-
-/-- If `gcd a (m * n) = 1`, then `gcd a n = 1`. -/
-theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
-    a.gcd n = 1 :=
-  Nat.dvd_one.mp <| h ▸ (gcd_dvd_gcd_mul_left_right a n m)
-#align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
-
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :
     ∃ a0 : ℤ, a = a0 ^ 2 ∨ a = -a0 ^ 2 := by
   have h' : IsUnit (GCDMonoid.gcd a b) := by

All removed items are virtually unused in mathlib and have been deprecated for over a year.

@@ -182,18 +182,16 @@ theorem gcd_ne_one_iff_gcd_mul_right_ne_one {a : ℤ} {m n : ℕ} :
   simp only [gcd_eq_one_iff_coprime, ← not_and_or, not_iff_not, IsCoprime.mul_right_iff]
 #align int.gcd_ne_one_iff_gcd_mul_right_ne_one Int.gcd_ne_one_iff_gcd_mul_right_ne_one
 
-set_option linter.deprecated false in -- trans_rel_left
 /-- If `gcd a (m * n) = 1`, then `gcd a m = 1`. -/
 theorem gcd_eq_one_of_gcd_mul_right_eq_one_left {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
     a.gcd m = 1 :=
-  Nat.dvd_one.mp <| trans_rel_left _ (gcd_dvd_gcd_mul_right_right a m n) h
+  Nat.dvd_one.mp <| h ▸ (gcd_dvd_gcd_mul_right_right a m n)
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_left Int.gcd_eq_one_of_gcd_mul_right_eq_one_left
 
-set_option linter.deprecated false in -- trans_rel_left
 /-- If `gcd a (m * n) = 1`, then `gcd a n = 1`. -/
 theorem gcd_eq_one_of_gcd_mul_right_eq_one_right {a : ℤ} {m n : ℕ} (h : a.gcd (m * n) = 1) :
     a.gcd n = 1 :=
-  Nat.dvd_one.mp <| trans_rel_left _ (gcd_dvd_gcd_mul_left_right a n m) h
+  Nat.dvd_one.mp <| h ▸ (gcd_dvd_gcd_mul_left_right a n m)
 #align int.gcd_eq_one_of_gcd_mul_right_eq_one_right Int.gcd_eq_one_of_gcd_mul_right_eq_one_right
 
 theorem sq_of_gcd_eq_one {a b c : ℤ} (h : Int.gcd a b = 1) (heq : a * b = c ^ 2) :

Previously Mathlib.GroupTheory.Perm.Fin knew about LinearMap for no good reason, because it relied on Mathlib.RingTheory.Int.Basic for some basic things, but that file also has heavy imports.

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

@@ -54,31 +54,6 @@ instance : UniqueFactorizationMonoid ℕ :=
 
 end Nat
 
-/-- `ℕ` is a gcd_monoid. -/
-instance : GCDMonoid ℕ where
-  gcd := Nat.gcd
-  lcm := Nat.lcm
-  gcd_dvd_left := Nat.gcd_dvd_left
-  gcd_dvd_right := Nat.gcd_dvd_right
-  dvd_gcd := Nat.dvd_gcd
-  gcd_mul_lcm a b := by rw [Nat.gcd_mul_lcm]; rfl
-  lcm_zero_left := Nat.lcm_zero_left
-  lcm_zero_right := Nat.lcm_zero_right
-
-instance : NormalizedGCDMonoid ℕ :=
-  { (inferInstance : GCDMonoid ℕ),
-    (inferInstance : NormalizationMonoid ℕ) with
-    normalize_gcd := fun _ _ => normalize_eq _
-    normalize_lcm := fun _ _ => normalize_eq _ }
-
-theorem gcd_eq_nat_gcd (m n : ℕ) : gcd m n = Nat.gcd m n :=
-  rfl
-#align gcd_eq_nat_gcd gcd_eq_nat_gcd
-
-theorem lcm_eq_nat_lcm (m n : ℕ) : lcm m n = Nat.lcm m n :=
-  rfl
-#align lcm_eq_nat_lcm lcm_eq_nat_lcm
-
 namespace Int
 
 section NormalizationMonoid

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

@@ -35,9 +35,8 @@ namespace Nat
 
 instance : WfDvdMonoid ℕ :=
   ⟨by
-    refine'
-      RelHomClass.wellFounded
-        (⟨fun x : ℕ => if x = 0 then (⊤ : ℕ∞) else x, _⟩ : DvdNotUnit →r (· < ·)) wellFounded_lt
+    refine RelHomClass.wellFounded
+      (⟨fun x : ℕ => if x = 0 then (⊤ : ℕ∞) else x, ?_⟩ : DvdNotUnit →r (· < ·)) wellFounded_lt
     intro a b h
     cases' a with a
     · exfalso
@@ -253,14 +252,12 @@ end Int
 
 /-- Maps an associate class of integers consisting of `-n, n` to `n : ℕ` -/
 def associatesIntEquivNat : Associates ℤ ≃ ℕ := by
-  refine' ⟨fun z => z.out.natAbs, fun n => Associates.mk n, _, _⟩
-  · refine' fun a =>
-      Quotient.inductionOn a fun a =>
-        Associates.mk_eq_mk_iff_associated.2 <| Associated.symm <| ⟨normUnit a, _⟩
+  refine ⟨(·.out.natAbs), (Associates.mk ·), ?_, fun n ↦ ?_⟩
+  · refine Associates.forall_associated.2 fun a ↦ ?_
+    refine Associates.mk_eq_mk_iff_associated.2 <| Associated.symm <| ⟨normUnit a, ?_⟩
     simp [Int.abs_eq_normalize]
-  · intro n
-    dsimp
-    rw [← normalize_apply, ← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
+  · dsimp only [Associates.out_mk]
+    rw [← Int.abs_eq_normalize, Int.natAbs_abs, Int.natAbs_ofNat]
 #align associates_int_equiv_nat associatesIntEquivNat
 
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :

This means Mathlib.NumberTheory.Padics.PadicVal no longer needs to depend on Mathlib.RingTheory.Int.Basic, which is surprisingly heavy (in particular through Mathlib.RingTheory.Noetherian).

@@ -327,26 +327,6 @@ theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
   exact not_irreducible_zero (h 0 con)
 #align nat.factors_multiset_prod_of_irreducible Nat.factors_multiset_prod_of_irreducible
 
-namespace multiplicity
-
-theorem finite_int_iff_natAbs_finite {a b : ℤ} : Finite a b ↔ Finite a.natAbs b.natAbs := by
-  simp only [finite_def, ← Int.natAbs_dvd_natAbs, Int.natAbs_pow]
-#align multiplicity.finite_int_iff_nat_abs_finite multiplicity.finite_int_iff_natAbs_finite
-
-theorem finite_int_iff {a b : ℤ} : Finite a b ↔ a.natAbs ≠ 1 ∧ b ≠ 0 := by
-  rw [finite_int_iff_natAbs_finite, finite_nat_iff, pos_iff_ne_zero, Int.natAbs_ne_zero]
-#align multiplicity.finite_int_iff multiplicity.finite_int_iff
-
-instance decidableNat : DecidableRel fun a b : ℕ => (multiplicity a b).Dom := fun _ _ =>
-  decidable_of_iff _ finite_nat_iff.symm
-#align multiplicity.decidable_nat multiplicity.decidableNat
-
-instance decidableInt : DecidableRel fun a b : ℤ => (multiplicity a b).Dom := fun _ _ =>
-  decidable_of_iff _ finite_int_iff.symm
-#align multiplicity.decidable_int multiplicity.decidableInt
-
-end multiplicity
-
 theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
     (h : ∀ p a : ℕ, p.Prime → P a → P (p * a)) (n : ℕ) : P n := by
   apply UniqueFactorizationMonoid.induction_on_prime

Reduce the diff of #11499

Renames

All in the Int namespace:

• ofNat_eq_cast → ofNat_eq_natCast
• cast_eq_cast_iff_Nat → natCast_inj
• natCast_eq_ofNat → ofNat_eq_natCast
• coe_nat_sub → natCast_sub
• coe_nat_nonneg → natCast_nonneg
• sign_coe_add_one → sign_natCast_add_one
• nat_succ_eq_int_succ → natCast_succ
• succ_neg_nat_succ → succ_neg_natCast_succ
• coe_pred_of_pos → natCast_pred_of_pos
• coe_nat_div → natCast_div
• coe_nat_ediv → natCast_ediv
• sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
• toNat_coe_nat → toNat_natCast
• toNat_coe_nat_add_one → toNat_natCast_add_one
• coe_nat_dvd → natCast_dvd_natCast
• coe_nat_dvd_left → natCast_dvd
• coe_nat_dvd_right → dvd_natCast
• le_coe_nat_sub → le_natCast_sub
• succ_coe_nat_pos → succ_natCast_pos
• coe_nat_modEq_iff → natCast_modEq_iff
• coe_natAbs → natCast_natAbs
• coe_nat_eq_zero → natCast_eq_zero
• coe_nat_ne_zero → natCast_ne_zero
• coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
• abs_coe_nat → abs_natCast
• coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

@@ -140,10 +140,10 @@ instance : GCDMonoid ℤ where
   gcd_dvd_right a b := Int.gcd_dvd_right
   dvd_gcd := dvd_gcd
   gcd_mul_lcm a b := by
-    rw [← Int.ofNat_mul, gcd_mul_lcm, coe_natAbs, abs_eq_normalize]
+    rw [← Int.ofNat_mul, gcd_mul_lcm, natCast_natAbs, abs_eq_normalize]
     exact normalize_associated (a * b)
-  lcm_zero_left a := coe_nat_eq_zero.2 <| Nat.lcm_zero_left _
-  lcm_zero_right a := coe_nat_eq_zero.2 <| Nat.lcm_zero_right _
+  lcm_zero_left a := natCast_eq_zero.2 <| Nat.lcm_zero_left _
+  lcm_zero_right a := natCast_eq_zero.2 <| Nat.lcm_zero_right _
 
 instance : NormalizedGCDMonoid ℤ :=
   { Int.normalizationMonoid,
@@ -194,8 +194,8 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     by_contra hg
     obtain ⟨p, ⟨hp, ha, hb⟩⟩ := Nat.Prime.not_coprime_iff_dvd.mp hg
     apply Nat.Prime.not_dvd_one hp
-    rw [← coe_nat_dvd, Int.ofNat_one, ← h]
-    exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
+    rw [← natCast_dvd_natCast, Int.ofNat_one, ← h]
+    exact dvd_add ((natCast_dvd.mpr ha).mul_left _) ((natCast_dvd.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
 theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.Coprime a.natAbs b.natAbs := by
@@ -242,7 +242,7 @@ theorem sq_of_coprime {a b c : ℤ} (h : IsCoprime a b) (heq : a * b = c ^ 2) :
 
 theorem natAbs_euclideanDomain_gcd (a b : ℤ) :
     Int.natAbs (EuclideanDomain.gcd a b) = Int.gcd a b := by
-  apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]
+  apply Nat.dvd_antisymm <;> rw [← Int.natCast_dvd_natCast]
   · rw [Int.natAbs_dvd]
     exact Int.dvd_gcd (EuclideanDomain.gcd_dvd_left _ _) (EuclideanDomain.gcd_dvd_right _ _)
   · rw [Int.dvd_natAbs]
@@ -265,24 +265,24 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ := by
 
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     p ∣ m.natAbs ∨ p ∣ n.natAbs := by
-  rwa [← hp.dvd_mul, ← Int.natAbs_mul, ← Int.coe_nat_dvd_left]
+  rwa [← hp.dvd_mul, ← Int.natAbs_mul, ← Int.natCast_dvd]
 #align int.prime.dvd_mul Int.Prime.dvd_mul
 
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     (p : ℤ) ∣ m ∨ (p : ℤ) ∣ n := by
-  rw [Int.coe_nat_dvd_left, Int.coe_nat_dvd_left]
+  rw [Int.natCast_dvd, Int.natCast_dvd]
   exact Int.Prime.dvd_mul hp h
 #align int.prime.dvd_mul' Int.Prime.dvd_mul'
 
 theorem Int.Prime.dvd_pow {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     p ∣ n.natAbs := by
-  rw [Int.coe_nat_dvd_left, Int.natAbs_pow] at h
+  rw [Int.natCast_dvd, Int.natAbs_pow] at h
   exact hp.dvd_of_dvd_pow h
 #align int.prime.dvd_pow Int.Prime.dvd_pow
 
 theorem Int.Prime.dvd_pow' {n : ℤ} {k p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ n ^ k) :
     (p : ℤ) ∣ n := by
-  rw [Int.coe_nat_dvd_left]
+  rw [Int.natCast_dvd]
   exact Int.Prime.dvd_pow hp h
 #align int.prime.dvd_pow' Int.Prime.dvd_pow'
 
@@ -298,7 +298,7 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
 
 theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime p ∧ p ∣ n := by
   obtain ⟨p, pp, pd⟩ := Nat.exists_prime_and_dvd hn
-  exact ⟨p, Nat.prime_iff_prime_int.mp pp, Int.coe_nat_dvd_left.mpr pd⟩
+  exact ⟨p, Nat.prime_iff_prime_int.mp pp, Int.natCast_dvd.mpr pd⟩
 #align int.exists_prime_and_dvd Int.exists_prime_and_dvd
 
 open UniqueFactorizationMonoid
@@ -359,7 +359,7 @@ theorem induction_on_primes {P : ℕ → Prop} (h₀ : P 0) (h₁ : P 1)
 #align induction_on_primes induction_on_primes
 
 theorem Int.associated_natAbs (k : ℤ) : Associated k k.natAbs :=
-  associated_of_dvd_dvd (Int.coe_nat_dvd_right.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
+  associated_of_dvd_dvd (Int.dvd_natCast.mpr dvd_rfl) (Int.natAbs_dvd.mpr dvd_rfl)
 #align int.associated_nat_abs Int.associated_natAbs
 
 theorem Int.prime_iff_natAbs_prime {k : ℤ} : Prime k ↔ Nat.Prime k.natAbs :=

@@ -322,7 +322,7 @@ theorem Nat.factors_multiset_prod_of_irreducible {s : Multiset ℕ}
   apply
     UniqueFactorizationMonoid.factors_unique irreducible_of_normalized_factor h
       (normalizedFactors_prod _)
-  rw [Ne.def, Multiset.prod_eq_zero_iff]
+  rw [Ne, Multiset.prod_eq_zero_iff]
   intro con
   exact not_irreducible_zero (h 0 con)
 #align nat.factors_multiset_prod_of_irreducible Nat.factors_multiset_prod_of_irreducible

These did not respect the naming convention by having the coe as a prefix instead of a suffix, or vice-versa. Also add a bunch of norm_cast

@@ -309,7 +309,7 @@ theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors := by
   | succ n =>
     rw [← Multiset.rel_eq, ← associated_eq_eq]
     apply UniqueFactorizationMonoid.factors_unique irreducible_of_normalized_factor _
-    · rw [Multiset.coe_prod, Nat.prod_factors n.succ_ne_zero]
+    · rw [Multiset.prod_coe, Nat.prod_factors n.succ_ne_zero]
       apply normalizedFactors_prod (Nat.succ_ne_zero _)
     · intro x hx
       rw [Nat.irreducible_iff_prime, ← Nat.prime_iff]

Notable changes: lemmas were added in https://github.com/leanprover/std4/pull/538 about gcd and lcm, that now have implicit arguments. Mostly this is a positive change in Mathlib, we can just delete the arguments. The one to consider in review is in ModEq.

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

@@ -136,8 +136,8 @@ section GCDMonoid
 instance : GCDMonoid ℤ where
   gcd a b := Int.gcd a b
   lcm a b := Int.lcm a b
-  gcd_dvd_left a b := Int.gcd_dvd_left _ _
-  gcd_dvd_right a b := Int.gcd_dvd_right _ _
+  gcd_dvd_left a b := Int.gcd_dvd_left
+  gcd_dvd_right a b := Int.gcd_dvd_right
   dvd_gcd := dvd_gcd
   gcd_mul_lcm a b := by
     rw [← Int.ofNat_mul, gcd_mul_lcm, coe_natAbs, abs_eq_normalize]
@@ -246,7 +246,7 @@ theorem natAbs_euclideanDomain_gcd (a b : ℤ) :
   · rw [Int.natAbs_dvd]
     exact Int.dvd_gcd (EuclideanDomain.gcd_dvd_left _ _) (EuclideanDomain.gcd_dvd_right _ _)
   · rw [Int.dvd_natAbs]
-    exact EuclideanDomain.dvd_gcd (Int.gcd_dvd_left _ _) (Int.gcd_dvd_right _ _)
+    exact EuclideanDomain.dvd_gcd Int.gcd_dvd_left Int.gcd_dvd_right
 #align int.nat_abs_euclidean_domain_gcd Int.natAbs_euclideanDomain_gcd
 
 end Int

This converts usages of the pattern

cases h
case inl h' => ...
case inr h' => ...

which derive from mathported code, to the "structured cases" syntax:

cases h with
| inl h' => ...
| inr h' => ...

The case where the subgoals are handled with · instead of case is more contentious (and much more numerous) so I left those alone. This pattern also appears with cases', induction, induction', and rcases. Furthermore, there is a similar transformation for by_cases:

by_cases h : cond
case pos => ...
case neg => ...

is replaced by:

if h : cond then
  ...
else
  ...

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -304,9 +304,9 @@ theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime
 open UniqueFactorizationMonoid
 
 theorem Nat.factors_eq {n : ℕ} : normalizedFactors n = n.factors := by
-  cases n
-  case zero => simp
-  case succ n =>
+  cases n with
+  | zero => simp
+  | succ n =>
     rw [← Multiset.rel_eq, ← associated_eq_eq]
     apply UniqueFactorizationMonoid.factors_unique irreducible_of_normalized_factor _
     · rw [Multiset.coe_prod, Nat.prod_factors n.succ_ne_zero]

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

@@ -265,7 +265,7 @@ def associatesIntEquivNat : Associates ℤ ≃ ℕ := by
 
 theorem Int.Prime.dvd_mul {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :
     p ∣ m.natAbs ∨ p ∣ n.natAbs := by
-  rwa [← hp.dvd_mul, ← Int.natAbs_mul, ←Int.coe_nat_dvd_left]
+  rwa [← hp.dvd_mul, ← Int.natAbs_mul, ← Int.coe_nat_dvd_left]
 #align int.prime.dvd_mul Int.Prime.dvd_mul
 
 theorem Int.Prime.dvd_mul' {m n : ℤ} {p : ℕ} (hp : Nat.Prime p) (h : (p : ℤ) ∣ m * n) :

We already have WellFoundedLT/WellFoundedGT as wrappers around IsWellFounded, but we didn't have the corresponding wrapper lemmas.

@@ -37,8 +37,7 @@ instance : WfDvdMonoid ℕ :=
   ⟨by
     refine'
       RelHomClass.wellFounded
-        (⟨fun x : ℕ => if x = 0 then (⊤ : ℕ∞) else x, _⟩ : DvdNotUnit →r (· < ·))
-        (WithTop.wellFounded_lt Nat.lt_wfRel.wf)
+        (⟨fun x : ℕ => if x = 0 then (⊤ : ℕ∞) else x, _⟩ : DvdNotUnit →r (· < ·)) wellFounded_lt
     intro a b h
     cases' a with a
     · exfalso

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

@@ -294,7 +294,7 @@ theorem prime_two_or_dvd_of_dvd_two_mul_pow_self_two {m : ℤ} {p : ℕ} (hp : N
     exact le_antisymm (Nat.le_of_dvd zero_lt_two hp2) (Nat.Prime.two_le hp)
   · apply Or.intro_right
     rw [sq, Int.natAbs_mul] at hpp
-    exact (or_self_iff _).mp ((Nat.Prime.dvd_mul hp).mp hpp)
+    exact or_self_iff.mp ((Nat.Prime.dvd_mul hp).mp hpp)
 #align prime_two_or_dvd_of_dvd_two_mul_pow_self_two prime_two_or_dvd_of_dvd_two_mul_pow_self_two
 
 theorem Int.exists_prime_and_dvd {n : ℤ} (hn : n.natAbs ≠ 1) : ∃ p, Prime p ∧ p ∣ n := by

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

@@ -199,7 +199,7 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
-theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
+theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.Coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_natAbs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
 

This reverts commit 6f8e8104. Unfortunately this bump was not linted correctly, as CI did not run runLinter Mathlib.

We can unrevert once that's fixed.

@@ -199,7 +199,7 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
-theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.Coprime a.natAbs b.natAbs := by
+theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_natAbs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
 

Some changes have already been review and delegated in #6910 and #7148.

The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac

The std bump PR was insta-merged already!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -199,7 +199,7 @@ theorem gcd_eq_one_iff_coprime {a b : ℤ} : Int.gcd a b = 1 ↔ IsCoprime a b :
     exact dvd_add ((coe_nat_dvd_left.mpr ha).mul_left _) ((coe_nat_dvd_left.mpr hb).mul_left _)
 #align int.gcd_eq_one_iff_coprime Int.gcd_eq_one_iff_coprime
 
-theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.coprime a.natAbs b.natAbs := by
+theorem coprime_iff_nat_coprime {a b : ℤ} : IsCoprime a b ↔ Nat.Coprime a.natAbs b.natAbs := by
   rw [← gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_natAbs]
 #align int.coprime_iff_nat_coprime Int.coprime_iff_nat_coprime
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-
-! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.EuclideanDomain.Basic
 import Mathlib.Data.Nat.Factors
 import Mathlib.RingTheory.Coprime.Basic
 import Mathlib.RingTheory.PrincipalIdealDomain
 
+#align_import ring_theory.int.basic from "leanprover-community/mathlib"@"e655e4ea5c6d02854696f97494997ba4c31be802"
+
 /-!
 # Divisibility over ℕ and ℤ
 

• set_theory.cardinal.basic: forward-ports leanprover-community/mathlib#18781, which backports some ad-hoc changes in #3247 in a more principled way
• ring_theory.int.basic: these changes were already forward-ported in #3278, but we forgot the SHA.
• linear_algebra.dimension: forward-ports leanprover-community/mathlib#18792
• linear_algebra.matrix.dot_product: forward-ports leanprover-community/mathlib#18783
• linear_algebra.finrank: forward-ports leanprover-community/mathlib#18794 which is itself a backport of #3378, hence no changes to the file

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
 
 ! This file was ported from Lean 3 source module ring_theory.int.basic
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit e655e4ea5c6d02854696f97494997ba4c31be802
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

https://github.com/leanprover-community/mathlib/pull/18668

• algebra.group_power.lemmas@05101c3df9d9cfe9430edc205860c79b6d660102..e655e4ea5c6d02854696f97494997ba4c31be802
• group_theory.submonoid.membership@2ec920d35348cb2d13ac0e1a2ad9df0fdf1a76b4..e655e4ea5c6d02854696f97494997ba4c31be802
• group_theory.subgroup.zpowers@f93c11933efbc3c2f0299e47b8ff83e9b539cbf6..e655e4ea5c6d02854696f97494997ba4c31be802
• group_theory.subgroup.pointwise@c10e724be91096453ee3db13862b9fb9a992fef2..e655e4ea5c6d02854696f97494997ba4c31be802
• ring_theory.int.basic@2196ab363eb097c008d4497125e0dde23fb36db2..e655e4ea5c6d02854696f97494997ba4c31be802

@@ -385,8 +385,8 @@ namespace Int
 
 theorem zmultiples_natAbs (a : ℤ) :
     AddSubgroup.zmultiples (a.natAbs : ℤ) = AddSubgroup.zmultiples a :=
-  le_antisymm (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (dvd_natAbs.mpr (dvd_refl a))))
-    (AddSubgroup.zmultiples_subset (mem_zmultiples_iff.mpr (natAbs_dvd.mpr (dvd_refl a))))
+  le_antisymm (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (dvd_natAbs.mpr dvd_rfl)))
+    (AddSubgroup.zmultiples_le_of_mem (mem_zmultiples_iff.mpr (natAbs_dvd.mpr dvd_rfl)))
 #align int.zmultiples_nat_abs Int.zmultiples_natAbs
 
 theorem span_natAbs (a : ℤ) : Ideal.span ({(a.natAbs : ℤ)} : Set ℤ) = Ideal.span {a} := by