Changes since the initial port

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

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

38df578a

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -58,14 +58,13 @@ theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by intro a; decide!
 
 #print ZMod.χ₄_nat_mod_four /-
 /-- The value of `χ₄ n`, for `n : ℕ`, depends only on `n % 4`. -/
-theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.nat_cast_mod n 4]
+theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.natCast_mod n 4]
 #align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_four
 -/
 
 #print ZMod.χ₄_int_mod_four /-
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
-theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by rw [← ZMod.int_cast_mod n 4];
-  norm_cast
+theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by rw [← ZMod.intCast_mod n 4]; norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
 -/
 
@@ -76,7 +75,7 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
   by
   have help : ∀ m : ℤ, 0 ≤ m → m < 4 → χ₄ m = if m % 2 = 0 then 0 else if m = 1 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 4), ← ZMod.int_cast_mod n 4]
+  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 4), ← ZMod.intCast_mod n 4]
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 -/
@@ -162,13 +161,13 @@ theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by intro a; decide!
 
 #print ZMod.χ₈_nat_mod_eight /-
 /-- The value of `χ₈ n`, for `n : ℕ`, depends only on `n % 8`. -/
-theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.nat_cast_mod n 8]
+theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.natCast_mod n 8]
 #align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eight
 -/
 
 #print ZMod.χ₈_int_mod_eight /-
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
-theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by rw [← ZMod.int_cast_mod n 8];
+theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by rw [← ZMod.intCast_mod n 8];
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
 -/
@@ -181,7 +180,7 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈ m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 7 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.intCast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 -/
@@ -220,7 +219,7 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈' m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 3 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.intCast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 -/

38df578a

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 -/
 import Data.Int.Range
-import Data.Zmod.Basic
+import Data.ZMod.Basic
 import NumberTheory.LegendreSymbol.MulCharacter
 
 #align_import number_theory.legendre_symbol.zmod_char from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

38df578a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 -/
-import Mathbin.Data.Int.Range
-import Mathbin.Data.Zmod.Basic
-import Mathbin.NumberTheory.LegendreSymbol.MulCharacter
+import Data.Int.Range
+import Data.Zmod.Basic
+import NumberTheory.LegendreSymbol.MulCharacter
 
 #align_import number_theory.legendre_symbol.zmod_char from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"

38df578a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
-
-! This file was ported from Lean 3 source module number_theory.legendre_symbol.zmod_char
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Int.Range
 import Mathbin.Data.Zmod.Basic
 import Mathbin.NumberTheory.LegendreSymbol.MulCharacter
 
+#align_import number_theory.legendre_symbol.zmod_char from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Quadratic characters on ℤ/nℤ

38df578a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -40,6 +40,7 @@ namespace ZMod
 
 section QuadCharModP
 
+#print ZMod.χ₄ /-
 /-- Define the nontrivial quadratic character on `zmod 4`, `χ₄`.
 It corresponds to the extension `ℚ(√-1)/ℚ`. -/
 @[simps]
@@ -50,20 +51,28 @@ def χ₄ : MulChar (ZMod 4) ℤ
   map_mul' := by decide
   map_nonunit' := by decide
 #align zmod.χ₄ ZMod.χ₄
+-/
 
+#print ZMod.isQuadratic_χ₄ /-
 /-- `χ₄` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄
+-/
 
+#print ZMod.χ₄_nat_mod_four /-
 /-- The value of `χ₄ n`, for `n : ℕ`, depends only on `n % 4`. -/
 theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.nat_cast_mod n 4]
 #align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_four
+-/
 
+#print ZMod.χ₄_int_mod_four /-
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
 theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by rw [← ZMod.int_cast_mod n 4];
   norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
+-/
 
+#print ZMod.χ₄_int_eq_if_mod_four /-
 /-- An explicit description of `χ₄` on integers / naturals -/
 theorem χ₄_int_eq_if_mod_four (n : ℤ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 :=
@@ -73,12 +82,16 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
   rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 4), ← ZMod.int_cast_mod n 4]
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
+-/
 
+#print ZMod.χ₄_nat_eq_if_mod_four /-
 theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
   exact_mod_cast χ₄_int_eq_if_mod_four n
 #align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_four
+-/
 
+#print ZMod.χ₄_eq_neg_one_pow /-
 /-- Alternative description of `χ₄ n` for odd `n : ℕ` in terms of powers of `-1` -/
 theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n / 2) :=
   by
@@ -93,24 +106,33 @@ theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n /
     help (n % 4) (Nat.mod_lt n (by norm_num))
       ((Nat.mod_mod_of_dvd n (by norm_num : 2 ∣ 4)).trans hn)
 #align zmod.χ₄_eq_neg_one_pow ZMod.χ₄_eq_neg_one_pow
+-/
 
+#print ZMod.χ₄_nat_one_mod_four /-
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_nat_mod_four, hn]; rfl
 #align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_four
+-/
 
+#print ZMod.χ₄_nat_three_mod_four /-
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_nat_mod_four, hn];
   rfl
 #align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_four
+-/
 
+#print ZMod.χ₄_int_one_mod_four /-
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_int_mod_four, hn]; rfl
 #align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_four
+-/
 
+#print ZMod.χ₄_int_three_mod_four /-
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_int_mod_four, hn];
   rfl
 #align zmod.χ₄_int_three_mod_four ZMod.χ₄_int_three_mod_four
+-/
 
 /-- If `n % 4 = 1`, then `(-1)^(n/2) = 1`. -/
 theorem neg_one_pow_div_two_of_one_mod_four {n : ℕ} (hn : n % 4 = 1) : (-1 : ℤ) ^ (n / 2) = 1 := by
@@ -122,6 +144,7 @@ theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) : (-1 :
   by rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← nat_cast_mod, hn]; rfl
 #align neg_one_pow_div_two_of_three_mod_four neg_one_pow_div_two_of_three_mod_four
 
+#print ZMod.χ₈ /-
 /-- Define the first primitive quadratic character on `zmod 8`, `χ₈`.
 It corresponds to the extension `ℚ(√2)/ℚ`. -/
 @[simps]
@@ -132,20 +155,28 @@ def χ₈ : MulChar (ZMod 8) ℤ
   map_mul' := by decide
   map_nonunit' := by decide
 #align zmod.χ₈ ZMod.χ₈
+-/
 
+#print ZMod.isQuadratic_χ₈ /-
 /-- `χ₈` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
+-/
 
+#print ZMod.χ₈_nat_mod_eight /-
 /-- The value of `χ₈ n`, for `n : ℕ`, depends only on `n % 8`. -/
 theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.nat_cast_mod n 8]
 #align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eight
+-/
 
+#print ZMod.χ₈_int_mod_eight /-
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
 theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by rw [← ZMod.int_cast_mod n 8];
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
+-/
 
+#print ZMod.χ₈_int_eq_if_mod_eight /-
 /-- An explicit description of `χ₈` on integers / naturals -/
 theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 :=
@@ -156,12 +187,16 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
+-/
 
+#print ZMod.χ₈_nat_eq_if_mod_eight /-
 theorem χ₈_nat_eq_if_mod_eight (n : ℕ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 := by
   exact_mod_cast χ₈_int_eq_if_mod_eight n
 #align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eight
+-/
 
+#print ZMod.χ₈' /-
 /-- Define the second primitive quadratic character on `zmod 8`, `χ₈'`.
 It corresponds to the extension `ℚ(√-2)/ℚ`. -/
 @[simps]
@@ -172,11 +207,15 @@ def χ₈' : MulChar (ZMod 8) ℤ
   map_mul' := by decide
   map_nonunit' := by decide
 #align zmod.χ₈' ZMod.χ₈'
+-/
 
+#print ZMod.isQuadratic_χ₈' /-
 /-- `χ₈'` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'
+-/
 
+#print ZMod.χ₈'_int_eq_if_mod_eight /-
 /-- An explicit description of `χ₈'` on integers / naturals -/
 theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 :=
@@ -187,21 +226,28 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
+-/
 
+#print ZMod.χ₈'_nat_eq_if_mod_eight /-
 theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 := by
   exact_mod_cast χ₈'_int_eq_if_mod_eight n
 #align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eight
+-/
 
+#print ZMod.χ₈'_eq_χ₄_mul_χ₈ /-
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/
 theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a := by decide!
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
+-/
 
+#print ZMod.χ₈'_int_eq_χ₄_mul_χ₈ /-
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a :=
   by
   rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by norm_num) a]
   exact χ₈'_eq_χ₄_mul_χ₈ a
 #align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈
+-/
 
 end QuadCharModP

38df578a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -40,12 +40,6 @@ namespace ZMod
 
 section QuadCharModP
 
-/- warning: zmod.χ₄ -> ZMod.χ₄ is a dubious translation:
-lean 3 declaration is
-  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)
-but is expected to have type
-  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))
-Case conversion may be inaccurate. Consider using '#align zmod.χ₄ ZMod.χ₄ₓ'. -/
 /-- Define the nontrivial quadratic character on `zmod 4`, `χ₄`.
 It corresponds to the extension `ℚ(√-1)/ℚ`. -/
 @[simps]
@@ -57,43 +51,19 @@ def χ₄ : MulChar (ZMod 4) ℤ
   map_nonunit' := by decide
 #align zmod.χ₄ ZMod.χ₄
 
-/- warning: zmod.is_quadratic_χ₄ -> ZMod.isQuadratic_χ₄ is a dubious translation:
-lean 3 declaration is
-  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) Int Int.commRing ZMod.χ₄
-but is expected to have type
-  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) Int Int.instCommRingInt ZMod.χ₄
-Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄ₓ'. -/
 /-- `χ₄` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄
 
-/- warning: zmod.χ₄_nat_mod_four -> ZMod.χ₄_nat_mod_four is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_fourₓ'. -/
 /-- The value of `χ₄ n`, for `n : ℕ`, depends only on `n % 4`. -/
 theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.nat_cast_mod n 4]
 #align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_four
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_fourₓ'. -/
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
 theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by rw [← ZMod.int_cast_mod n 4];
   norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_fourₓ'. -/
 /-- An explicit description of `χ₄` on integers / naturals -/
 theorem χ₄_int_eq_if_mod_four (n : ℤ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 :=
@@ -104,23 +74,11 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_fourₓ'. -/
 theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
   exact_mod_cast χ₄_int_eq_if_mod_four n
 #align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_four
 
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 /-- Alternative description of `χ₄ n` for odd `n : ℕ` in terms of powers of `-1` -/
 theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n / 2) :=
   by
@@ -136,43 +94,19 @@ theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n /
       ((Nat.mod_mod_of_dvd n (by norm_num : 2 ∣ 4)).trans hn)
 #align zmod.χ₄_eq_neg_one_pow ZMod.χ₄_eq_neg_one_pow
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_fourₓ'. -/
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_nat_mod_four, hn]; rfl
 #align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_four
 
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 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_nat_mod_four, hn];
   rfl
 #align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_four
 
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 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_int_mod_four, hn]; rfl
 #align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_four
 
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 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_int_mod_four, hn];
   rfl
@@ -188,12 +122,6 @@ theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) : (-1 :
   by rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← nat_cast_mod, hn]; rfl
 #align neg_one_pow_div_two_of_three_mod_four neg_one_pow_div_two_of_three_mod_four
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈ ZMod.χ₈ₓ'. -/
 /-- Define the first primitive quadratic character on `zmod 8`, `χ₈`.
 It corresponds to the extension `ℚ(√2)/ℚ`. -/
 @[simps]
@@ -205,43 +133,19 @@ def χ₈ : MulChar (ZMod 8) ℤ
   map_nonunit' := by decide
 #align zmod.χ₈ ZMod.χ₈
 
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-Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈ₓ'. -/
 /-- `χ₈` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eightₓ'. -/
 /-- The value of `χ₈ n`, for `n : ℕ`, depends only on `n % 8`. -/
 theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.nat_cast_mod n 8]
 #align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eight
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eightₓ'. -/
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
 theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by rw [← ZMod.int_cast_mod n 8];
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eightₓ'. -/
 /-- An explicit description of `χ₈` on integers / naturals -/
 theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 :=
@@ -253,23 +157,11 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eightₓ'. -/
 theorem χ₈_nat_eq_if_mod_eight (n : ℕ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 := by
   exact_mod_cast χ₈_int_eq_if_mod_eight n
 #align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eight
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈' ZMod.χ₈'ₓ'. -/
 /-- Define the second primitive quadratic character on `zmod 8`, `χ₈'`.
 It corresponds to the extension `ℚ(√-2)/ℚ`. -/
 @[simps]
@@ -281,22 +173,10 @@ def χ₈' : MulChar (ZMod 8) ℤ
   map_nonunit' := by decide
 #align zmod.χ₈' ZMod.χ₈'
 
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-Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'ₓ'. -/
 /-- `χ₈'` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eightₓ'. -/
 /-- An explicit description of `χ₈'` on integers / naturals -/
 theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 :=
@@ -308,30 +188,15 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 
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-Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eightₓ'. -/
 theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 := by
   exact_mod_cast χ₈'_int_eq_if_mod_eight n
 #align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eight
 
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Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.hasCoeT.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) a)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ a))
-but is expected to have type
-  forall (a : ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (ZMod.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)) a)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ a))
-Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈ₓ'. -/
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/
 theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a := by decide!
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
 
-/- warning: zmod.χ₈'_int_eq_χ₄_mul_χ₈ -> ZMod.χ₈'_int_eq_χ₄_mul_χ₈ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈ₓ'. -/
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a :=
   by
   rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by norm_num) a]

38df578a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -64,9 +64,7 @@ but is expected to have type
   MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) Int Int.instCommRingInt ZMod.χ₄
 Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄ₓ'. -/
 /-- `χ₄` takes values in `{0, 1, -1}` -/
-theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by
-  intro a
-  decide!
+theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄
 
 /- warning: zmod.χ₄_nat_mod_four -> ZMod.χ₄_nat_mod_four is a dubious translation:
@@ -86,9 +84,7 @@ but is expected to have type
   forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4)))))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_fourₓ'. -/
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
-theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) :=
-  by
-  rw [← ZMod.int_cast_mod n 4]
+theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by rw [← ZMod.int_cast_mod n 4];
   norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
 
@@ -147,10 +143,7 @@ but is expected to have type
   forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_fourₓ'. -/
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
-theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 :=
-  by
-  rw [χ₄_nat_mod_four, hn]
-  rfl
+theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_nat_mod_four, hn]; rfl
 #align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_four
 
 /- warning: zmod.χ₄_nat_three_mod_four -> ZMod.χ₄_nat_three_mod_four is a dubious translation:
@@ -160,9 +153,7 @@ but is expected to have type
   forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_fourₓ'. -/
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
-theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 :=
-  by
-  rw [χ₄_nat_mod_four, hn]
+theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_nat_mod_four, hn];
   rfl
 #align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_four
 
@@ -173,10 +164,7 @@ but is expected to have type
   forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_fourₓ'. -/
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
-theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 :=
-  by
-  rw [χ₄_int_mod_four, hn]
-  rfl
+theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 := by rw [χ₄_int_mod_four, hn]; rfl
 #align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_four
 
 /- warning: zmod.χ₄_int_three_mod_four -> ZMod.χ₄_int_three_mod_four is a dubious translation:
@@ -186,24 +174,18 @@ but is expected to have type
   forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_three_mod_four ZMod.χ₄_int_three_mod_fourₓ'. -/
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
-theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 :=
-  by
-  rw [χ₄_int_mod_four, hn]
+theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 := by rw [χ₄_int_mod_four, hn];
   rfl
 #align zmod.χ₄_int_three_mod_four ZMod.χ₄_int_three_mod_four
 
 /-- If `n % 4 = 1`, then `(-1)^(n/2) = 1`. -/
-theorem neg_one_pow_div_two_of_one_mod_four {n : ℕ} (hn : n % 4 = 1) : (-1 : ℤ) ^ (n / 2) = 1 :=
-  by
-  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_one hn), ← nat_cast_mod, hn]
-  rfl
+theorem neg_one_pow_div_two_of_one_mod_four {n : ℕ} (hn : n % 4 = 1) : (-1 : ℤ) ^ (n / 2) = 1 := by
+  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_one hn), ← nat_cast_mod, hn]; rfl
 #align neg_one_pow_div_two_of_one_mod_four neg_one_pow_div_two_of_one_mod_four
 
 /-- If `n % 4 = 3`, then `(-1)^(n/2) = -1`. -/
 theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) : (-1 : ℤ) ^ (n / 2) = -1 :=
-  by
-  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← nat_cast_mod, hn]
-  rfl
+  by rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← nat_cast_mod, hn]; rfl
 #align neg_one_pow_div_two_of_three_mod_four neg_one_pow_div_two_of_three_mod_four
 
 /- warning: zmod.χ₈ -> ZMod.χ₈ is a dubious translation:
@@ -230,9 +212,7 @@ but is expected to have type
   MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) Int Int.instCommRingInt ZMod.χ₈
 Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈ₓ'. -/
 /-- `χ₈` takes values in `{0, 1, -1}` -/
-theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by
-  intro a
-  decide!
+theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
 
 /- warning: zmod.χ₈_nat_mod_eight -> ZMod.χ₈_nat_mod_eight is a dubious translation:
@@ -252,9 +232,7 @@ but is expected to have type
   forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8)))))
 Case conversion may be inaccurate. Consider using '#align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eightₓ'. -/
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
-theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) :=
-  by
-  rw [← ZMod.int_cast_mod n 8]
+theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by rw [← ZMod.int_cast_mod n 8];
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
 
@@ -310,9 +288,7 @@ but is expected to have type
   MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) Int Int.instCommRingInt ZMod.χ₈'
 Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'ₓ'. -/
 /-- `χ₈'` takes values in `{0, 1, -1}` -/
-theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by
-  intro a
-  decide!
+theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by intro a; decide!
 #align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'
 
 /- warning: zmod.χ₈'_int_eq_if_mod_eight -> ZMod.χ₈'_int_eq_if_mod_eight is a dubious translation:

38df578a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -354,10 +354,7 @@ theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a :=
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
 
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(bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) a)))
-but is expected to have type
-  forall (a : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) a)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈ₓ'. -/
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a :=
   by

38df578a

bump to nightly-2023-05-24-03

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

2c55cf2c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 
 ! This file was ported from Lean 3 source module number_theory.legendre_symbol.zmod_char
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.NumberTheory.LegendreSymbol.MulCharacter
 /-!
 # Quadratic characters on ℤ/nℤ
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines some quadratic characters on the rings ℤ/4ℤ and ℤ/8ℤ.
 
 We set them up to be of type `mul_char (zmod n) ℤ`, where `n` is `4` or `8`.

70fd9563

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -37,6 +37,12 @@ namespace ZMod
 
 section QuadCharModP
 
+/- warning: zmod.χ₄ -> ZMod.χ₄ is a dubious translation:
+lean 3 declaration is
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)
+but is expected to have type
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄ ZMod.χ₄ₓ'. -/
 /-- Define the nontrivial quadratic character on `zmod 4`, `χ₄`.
 It corresponds to the extension `ℚ(√-1)/ℚ`. -/
 @[simps]
@@ -48,16 +54,34 @@ def χ₄ : MulChar (ZMod 4) ℤ
   map_nonunit' := by decide
 #align zmod.χ₄ ZMod.χ₄
 
+/- warning: zmod.is_quadratic_χ₄ -> ZMod.isQuadratic_χ₄ is a dubious translation:
+lean 3 declaration is
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) Int Int.commRing ZMod.χ₄
+but is expected to have type
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) Int Int.instCommRingInt ZMod.χ₄
+Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄ₓ'. -/
 /-- `χ₄` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by
   intro a
   decide!
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄
 
+/- warning: zmod.χ₄_nat_mod_four -> ZMod.χ₄_nat_mod_four is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_fourₓ'. -/
 /-- The value of `χ₄ n`, for `n : ℕ`, depends only on `n % 4`. -/
 theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.nat_cast_mod n 4]
 #align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_four
 
+/- warning: zmod.χ₄_int_mod_four -> ZMod.χ₄_int_mod_four is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) n)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))))
+but is expected to have type
+  forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_fourₓ'. -/
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
 theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) :=
   by
@@ -65,6 +89,12 @@ theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) :=
   norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
 
+/- warning: zmod.χ₄_int_eq_if_mod_four -> ZMod.χ₄_int_eq_if_mod_four is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))
+but is expected to have type
+  forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_fourₓ'. -/
 /-- An explicit description of `χ₄` on integers / naturals -/
 theorem χ₄_int_eq_if_mod_four (n : ℤ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 :=
@@ -75,11 +105,23 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 
+/- warning: zmod.χ₄_nat_eq_if_mod_four -> ZMod.χ₄_nat_eq_if_mod_four is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Nat.decidableEq (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_fourₓ'. -/
 theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
   exact_mod_cast χ₄_int_eq_if_mod_four n
 #align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_four
 
+/- warning: zmod.χ₄_eq_neg_one_pow -> ZMod.χ₄_eq_neg_one_pow is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) n (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 {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_eq_neg_one_pow ZMod.χ₄_eq_neg_one_powₓ'. -/
 /-- Alternative description of `χ₄ n` for odd `n : ℕ` in terms of powers of `-1` -/
 theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n / 2) :=
   by
@@ -95,6 +137,12 @@ theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n /
       ((Nat.mod_mod_of_dvd n (by norm_num : 2 ∣ 4)).trans hn)
 #align zmod.χ₄_eq_neg_one_pow ZMod.χ₄_eq_neg_one_pow
 
+/- warning: zmod.χ₄_nat_one_mod_four -> ZMod.χ₄_nat_one_mod_four is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) -> (Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))
+but is expected to have type
+  forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_fourₓ'. -/
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 :=
   by
@@ -102,6 +150,12 @@ theorem χ₄_nat_one_mod_four {n : ℕ} (hn : n % 4 = 1) : χ₄ n = 1 :=
   rfl
 #align zmod.χ₄_nat_one_mod_four ZMod.χ₄_nat_one_mod_four
 
+/- warning: zmod.χ₄_nat_three_mod_four -> ZMod.χ₄_nat_three_mod_four is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))
+but is expected to have type
+  forall {n : Nat}, (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))))) n)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_fourₓ'. -/
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 :=
   by
@@ -109,6 +163,12 @@ theorem χ₄_nat_three_mod_four {n : ℕ} (hn : n % 4 = 3) : χ₄ n = -1 :=
   rfl
 #align zmod.χ₄_nat_three_mod_four ZMod.χ₄_nat_three_mod_four
 
+/- warning: zmod.χ₄_int_one_mod_four -> ZMod.χ₄_int_one_mod_four is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) -> (Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) n)) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))
+but is expected to have type
+  forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_fourₓ'. -/
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
 theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 :=
   by
@@ -116,6 +176,12 @@ theorem χ₄_int_one_mod_four {n : ℤ} (hn : n % 4 = 1) : χ₄ n = 1 :=
   rfl
 #align zmod.χ₄_int_one_mod_four ZMod.χ₄_int_one_mod_four
 
+/- warning: zmod.χ₄_int_three_mod_four -> ZMod.χ₄_int_three_mod_four is a dubious translation:
+lean 3 declaration is
+  forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 4 (OfNat.mk.{0} Int 4 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 3 (OfNat.mk.{0} Int 3 (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne))))) -> (Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) n)) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))
+but is expected to have type
+  forall {n : Int}, (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 4 (instOfNatInt 4))) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3))) -> (Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) n)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₄_int_three_mod_four ZMod.χ₄_int_three_mod_fourₓ'. -/
 /-- If `n % 4 = 3`, then `χ₄ n = -1`. -/
 theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 :=
   by
@@ -137,6 +203,12 @@ theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) : (-1 :
   rfl
 #align neg_one_pow_div_two_of_three_mod_four neg_one_pow_div_two_of_three_mod_four
 
+/- warning: zmod.χ₈ -> ZMod.χ₈ is a dubious translation:
+lean 3 declaration is
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)
+but is expected to have type
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈ ZMod.χ₈ₓ'. -/
 /-- Define the first primitive quadratic character on `zmod 8`, `χ₈`.
 It corresponds to the extension `ℚ(√2)/ℚ`. -/
 @[simps]
@@ -148,16 +220,34 @@ def χ₈ : MulChar (ZMod 8) ℤ
   map_nonunit' := by decide
 #align zmod.χ₈ ZMod.χ₈
 
+/- warning: zmod.is_quadratic_χ₈ -> ZMod.isQuadratic_χ₈ is a dubious translation:
+lean 3 declaration is
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int Int.commRing ZMod.χ₈
+but is expected to have type
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) Int Int.instCommRingInt ZMod.χ₈
+Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈ₓ'. -/
 /-- `χ₈` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by
   intro a
   decide!
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
 
+/- warning: zmod.χ₈_nat_mod_eight -> ZMod.χ₈_nat_mod_eight is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))))) n)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : 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(OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))))) (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eightₓ'. -/
 /-- The value of `χ₈ n`, for `n : ℕ`, depends only on `n % 8`. -/
 theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.nat_cast_mod n 8]
 #align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eight
 
+/- warning: zmod.χ₈_int_mod_eight -> ZMod.χ₈_int_mod_eight is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne)))))))))
+but is expected to have type
+  forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) n)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eightₓ'. -/
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
 theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) :=
   by
@@ -165,6 +255,12 @@ theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) :=
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
 
+/- warning: zmod.χ₈_int_eq_if_mod_eight -> ZMod.χ₈_int_eq_if_mod_eight is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (ite.{1} Int (Or (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 7 (OfNat.mk.{0} Int 7 (bit1.{0} Int Int.hasOne Int.hasAdd (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (Or.decidable (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 7 (OfNat.mk.{0} Int 7 (bit1.{0} Int Int.hasOne Int.hasAdd (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 7 (OfNat.mk.{0} Int 7 (bit1.{0} Int Int.hasOne Int.hasAdd (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))
+but is expected to have type
+  forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Or (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 7 (instOfNatInt 7)))) (instDecidableOr (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 7 (instOfNatInt 7))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 7 (instOfNatInt 7)))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eightₓ'. -/
 /-- An explicit description of `χ₈` on integers / naturals -/
 theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 :=
@@ -176,11 +272,23 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 
+/- warning: zmod.χ₈_nat_eq_if_mod_eight -> ZMod.χ₈_nat_eq_if_mod_eight is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (n : Nat), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))))) n)) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Or (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 7 (instOfNatNat 7)))) (instDecidableOr (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 7 (instOfNatNat 7))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 7 (instOfNatNat 7)))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eightₓ'. -/
 theorem χ₈_nat_eq_if_mod_eight (n : ℕ) :
     χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 := by
   exact_mod_cast χ₈_int_eq_if_mod_eight n
 #align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eight
 
+/- warning: zmod.χ₈' -> ZMod.χ₈' is a dubious translation:
+lean 3 declaration is
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)
+but is expected to have type
+  MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈' ZMod.χ₈'ₓ'. -/
 /-- Define the second primitive quadratic character on `zmod 8`, `χ₈'`.
 It corresponds to the extension `ℚ(√-2)/ℚ`. -/
 @[simps]
@@ -192,12 +300,24 @@ def χ₈' : MulChar (ZMod 8) ℤ
   map_nonunit' := by decide
 #align zmod.χ₈' ZMod.χ₈'
 
+/- warning: zmod.is_quadratic_χ₈' -> ZMod.isQuadratic_χ₈' is a dubious translation:
+lean 3 declaration is
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int Int.commRing ZMod.χ₈'
+but is expected to have type
+  MulChar.IsQuadratic.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) Int Int.instCommRingInt ZMod.χ₈'
+Case conversion may be inaccurate. Consider using '#align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'ₓ'. -/
 /-- `χ₈'` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by
   intro a
   decide!
 #align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'
 
+/- warning: zmod.χ₈'_int_eq_if_mod_eight -> ZMod.χ₈'_int_eq_if_mod_eight is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈' ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (ite.{1} Int (Or (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 3 (OfNat.mk.{0} Int 3 (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (Or.decidable (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 3 (OfNat.mk.{0} Int 3 (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne))))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) (Int.decidableEq (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.hasMod) n (OfNat.ofNat.{0} Int 8 (OfNat.mk.{0} Int 8 (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))))) (OfNat.ofNat.{0} Int 3 (OfNat.mk.{0} Int 3 (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))
+but is expected to have type
+  forall (n : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) n)) (ite.{1} Int (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Or (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3)))) (instDecidableOr (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Eq.{1} Int (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) (Int.instDecidableEqInt (HMod.hMod.{0, 0, 0} Int Int Int (instHMod.{0} Int Int.instModInt_1) n (OfNat.ofNat.{0} Int 8 (instOfNatInt 8))) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3)))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eightₓ'. -/
 /-- An explicit description of `χ₈'` on integers / naturals -/
 theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 :=
@@ -209,15 +329,33 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 
+/- warning: zmod.χ₈'_nat_eq_if_mod_eight -> ZMod.χ₈'_nat_eq_if_mod_eight is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈' ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Nat (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Nat.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddMonoidWithOne.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd 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(Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Nat.decidableEq (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) (ite.{1} Int (Or (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Or.decidable (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Nat.decidableEq (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Nat.decidableEq (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) n (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' (Nat.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Semiring.toNatCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommSemiring.toSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommSemiring.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))))) n)) (ite.{1} Int (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) (ite.{1} Int (Or (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) (instDecidableOr (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Eq.{1} Nat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (instDecidableEqNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) n (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eightₓ'. -/
 theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
     χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 := by
   exact_mod_cast χ₈'_int_eq_if_mod_eight n
 #align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eight
 
+/- warning: zmod.χ₈'_eq_χ₄_mul_χ₈ -> ZMod.χ₈'_eq_χ₄_mul_χ₈ is a dubious translation:
+lean 3 declaration is
+  forall (a : ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈' a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.hasCoeT.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))) a)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ a))
+but is expected to have type
+  forall (a : ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (ZMod.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)) a)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ a))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈ₓ'. -/
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/
 theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a := by decide!
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
 
+/- warning: zmod.χ₈'_int_eq_χ₄_mul_χ₈ -> ZMod.χ₈'_int_eq_χ₄_mul_χ₈ is a dubious translation:
+lean 3 declaration is
+  forall (a : Int), Eq.{1} Int (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈' ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₄ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))))) a)) (coeFn.{1, 1} (MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) (fun (_x : MulChar.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) => (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> Int) (MulChar.coeToFun.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))) Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring)) ZMod.χ₈ ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HasLiftT.mk.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CoeTCₓ.coe.{1, 1} Int (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Int.castCoe.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddGroupWithOne.toHasIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (AddCommGroupWithOne.toAddGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (Ring.toAddCommGroupWithOne.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (OfNat.mk.{0} Nat 8 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))))) a)))
+but is expected to have type
+  forall (a : Int), Eq.{1} Int (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈' (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) a)) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₄ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (ZMod.commRing (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))) a)) (MulChar.toFun'.{0, 0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toCommMonoid.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8)))) Int (CancelCommMonoidWithZero.toCommMonoidWithZero.{0} Int (IsDomain.toCancelCommMonoidWithZero.{0} Int Int.instCommSemiringInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)))) ZMod.χ₈ (Int.cast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (Ring.toIntCast.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (CommRing.toRing.{0} (ZMod (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))) (ZMod.commRing (OfNat.ofNat.{0} Nat 8 (instOfNatNat 8))))) a)))
+Case conversion may be inaccurate. Consider using '#align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈ₓ'. -/
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a :=
   by
   rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by norm_num) a]

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -53,12 +53,12 @@ theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄
 
 /-- The value of `χ₄ n`, for `n : ℕ`, depends only on `n % 4`. -/
-theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.nat_cast_mod n 4]
+theorem χ₄_nat_mod_four (n : ℕ) : χ₄ n = χ₄ (n % 4 : ℕ) := by rw [← ZMod.natCast_mod n 4]
 #align zmod.χ₄_nat_mod_four ZMod.χ₄_nat_mod_four
 
 /-- The value of `χ₄ n`, for `n : ℤ`, depends only on `n % 4`. -/
 theorem χ₄_int_mod_four (n : ℤ) : χ₄ n = χ₄ (n % 4 : ℤ) := by
-  rw [← ZMod.int_cast_mod n 4]
+  rw [← ZMod.intCast_mod n 4]
   norm_cast
 #align zmod.χ₄_int_mod_four ZMod.χ₄_int_mod_four
 
@@ -67,7 +67,7 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
   have help : ∀ m : ℤ, 0 ≤ m → m < 4 → χ₄ m = if m % 2 = 0 then 0 else if m = 1 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 4), ← ZMod.int_cast_mod n 4]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 4), ← ZMod.intCast_mod n 4]
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 
@@ -117,14 +117,14 @@ theorem χ₄_int_three_mod_four {n : ℤ} (hn : n % 4 = 3) : χ₄ n = -1 := by
 
 /-- If `n % 4 = 1`, then `(-1)^(n/2) = 1`. -/
 theorem neg_one_pow_div_two_of_one_mod_four {n : ℕ} (hn : n % 4 = 1) : (-1 : ℤ) ^ (n / 2) = 1 := by
-  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_one hn), ← nat_cast_mod, hn]
+  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_one hn), ← natCast_mod, hn]
   rfl
 #align zmod.neg_one_pow_div_two_of_one_mod_four ZMod.neg_one_pow_div_two_of_one_mod_four
 
 /-- If `n % 4 = 3`, then `(-1)^(n/2) = -1`. -/
 theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) :
     (-1 : ℤ) ^ (n / 2) = -1 := by
-  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← nat_cast_mod, hn]
+  rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_three hn), ← natCast_mod, hn]
   rfl
 #align zmod.neg_one_pow_div_two_of_three_mod_four ZMod.neg_one_pow_div_two_of_three_mod_four
 
@@ -147,12 +147,12 @@ theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
 
 /-- The value of `χ₈ n`, for `n : ℕ`, depends only on `n % 8`. -/
-theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.nat_cast_mod n 8]
+theorem χ₈_nat_mod_eight (n : ℕ) : χ₈ n = χ₈ (n % 8 : ℕ) := by rw [← ZMod.natCast_mod n 8]
 #align zmod.χ₈_nat_mod_eight ZMod.χ₈_nat_mod_eight
 
 /-- The value of `χ₈ n`, for `n : ℤ`, depends only on `n % 8`. -/
 theorem χ₈_int_mod_eight (n : ℤ) : χ₈ n = χ₈ (n % 8 : ℤ) := by
-  rw [← ZMod.int_cast_mod n 8]
+  rw [← ZMod.intCast_mod n 8]
   norm_cast
 #align zmod.χ₈_int_mod_eight ZMod.χ₈_int_mod_eight
 
@@ -162,7 +162,7 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈ m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 7 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.intCast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 
@@ -195,7 +195,7 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈' m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 3 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.intCast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 
@@ -212,7 +212,7 @@ theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ (cast a) * χ
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
 
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a := by
-  rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by decide) a]
+  rw [← @cast_intCast 8 (ZMod 4) _ 4 _ (by decide) a]
   exact χ₈'_eq_χ₄_mul_χ₈ a
 #align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈

70fd9563

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -141,7 +141,7 @@ def χ₈ : MulChar (ZMod 8) ℤ where
 /-- `χ₈` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈ : χ₈.IsQuadratic := by
   intro a
-  --porting note: was `decide!`
+  -- Porting note: was `decide!`
   fin_cases a
   all_goals decide
 #align zmod.is_quadratic_χ₈ ZMod.isQuadratic_χ₈
@@ -184,7 +184,7 @@ def χ₈' : MulChar (ZMod 8) ℤ where
 /-- `χ₈'` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₈' : χ₈'.IsQuadratic := by
   intro a
-  --porting note: was `decide!`
+  -- Porting note: was `decide!`
   fin_cases a
   all_goals decide
 #align zmod.is_quadratic_χ₈' ZMod.isQuadratic_χ₈'
@@ -206,7 +206,7 @@ theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
 
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/
 theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ (cast a) * χ₈ a := by
-    --porting note: was `decide!`
+    -- Porting note: was `decide!`
   fin_cases a
   all_goals decide
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈

70fd9563

chore: classify was decide! porting notes (#11044)

Classifies by adding issue number #11043 to porting notes claiming:

was decide!

bc380937

Diff

@@ -47,7 +47,7 @@ def χ₄ : MulChar (ZMod 4) ℤ where
 /-- `χ₄` takes values in `{0, 1, -1}` -/
 theorem isQuadratic_χ₄ : χ₄.IsQuadratic := by
   intro a
-  -- Porting note: was `decide!`
+  -- Porting note (#11043): was `decide!`
   fin_cases a
   all_goals decide
 #align zmod.is_quadratic_χ₄ ZMod.isQuadratic_χ₄

70fd9563

refactor(ZMod): remove coe out of ZMod (#9839)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>

c27bc4e1

Diff

@@ -205,7 +205,7 @@ theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
 #align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eight
 
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/
-theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a := by
+theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ (cast a) * χ₈ a := by
     --porting note: was `decide!`
   fin_cases a
   all_goals decide

70fd9563

chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

693fd795

Diff

@@ -72,8 +72,8 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 
 theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
-    χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
-  exact_mod_cast χ₄_int_eq_if_mod_four n
+    χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 :=
+  mod_cast χ₄_int_eq_if_mod_four n
 #align zmod.χ₄_nat_eq_if_mod_four ZMod.χ₄_nat_eq_if_mod_four
 
 /-- Alternative description of `χ₄ n` for odd `n : ℕ` in terms of powers of `-1` -/
@@ -167,8 +167,8 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 
 theorem χ₈_nat_eq_if_mod_eight (n : ℕ) :
-    χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 := by
-  exact_mod_cast χ₈_int_eq_if_mod_eight n
+    χ₈ n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1 :=
+  mod_cast χ₈_int_eq_if_mod_eight n
 #align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eight
 
 /-- Define the second primitive quadratic character on `ZMod 8`, `χ₈'`.
@@ -200,8 +200,8 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 
 theorem χ₈'_nat_eq_if_mod_eight (n : ℕ) :
-    χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 := by
-  exact_mod_cast χ₈'_int_eq_if_mod_eight n
+    χ₈' n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1 :=
+  mod_cast χ₈'_int_eq_if_mod_eight n
 #align zmod.χ₈'_nat_eq_if_mod_eight ZMod.χ₈'_nat_eq_if_mod_eight
 
 /-- The relation between `χ₄`, `χ₈` and `χ₈'` -/

70fd9563

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -67,7 +67,7 @@ theorem χ₄_int_eq_if_mod_four (n : ℤ) :
     χ₄ n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1 := by
   have help : ∀ m : ℤ, 0 ≤ m → m < 4 → χ₄ m = if m % 2 = 0 then 0 else if m = 1 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 4), ← ZMod.int_cast_mod n 4]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 4), ← ZMod.int_cast_mod n 4]
   exact help (n % 4) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₄_int_eq_if_mod_four ZMod.χ₄_int_eq_if_mod_four
 
@@ -88,7 +88,7 @@ theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n /
   have help : ∀ m : ℕ, m < 4 → m % 2 = 1 → ite (m = 1) (1 : ℤ) (-1) = (-1) ^ (m / 2) := by decide
   exact
     help (n % 4) (Nat.mod_lt n (by norm_num))
-      ((Nat.mod_mod_of_dvd n (by norm_num : 2 ∣ 4)).trans hn)
+      ((Nat.mod_mod_of_dvd n (by decide : 2 ∣ 4)).trans hn)
 #align zmod.χ₄_eq_neg_one_pow ZMod.χ₄_eq_neg_one_pow
 
 /-- If `n % 4 = 1`, then `χ₄ n = 1`. -/
@@ -162,7 +162,7 @@ theorem χ₈_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈ m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 7 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈_int_eq_if_mod_eight ZMod.χ₈_int_eq_if_mod_eight
 
@@ -195,7 +195,7 @@ theorem χ₈'_int_eq_if_mod_eight (n : ℤ) :
   have help :
     ∀ m : ℤ, 0 ≤ m → m < 8 → χ₈' m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 3 then 1 else -1 := by
     decide
-  rw [← Int.emod_emod_of_dvd n (by norm_num : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
+  rw [← Int.emod_emod_of_dvd n (by decide : (2 : ℤ) ∣ 8), ← ZMod.int_cast_mod n 8]
   exact help (n % 8) (Int.emod_nonneg n (by norm_num)) (Int.emod_lt n (by norm_num))
 #align zmod.χ₈'_int_eq_if_mod_eight ZMod.χ₈'_int_eq_if_mod_eight
 
@@ -212,7 +212,7 @@ theorem χ₈'_eq_χ₄_mul_χ₈ (a : ZMod 8) : χ₈' a = χ₄ a * χ₈ a :=
 #align zmod.χ₈'_eq_χ₄_mul_χ₈ ZMod.χ₈'_eq_χ₄_mul_χ₈
 
 theorem χ₈'_int_eq_χ₄_mul_χ₈ (a : ℤ) : χ₈' a = χ₄ a * χ₈ a := by
-  rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by norm_num) a]
+  rw [← @cast_int_cast 8 (ZMod 4) _ 4 _ (by decide) a]
   exact χ₈'_eq_χ₄_mul_χ₈ a
 #align zmod.χ₈'_int_eq_χ₄_mul_χ₈ ZMod.χ₈'_int_eq_χ₄_mul_χ₈

70fd9563

chore: removing unneeded maxHeartbeats (#7761)

Due to recent changes in core we can reduce or remove many set_option maxHeartbeats statements.

I have tried to be careful to not leave anything too close to the line, so don't be surprised if some of these can still be reduced further.

This reduces us from 96 maxHeartbeats statements to 44. (There are 10 false positives in meta or testing code.)

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

ae7ec61a

Diff

@@ -128,7 +128,6 @@ theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) :
   rfl
 #align zmod.neg_one_pow_div_two_of_three_mod_four ZMod.neg_one_pow_div_two_of_three_mod_four
 
-set_option maxHeartbeats 250000 in -- Porting note: otherwise `map_nonunit'` times out
 /-- Define the first primitive quadratic character on `ZMod 8`, `χ₈`.
 It corresponds to the extension `ℚ(√2)/ℚ`. -/
 @[simps]
@@ -172,7 +171,6 @@ theorem χ₈_nat_eq_if_mod_eight (n : ℕ) :
   exact_mod_cast χ₈_int_eq_if_mod_eight n
 #align zmod.χ₈_nat_eq_if_mod_eight ZMod.χ₈_nat_eq_if_mod_eight
 
-set_option maxHeartbeats 250000 in -- Porting note: otherwise `map_nonunit'` times out
 /-- Define the second primitive quadratic character on `ZMod 8`, `χ₈'`.
 It corresponds to the extension `ℚ(√-2)/ℚ`. -/
 @[simps]

70fd9563

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
-
-! This file was ported from Lean 3 source module number_theory.legendre_symbol.zmod_char
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Int.Range
 import Mathlib.Data.ZMod.Basic
 import Mathlib.NumberTheory.LegendreSymbol.MulCharacter
 
+#align_import number_theory.legendre_symbol.zmod_char from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Quadratic characters on ℤ/nℤ

70fd9563

feat: port NumberTheory.LegendreSymbol.GaussSum (#5419)

This PR incorporates also the changes to NumberTheory.LegendreSymbol.MulCharacter discussed here

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5775c852

Diff

@@ -83,9 +83,9 @@ theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
 theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n / 2) := by
   rw [χ₄_nat_eq_if_mod_four]
   simp only [hn, Nat.one_ne_zero, if_false]
-  --porting note: `nth_rw` didn't work here anymore. artificial workaround
-  nth_rw 3 [← Nat.div_add_mod n 4]
-  nth_rw 3 [(by norm_num : 4 = 2 * 2)]
+  conv_rhs => -- Porting note: was `nth_rw`
+    arg 2; rw [← Nat.div_add_mod n 4]
+    enter [1, 1, 1]; rw [(by norm_num : 4 = 2 * 2)]
   rw [mul_assoc, add_comm, Nat.add_mul_div_left _ _ (by norm_num : 0 < 2), pow_add, pow_mul,
     neg_one_sq, one_pow, mul_one]
   have help : ∀ m : ℕ, m < 4 → m % 2 = 1 → ite (m = 1) (1 : ℤ) (-1) = (-1) ^ (m / 2) := by decide

70fd9563

chore: fix many typos (#4535)

Run codespell Mathlib and keep some suggestions.

92f5c622

Diff

@@ -83,7 +83,7 @@ theorem χ₄_nat_eq_if_mod_four (n : ℕ) :
 theorem χ₄_eq_neg_one_pow {n : ℕ} (hn : n % 2 = 1) : χ₄ n = (-1) ^ (n / 2) := by
   rw [χ₄_nat_eq_if_mod_four]
   simp only [hn, Nat.one_ne_zero, if_false]
-  --porting note: `nth_rw` didn't work here anymore. artifical workaround
+  --porting note: `nth_rw` didn't work here anymore. artificial workaround
   nth_rw 3 [← Nat.div_add_mod n 4]
   nth_rw 3 [(by norm_num : 4 = 2 * 2)]
   rw [mul_assoc, add_comm, Nat.add_mul_div_left _ _ (by norm_num : 0 < 2), pow_add, pow_mul,

70fd9563

chore: tidy various files (#4304)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

8214f469

Diff

@@ -131,10 +131,6 @@ theorem neg_one_pow_div_two_of_three_mod_four {n : ℕ} (hn : n % 4 = 3) :
   rfl
 #align zmod.neg_one_pow_div_two_of_three_mod_four ZMod.neg_one_pow_div_two_of_three_mod_four
 
-lemma test : IsUnit (7 : ZMod 8) := by
-  have : (7 : ZMod 8) * 7 = 1 := by decide
-  exact isUnit_of_mul_eq_one (7 : ZMod 8) 7 this
-
 set_option maxHeartbeats 250000 in -- Porting note: otherwise `map_nonunit'` times out
 /-- Define the first primitive quadratic character on `ZMod 8`, `χ₈`.
 It corresponds to the extension `ℚ(√2)/ℚ`. -/

70fd9563

feat: port NumberTheory.LegendreSymbol.ZModChar (#4205)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

6210e2d9

`number_theory.legendre_symbol.zmod_char` ⟷ `Mathlib.NumberTheory.LegendreSymbol.ZModChar`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 484

number_theory.legendre_symbol.zmod_char ⟷ Mathlib.NumberTheory.LegendreSymbol.ZModChar

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 484

`number_theory.legendre_symbol.zmod_char` ⟷ `Mathlib.NumberTheory.LegendreSymbol.ZModChar`