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

@@ -86,12 +86,12 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
   congr 1
   · rcases eq_or_ne p 2 with (rfl | hp2)
     · rcases Nat.exists_eq_succ_of_ne_zero (hp2 rfl) with ⟨k, rfl⟩
-      rw [PNat.coe_bit0, PNat.one_coe, succ_sub_succ_eq_sub, tsub_zero, mul_one, pow_succ,
+      rw [PNat.coe_bit0, PNat.one_coe, succ_sub_succ_eq_sub, tsub_zero, mul_one, pow_succ',
         mul_assoc, Nat.mul_div_cancel_left _ zero_lt_two, Nat.mul_div_cancel_left _ zero_lt_two]
       cases k
       · simp
       ·
-        rw [pow_succ, (even_two.mul_right _).neg_one_pow,
+        rw [pow_succ', (even_two.mul_right _).neg_one_pow,
           ((even_two.mul_right _).hMul_right _).neg_one_pow]
     · replace hp2 : (p : ℕ) ≠ 2
       · rwa [Ne.def, ← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj]

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

@@ -106,10 +106,10 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
   · have H := congr_arg derivative (cyclotomic_prime_pow_mul_X_pow_sub_one K p k)
     rw [derivative_mul, derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast,
       derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast, ← PNat.pow_coe,
-      hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H 
+      hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H
     replace H := congr_arg (fun P => aeval ζ P) H
     simp only [aeval_add, aeval_mul, minpoly.aeval, MulZeroClass.zero_mul, add_zero, aeval_nat_cast,
-      _root_.map_sub, aeval_one, aeval_X_pow] at H 
+      _root_.map_sub, aeval_one, aeval_X_pow] at H
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = p ^ (p : ℕ) ^ k :=
       by
@@ -120,13 +120,13 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       Algebra.norm_algebraMap, finrank L hirr, PNat.pow_coe, totient_prime_pow hp.out (succ_pos k),
       Nat.sub_one, Nat.pred_succ, ← hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_pow,
       hζ.norm_eq_one hk hirr, one_pow, mul_one, cast_pow, ← coe_coe, ← pow_mul, ← mul_assoc,
-      mul_comm (k + 1), mul_assoc] at H 
+      mul_comm (k + 1), mul_assoc] at H
     · have := mul_pos (succ_pos k) (tsub_pos_of_lt hp.out.one_lt)
-      rw [← succ_pred_eq_of_pos this, mul_succ, pow_add _ _ ((p : ℕ) ^ k)] at H 
+      rw [← succ_pred_eq_of_pos this, mul_succ, pow_add _ _ ((p : ℕ) ^ k)] at H
       replace H := (mul_left_inj' fun h => _).1 H
       · simpa only [← PNat.pow_coe, H, mul_comm _ (k + 1)]
       · replace h := pow_eq_zero h
-        rw [coe_coe] at h 
+        rw [coe_coe] at h
         simpa using hne.1
 #align is_cyclotomic_extension.discr_prime_pow_ne_two IsCyclotomicExtension.discr_prime_pow_ne_two
 -/
@@ -169,15 +169,15 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
   · by_cases hk : p ^ (k + 1) = 2
     · have hp : p = 2 :=
         by
-        rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at hk 
+        rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at hk
         replace hk :=
           eq_of_prime_pow_eq (prime_iff.1 hp.out) (prime_iff.1 Nat.prime_two) (succ_pos _) hk
-        rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at hk 
-      rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at hk 
-      nth_rw 2 [← pow_one 2] at hk 
+        rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at hk
+      rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at hk
+      nth_rw 2 [← pow_one 2] at hk
       replace hk := Nat.pow_right_injective rfl.le hk
-      rw [add_left_eq_self] at hk 
-      simp only [hp, hk, pow_one, PNat.coe_bit0, PNat.one_coe] at hζ 
+      rw [add_left_eq_self] at hk
+      simp only [hp, hk, pow_one, PNat.coe_bit0, PNat.one_coe] at hζ
       simp only [hp, hk, show 1 / 2 = 0 by rfl, coe_basis, pow_one, power_basis_gen, PNat.coe_bit0,
         PNat.one_coe, totient_two, pow_zero, mul_one, MulZeroClass.mul_zero]
       rw [power_basis_dim, hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,

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

@@ -52,9 +52,9 @@ theorem discr_zeta_eq_discr_zeta_sub_one (hζ : IsPrimitiveRoot ζ n) :
       fun i j => to_matrix_is_integral H₂ _ _ _ _
   · exact hζ.is_integral n.pos
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' _ (hζ.is_integral n.pos)
-  · exact isIntegral_sub (hζ.is_integral n.pos) isIntegral_one
+  · exact IsIntegral.sub (hζ.is_integral n.pos) isIntegral_one
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' _ _
-    exact isIntegral_sub (hζ.is_integral n.pos) isIntegral_one
+    exact IsIntegral.sub (hζ.is_integral n.pos) isIntegral_one
 #align is_primitive_root.discr_zeta_eq_discr_zeta_sub_one IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.NumberTheory.Cyclotomic.PrimitiveRoots
-import Mathbin.RingTheory.Discriminant
+import NumberTheory.Cyclotomic.PrimitiveRoots
+import RingTheory.Discriminant
 
 #align_import number_theory.cyclotomic.discriminant from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
 

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

@@ -92,7 +92,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       · simp
       ·
         rw [pow_succ, (even_two.mul_right _).neg_one_pow,
-          ((even_two.mul_right _).mul_right _).neg_one_pow]
+          ((even_two.mul_right _).hMul_right _).neg_one_pow]
     · replace hp2 : (p : ℕ) ≠ 2
       · rwa [Ne.def, ← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj]
       have hpo : Odd (p : ℕ) := hp.out.odd_of_ne_two hp2

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.discriminant
-! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.Cyclotomic.PrimitiveRoots
 import Mathbin.RingTheory.Discriminant
 
+#align_import number_theory.cyclotomic.discriminant from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
+
 /-!
 # Discriminant of cyclotomic fields
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.discriminant
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
+! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Discriminant
 
 /-!
 # Discriminant of cyclotomic fields
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 We compute the discriminant of a `p ^ n`-th cyclotomic extension.
 
 ## Main results

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -76,7 +76,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
     discr K (hζ.PowerBasis K).basis =
       (-1) ^ ((p ^ (k + 1) : ℕ).totient / 2) * p ^ ((p : ℕ) ^ k * ((p - 1) * (k + 1) - 1)) :=
   by
-  haveI hne := IsCyclotomicExtension.ne_zero' (p ^ (k + 1)) K L
+  haveI hne := IsCyclotomicExtension.neZero' (p ^ (k + 1)) K L
   rw [discr_power_basis_eq_norm, finrank L hirr, hζ.power_basis_gen _, ←
     hζ.minpoly_eq_cyclotomic_of_irreducible hirr, PNat.pow_coe,
     totient_prime_pow hp.out (succ_pos k), succ_sub_one]

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -36,6 +36,7 @@ variable {n : ℕ+} {K : Type u} [Field K] [CharZero K] {ζ : K}
 
 variable [IsCyclotomicExtension {n} ℚ K]
 
+#print IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one /-
 /-- The discriminant of the power basis given by a primitive root of unity `ζ` is the same as the
 discriminant of the power basis given by `ζ - 1`. -/
 theorem discr_zeta_eq_discr_zeta_sub_one (hζ : IsPrimitiveRoot ζ n) :
@@ -55,6 +56,7 @@ theorem discr_zeta_eq_discr_zeta_sub_one (hζ : IsPrimitiveRoot ζ n) :
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' _ _
     exact isIntegral_sub (hζ.is_integral n.pos) isIntegral_one
 #align is_primitive_root.discr_zeta_eq_discr_zeta_sub_one IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one
+-/
 
 end IsPrimitiveRoot
 
@@ -64,6 +66,7 @@ variable {p : ℕ+} {k : ℕ} {K : Type u} {L : Type v} {ζ : L} [Field K] [Fiel
 
 variable [Algebra K L]
 
+#print IsCyclotomicExtension.discr_prime_pow_ne_two /-
 /-- If `p` is a prime and `is_cyclotomic_extension {p ^ (k + 1)} K L`, then the discriminant of
 `hζ.power_basis K` is `(-1) ^ ((p ^ (k + 1).totient) / 2) * p ^ (p ^ k * ((p - 1) * (k + 1) - 1))`
 if `irreducible (cyclotomic (p ^ (k + 1)) K))`, and `p ^ (k + 1) ≠ 2`. -/
@@ -126,7 +129,9 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
         rw [coe_coe] at h 
         simpa using hne.1
 #align is_cyclotomic_extension.discr_prime_pow_ne_two IsCyclotomicExtension.discr_prime_pow_ne_two
+-/
 
+#print IsCyclotomicExtension.discr_prime_pow_ne_two' /-
 /-- If `p` is a prime and `is_cyclotomic_extension {p ^ (k + 1)} K L`, then the discriminant of
 `hζ.power_basis K` is `(-1) ^ (p ^ k * (p - 1) / 2) * p ^ (p ^ k * ((p - 1) * (k + 1) - 1))`
 if `irreducible (cyclotomic (p ^ (k + 1)) K))`, and `p ^ (k + 1) ≠ 2`. -/
@@ -137,7 +142,9 @@ theorem discr_prime_pow_ne_two' [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp :
       (-1) ^ ((p : ℕ) ^ k * (p - 1) / 2) * p ^ ((p : ℕ) ^ k * ((p - 1) * (k + 1) - 1)) :=
   by simpa [totient_prime_pow hp.out (succ_pos k)] using discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow_ne_two' IsCyclotomicExtension.discr_prime_pow_ne_two'
+-/
 
+#print IsCyclotomicExtension.discr_prime_pow /-
 /-- If `p` is a prime and `is_cyclotomic_extension {p ^ k} K L`, then the discriminant of
 `hζ.power_basis K` is `(-1) ^ ((p ^ k).totient / 2) * p ^ (p ^ (k - 1) * ((p - 1) * k - 1))`
 if `irreducible (cyclotomic (p ^ k) K))`. Beware that in the cases `p ^ k = 1` and `p ^ k = 2`
@@ -183,7 +190,9 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       · exact hcycl
     · exact discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow IsCyclotomicExtension.discr_prime_pow
+-/
 
+#print IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow /-
 /-- If `p` is a prime and `is_cyclotomic_extension {p ^ k} K L`, then there are `u : ℤˣ` and
 `n : ℕ` such that the discriminant of `hζ.power_basis K` is `u * p ^ n`. Often this is enough and
 less cumbersome to use than `is_cyclotomic_extension.discr_prime_pow`. -/
@@ -199,7 +208,9 @@ theorem discr_prime_pow_eq_unit_mul_pow [IsCyclotomicExtension {p ^ k} K L]
     exact
       ⟨-1, (p : ℕ) ^ (k - 1) * ((p - 1) * k - 1), by simp [(odd_iff_not_even.2 heven).neg_one_pow]⟩
 #align is_cyclotomic_extension.discr_prime_pow_eq_unit_mul_pow IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow
+-/
 
+#print IsCyclotomicExtension.discr_odd_prime /-
 /-- If `p` is an odd prime and `is_cyclotomic_extension {p} K L`, then
 `discr K (hζ.power_basis K).basis = (-1) ^ ((p - 1) / 2) * p ^ (p - 2)` if
 `irreducible (cyclotomic p K)`. -/
@@ -216,6 +227,7 @@ theorem discr_odd_prime [IsCyclotomicExtension {p} K L] [hp : Fact (p : ℕ).Pri
   · rw [zero_add, pow_one, totient_prime hp.out]
   · rw [pow_zero, one_mul, zero_add, mul_one, Nat.sub_sub]
 #align is_cyclotomic_extension.discr_odd_prime IsCyclotomicExtension.discr_odd_prime
+-/
 
 end IsCyclotomicExtension
 

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

@@ -103,10 +103,10 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
   · have H := congr_arg derivative (cyclotomic_prime_pow_mul_X_pow_sub_one K p k)
     rw [derivative_mul, derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast,
       derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast, ← PNat.pow_coe,
-      hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H
+      hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H 
     replace H := congr_arg (fun P => aeval ζ P) H
     simp only [aeval_add, aeval_mul, minpoly.aeval, MulZeroClass.zero_mul, add_zero, aeval_nat_cast,
-      _root_.map_sub, aeval_one, aeval_X_pow] at H
+      _root_.map_sub, aeval_one, aeval_X_pow] at H 
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = p ^ (p : ℕ) ^ k :=
       by
@@ -117,13 +117,13 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       Algebra.norm_algebraMap, finrank L hirr, PNat.pow_coe, totient_prime_pow hp.out (succ_pos k),
       Nat.sub_one, Nat.pred_succ, ← hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_pow,
       hζ.norm_eq_one hk hirr, one_pow, mul_one, cast_pow, ← coe_coe, ← pow_mul, ← mul_assoc,
-      mul_comm (k + 1), mul_assoc] at H
+      mul_comm (k + 1), mul_assoc] at H 
     · have := mul_pos (succ_pos k) (tsub_pos_of_lt hp.out.one_lt)
-      rw [← succ_pred_eq_of_pos this, mul_succ, pow_add _ _ ((p : ℕ) ^ k)] at H
+      rw [← succ_pred_eq_of_pos this, mul_succ, pow_add _ _ ((p : ℕ) ^ k)] at H 
       replace H := (mul_left_inj' fun h => _).1 H
       · simpa only [← PNat.pow_coe, H, mul_comm _ (k + 1)]
       · replace h := pow_eq_zero h
-        rw [coe_coe] at h
+        rw [coe_coe] at h 
         simpa using hne.1
 #align is_cyclotomic_extension.discr_prime_pow_ne_two IsCyclotomicExtension.discr_prime_pow_ne_two
 
@@ -162,15 +162,15 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
   · by_cases hk : p ^ (k + 1) = 2
     · have hp : p = 2 :=
         by
-        rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at hk
+        rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at hk 
         replace hk :=
           eq_of_prime_pow_eq (prime_iff.1 hp.out) (prime_iff.1 Nat.prime_two) (succ_pos _) hk
-        rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at hk
-      rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at hk
-      nth_rw 2 [← pow_one 2] at hk
+        rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at hk 
+      rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at hk 
+      nth_rw 2 [← pow_one 2] at hk 
       replace hk := Nat.pow_right_injective rfl.le hk
-      rw [add_left_eq_self] at hk
-      simp only [hp, hk, pow_one, PNat.coe_bit0, PNat.one_coe] at hζ
+      rw [add_left_eq_self] at hk 
+      simp only [hp, hk, pow_one, PNat.coe_bit0, PNat.one_coe] at hζ 
       simp only [hp, hk, show 1 / 2 = 0 by rfl, coe_basis, pow_one, power_basis_gen, PNat.coe_bit0,
         PNat.one_coe, totient_two, pow_zero, mul_one, MulZeroClass.mul_zero]
       rw [power_basis_dim, hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
@@ -190,7 +190,7 @@ less cumbersome to use than `is_cyclotomic_extension.discr_prime_pow`. -/
 theorem discr_prime_pow_eq_unit_mul_pow [IsCyclotomicExtension {p ^ k} K L]
     [hp : Fact (p : ℕ).Prime] (hζ : IsPrimitiveRoot ζ ↑(p ^ k))
     (hirr : Irreducible (cyclotomic (↑(p ^ k) : ℕ) K)) :
-    ∃ (u : ℤˣ)(n : ℕ), discr K (hζ.PowerBasis K).basis = u * p ^ n :=
+    ∃ (u : ℤˣ) (n : ℕ), discr K (hζ.PowerBasis K).basis = u * p ^ n :=
   by
   rw [discr_prime_pow hζ hirr]
   by_cases heven : Even ((p ^ k : ℕ).totient / 2)
@@ -212,7 +212,7 @@ theorem discr_odd_prime [IsCyclotomicExtension {p} K L] [hp : Fact (p : ℕ).Pri
     rw [zero_add, pow_one]
     infer_instance
   have hζ' : IsPrimitiveRoot ζ ↑(p ^ (0 + 1)) := by simpa using hζ
-  convert discr_prime_pow_ne_two hζ' (by simpa [hirr] ) (by simp [hodd])
+  convert discr_prime_pow_ne_two hζ' (by simpa [hirr]) (by simp [hodd])
   · rw [zero_add, pow_one, totient_prime hp.out]
   · rw [pow_zero, one_mul, zero_add, mul_one, Nat.sub_sub]
 #align is_cyclotomic_extension.discr_odd_prime IsCyclotomicExtension.discr_odd_prime

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

@@ -28,7 +28,7 @@ universe u v
 
 open Algebra Polynomial Nat IsPrimitiveRoot PowerBasis
 
-open Polynomial Cyclotomic
+open scoped Polynomial Cyclotomic
 
 namespace IsPrimitiveRoot
 

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

@@ -153,7 +153,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       show 1 / 2 = 0 by rfl, discr, trace_matrix]
     have hζone : ζ = 1 := by simpa using hζ
     rw [hζ.power_basis_dim _, hζone, ← (algebraMap K L).map_one,
-      minpoly.eq_x_sub_c_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
+      minpoly.eq_X_sub_C_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
     simp only [trace_matrix, map_one, one_pow, Matrix.det_unique, trace_form_apply, mul_one]
     rw [← (algebraMap K L).map_one, trace_algebra_map, finrank _ hirr]
     · simp
@@ -174,7 +174,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       simp only [hp, hk, show 1 / 2 = 0 by rfl, coe_basis, pow_one, power_basis_gen, PNat.coe_bit0,
         PNat.one_coe, totient_two, pow_zero, mul_one, MulZeroClass.mul_zero]
       rw [power_basis_dim, hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
-        minpoly.eq_x_sub_c_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
+        minpoly.eq_X_sub_C_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
       simp only [discr, trace_matrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
         pow_zero, trace_form_apply, mul_one]
       rw [← (algebraMap K L).map_one, trace_algebra_map, finrank _ hirr, hp, hk]

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.discriminant
-! leanprover-community/mathlib commit 8631e2d5ea77f6c13054d9151d82b83069680cb1
+! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -175,7 +175,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
         PNat.one_coe, totient_two, pow_zero, mul_one, MulZeroClass.mul_zero]
       rw [power_basis_dim, hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
         minpoly.eq_x_sub_c_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
-      simp only [discr, trace_matrix, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
+      simp only [discr, trace_matrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
         pow_zero, trace_form_apply, mul_one]
       rw [← (algebraMap K L).map_one, trace_algebra_map, finrank _ hirr, hp, hk]
       · simp

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

@@ -105,7 +105,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast, ← PNat.pow_coe,
       hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H
     replace H := congr_arg (fun P => aeval ζ P) H
-    simp only [aeval_add, aeval_mul, minpoly.aeval, zero_mul, add_zero, aeval_nat_cast,
+    simp only [aeval_add, aeval_mul, minpoly.aeval, MulZeroClass.zero_mul, add_zero, aeval_nat_cast,
       _root_.map_sub, aeval_one, aeval_X_pow] at H
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = p ^ (p : ℕ) ^ k :=
@@ -149,7 +149,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       (-1) ^ ((p ^ k : ℕ).totient / 2) * p ^ ((p : ℕ) ^ (k - 1) * ((p - 1) * k - 1)) :=
   by
   cases k
-  · simp only [coe_basis, pow_zero, power_basis_gen, totient_one, mul_zero, mul_one,
+  · simp only [coe_basis, pow_zero, power_basis_gen, totient_one, MulZeroClass.mul_zero, mul_one,
       show 1 / 2 = 0 by rfl, discr, trace_matrix]
     have hζone : ζ = 1 := by simpa using hζ
     rw [hζ.power_basis_dim _, hζone, ← (algebraMap K L).map_one,
@@ -172,7 +172,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       rw [add_left_eq_self] at hk
       simp only [hp, hk, pow_one, PNat.coe_bit0, PNat.one_coe] at hζ
       simp only [hp, hk, show 1 / 2 = 0 by rfl, coe_basis, pow_one, power_basis_gen, PNat.coe_bit0,
-        PNat.one_coe, totient_two, pow_zero, mul_one, mul_zero]
+        PNat.one_coe, totient_two, pow_zero, mul_one, MulZeroClass.mul_zero]
       rw [power_basis_dim, hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
         minpoly.eq_x_sub_c_of_algebraMap_inj _ (algebraMap K L).Injective, nat_degree_X_sub_C]
       simp only [discr, trace_matrix, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,

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

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

@@ -81,7 +81,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       rw [mul_assoc, Nat.mul_div_cancel_left _ zero_lt_two, Nat.mul_div_cancel_left _ zero_lt_two]
       cases k
       · simp
-      · norm_num; simp_rw [_root_.pow_succ', (even_two.mul_right _).neg_one_pow,
+      · simp_rw [_root_.pow_succ', (even_two.mul_right _).neg_one_pow,
           ((even_two.mul_right _).mul_right _).neg_one_pow]
     · replace hp2 : (p : ℕ) ≠ 2 := by rwa [Ne, ← coe_two, PNat.coe_inj]
       have hpo : Odd (p : ℕ) := hp.out.odd_of_ne_two hp2

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.

@@ -93,11 +93,11 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       rw [mul_left_comm, ← ha]
       exact one_le_mul (one_le_pow _ _ hp.1.pos) (succ_le_iff.2 <| tsub_pos_of_lt hp.1.one_lt)
   · have H := congr_arg (@derivative K _) (cyclotomic_prime_pow_mul_X_pow_sub_one K p k)
-    rw [derivative_mul, derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast,
-      derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast, ← PNat.pow_coe,
+    rw [derivative_mul, derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_natCast,
+      derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_natCast, ← PNat.pow_coe,
       hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H
     replace H := congr_arg (fun P => aeval ζ P) H
-    simp only [aeval_add, aeval_mul, minpoly.aeval, zero_mul, add_zero, aeval_nat_cast,
+    simp only [aeval_add, aeval_mul, minpoly.aeval, zero_mul, add_zero, aeval_natCast,
       _root_.map_sub, aeval_one, aeval_X_pow] at H
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = (p : K) ^ (p : ℕ) ^ k := by

@@ -83,7 +83,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       · simp
       · norm_num; simp_rw [_root_.pow_succ', (even_two.mul_right _).neg_one_pow,
           ((even_two.mul_right _).mul_right _).neg_one_pow]
-    · replace hp2 : (p : ℕ) ≠ 2 := by rwa [Ne.def, ← coe_two, PNat.coe_inj]
+    · replace hp2 : (p : ℕ) ≠ 2 := by rwa [Ne, ← coe_two, PNat.coe_inj]
       have hpo : Odd (p : ℕ) := hp.out.odd_of_ne_two hp2
       obtain ⟨a, ha⟩ := (hp.out.even_sub_one hp2).two_dvd
       rw [ha, mul_left_comm, mul_assoc, Nat.mul_div_cancel_left _ two_pos,
@@ -118,7 +118,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
     · simp only [H, mul_comm _ (k + 1)]; norm_cast
     · -- Porting note: was `replace h := pow_eq_zero h; rw [coe_coe] at h; simpa using hne.1`
       have := hne.1
-      rw [PNat.pow_coe, Nat.cast_pow, Ne.def, pow_eq_zero_iff (by omega)] at this
+      rw [PNat.pow_coe, Nat.cast_pow, Ne, pow_eq_zero_iff (by omega)] at this
       exact absurd (pow_eq_zero h) this
 #align is_cyclotomic_extension.discr_prime_pow_ne_two IsCyclotomicExtension.discr_prime_pow_ne_two
 

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -77,11 +77,11 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
   congr 1
   · rcases eq_or_ne p 2 with (rfl | hp2)
     · rcases Nat.exists_eq_succ_of_ne_zero (hp2 rfl) with ⟨k, rfl⟩
-      rw [coe_two, succ_sub_succ_eq_sub, tsub_zero, mul_one]; simp only [_root_.pow_succ]
+      rw [coe_two, succ_sub_succ_eq_sub, tsub_zero, mul_one]; simp only [_root_.pow_succ']
       rw [mul_assoc, Nat.mul_div_cancel_left _ zero_lt_two, Nat.mul_div_cancel_left _ zero_lt_two]
       cases k
       · simp
-      · norm_num; simp_rw [_root_.pow_succ, (even_two.mul_right _).neg_one_pow,
+      · norm_num; simp_rw [_root_.pow_succ', (even_two.mul_right _).neg_one_pow,
           ((even_two.mul_right _).mul_right _).neg_one_pow]
     · replace hp2 : (p : ℕ) ≠ 2 := by rwa [Ne.def, ← coe_two, PNat.coe_inj]
       have hpo : Odd (p : ℕ) := hp.out.odd_of_ne_two hp2

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -30,7 +30,6 @@ open scoped Polynomial Cyclotomic
 namespace IsPrimitiveRoot
 
 variable {n : ℕ+} {K : Type u} [Field K] [CharZero K] {ζ : K}
-
 variable [ce : IsCyclotomicExtension {n} ℚ K]
 
 /-- The discriminant of the power basis given by a primitive root of unity `ζ` is the same as the
@@ -54,7 +53,6 @@ end IsPrimitiveRoot
 namespace IsCyclotomicExtension
 
 variable {p : ℕ+} {k : ℕ} {K : Type u} {L : Type v} {ζ : L} [Field K] [Field L]
-
 variable [Algebra K L]
 
 set_option tactic.skipAssignedInstances false in

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -57,6 +57,7 @@ variable {p : ℕ+} {k : ℕ} {K : Type u} {L : Type v} {ζ : L} [Field K] [Fiel
 
 variable [Algebra K L]
 
+set_option tactic.skipAssignedInstances false in
 /-- If `p` is a prime and `IsCyclotomicExtension {p ^ (k + 1)} K L`, then the discriminant of
 `hζ.powerBasis K` is `(-1) ^ ((p ^ (k + 1).totient) / 2) * p ^ (p ^ k * ((p - 1) * (k + 1) - 1))`
 if `Irreducible (cyclotomic (p ^ (k + 1)) K))`, and `p ^ (k + 1) ≠ 2`. -/
@@ -133,6 +134,7 @@ theorem discr_prime_pow_ne_two' [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp :
   by simpa [totient_prime_pow hp.out (succ_pos k)] using discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow_ne_two' IsCyclotomicExtension.discr_prime_pow_ne_two'
 
+set_option tactic.skipAssignedInstances false in
 /-- If `p` is a prime and `IsCyclotomicExtension {p ^ k} K L`, then the discriminant of
 `hζ.powerBasis K` is `(-1) ^ ((p ^ k).totient / 2) * p ^ (p ^ (k - 1) * ((p - 1) * k - 1))`
 if `Irreducible (cyclotomic (p ^ k) K))`. Beware that in the cases `p ^ k = 1` and `p ^ k = 2`
@@ -186,6 +188,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
     · exact discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow IsCyclotomicExtension.discr_prime_pow
 
+set_option tactic.skipAssignedInstances false in
 /-- If `p` is a prime and `IsCyclotomicExtension {p ^ k} K L`, then there are `u : ℤˣ` and
 `n : ℕ` such that the discriminant of `hζ.powerBasis K` is `u * p ^ n`. Often this is enough and
 less cumbersome to use than `IsCyclotomicExtension.discr_prime_pow`. -/

We prove that the ring of integers of the p-th cyclotomic field is a PID if p = 3 or p = 5.

From flt-regular

• depends on: #10492
• depends on: #10502

@@ -183,7 +183,6 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       · simp only [discr, traceMatrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
           _root_.pow_zero, traceForm_apply, mul_one]
         rw [← (algebraMap K L).map_one, trace_algebraMap, finrank _ hirr]; norm_num
-        simp [← coe_two, Even.neg_pow (by decide : Even (1 / 2))]
     · exact discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow IsCyclotomicExtension.discr_prime_pow
 

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -119,7 +119,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
     · simp only [H, mul_comm _ (k + 1)]; norm_cast
     · -- Porting note: was `replace h := pow_eq_zero h; rw [coe_coe] at h; simpa using hne.1`
       have := hne.1
-      rw [PNat.pow_coe, Nat.cast_pow, Ne.def, pow_eq_zero_iff (by linarith)] at this
+      rw [PNat.pow_coe, Nat.cast_pow, Ne.def, pow_eq_zero_iff (by omega)] at this
       exact absurd (pow_eq_zero h) this
 #align is_cyclotomic_extension.discr_prime_pow_ne_two IsCyclotomicExtension.discr_prime_pow_ne_two
 

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

This follows on from #6964.

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

@@ -84,8 +84,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       · simp
       · norm_num; simp_rw [_root_.pow_succ, (even_two.mul_right _).neg_one_pow,
           ((even_two.mul_right _).mul_right _).neg_one_pow]
-    · replace hp2 : (p : ℕ) ≠ 2
-      · rwa [Ne.def, ← coe_two, PNat.coe_inj]
+    · replace hp2 : (p : ℕ) ≠ 2 := by rwa [Ne.def, ← coe_two, PNat.coe_inj]
       have hpo : Odd (p : ℕ) := hp.out.odd_of_ne_two hp2
       obtain ⟨a, ha⟩ := (hp.out.even_sub_one hp2).two_dvd
       rw [ha, mul_left_comm, mul_assoc, Nat.mul_div_cancel_left _ two_pos,

The new proof is more robust and does not rewrite a type equality.

@@ -159,22 +159,32 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
         replace hk :=
           eq_of_prime_pow_eq (prime_iff.1 hp.out) (prime_iff.1 Nat.prime_two) (succ_pos _) hk
         rwa [coe_two, PNat.coe_inj] at hk
-      rw [hp, ← PNat.coe_inj, PNat.pow_coe] at hk
+      subst hp
+      rw [← PNat.coe_inj, PNat.pow_coe] at hk
       nth_rw 2 [← pow_one 2] at hk
       replace hk := Nat.pow_right_injective rfl.le hk
       rw [add_left_eq_self] at hk
-      rw [hp, hk] at hζ; norm_num at hζ; rw [← coe_two] at hζ
-      rw [coe_basis, powerBasis_gen]; simp only [hp, hk]; norm_num
-      -- Porting note: the goal at this point is `(discr K fun i ↦ ζ ^ ↑i) = 1`.
-      -- This `simp_rw` is needed so the next `rw` can rewrite the type of `i` from
-      -- `Fin (natDegree (minpoly K ζ))` to `Fin 1`
+      subst hk
+      rw [← Nat.one_eq_succ_zero, pow_one] at hζ hcycl
+      have : natDegree (minpoly K ζ) = 1 := by
+        rw [hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
+          minpoly.eq_X_sub_C_of_algebraMap_inj _ (NoZeroSMulDivisors.algebraMap_injective K L)]
+        exact natDegree_X_sub_C (-1)
+      rcases Fin.equiv_iff_eq.2 this with ⟨e⟩
+      rw [← Algebra.discr_reindex K (hζ.powerBasis K).basis e, coe_basis, powerBasis_gen]; norm_num
       simp_rw [hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp]
-      rw [hζ.eq_neg_one_of_two_right, show (-1 : L) = algebraMap K L (-1) by simp,
-        minpoly.eq_X_sub_C_of_algebraMap_inj _ (algebraMap K L).injective, natDegree_X_sub_C]
-      simp only [discr, traceMatrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
-        _root_.pow_zero, traceForm_apply, mul_one]
-      rw [← (algebraMap K L).map_one, trace_algebraMap, finrank _ hirr, hp, hk]; norm_num
-      simp [← coe_two, Even.neg_pow (by decide : Even (1 / 2))]
+      convert_to (discr K fun i : Fin 1 ↦ (algebraMap K L) (-1) ^ ↑i) = _
+      · congr
+        ext i
+        simp only [map_neg, map_one, Function.comp_apply, Fin.coe_fin_one, _root_.pow_zero]
+        suffices (e.symm i : ℕ) = 0 by simp [this]
+        rw [← Nat.lt_one_iff]
+        convert (e.symm i).2
+        rw [this]
+      · simp only [discr, traceMatrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
+          _root_.pow_zero, traceForm_apply, mul_one]
+        rw [← (algebraMap K L).map_one, trace_algebraMap, finrank _ hirr]; norm_num
+        simp [← coe_two, Even.neg_pow (by decide : Even (1 / 2))]
     · exact discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow IsCyclotomicExtension.discr_prime_pow
 

Also moved Algebra.discr_eq_discr_of_toMatrix_coeff_isIntegral to Mathlib/NumberTheory/NumberField/Discriminant.lean.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
 import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
-import Mathlib.RingTheory.Discriminant
+import Mathlib.NumberTheory.NumberField.Discriminant
 
 #align_import number_theory.cyclotomic.discriminant from "leanprover-community/mathlib"@"3e068ece210655b7b9a9477c3aff38a492400aa1"
 

@@ -70,7 +70,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
   haveI se : IsSeparable K L := (isGalois (p ^ (k + 1)) K L).to_isSeparable
   rw [discr_powerBasis_eq_norm, finrank L hirr, hζ.powerBasis_gen _, ←
     hζ.minpoly_eq_cyclotomic_of_irreducible hirr, PNat.pow_coe,
-    totient_prime_pow hp.out (succ_pos k), succ_sub_one]
+    totient_prime_pow hp.out (succ_pos k), Nat.add_one_sub_one]
   have coe_two : ((2 : ℕ+) : ℕ) = 2 := rfl
   have hp2 : p = 2 → k ≠ 0 := by
     rintro rfl rfl

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>

@@ -104,8 +104,8 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = (p : K) ^ (p : ℕ) ^ k := by
       by_cases hp : p = 2
-      · exact_mod_cast hζ.pow_sub_one_norm_prime_pow_of_ne_zero hirr le_rfl (hp2 hp)
-      · exact_mod_cast hζ.pow_sub_one_norm_prime_ne_two hirr le_rfl hp
+      · exact mod_cast hζ.pow_sub_one_norm_prime_pow_of_ne_zero hirr le_rfl (hp2 hp)
+      · exact mod_cast hζ.pow_sub_one_norm_prime_ne_two hirr le_rfl hp
     rw [MonoidHom.map_mul, hnorm, MonoidHom.map_mul, ← map_natCast (algebraMap K L),
       Algebra.norm_algebraMap, finrank L hirr] at H
     conv_rhs at H => -- Porting note: need to drill down to successfully rewrite the totient

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

• Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.

• Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit

• Add a lemma Algebra.IsIntegral.of_injective.

• Move isIntegral_of_(submodule_)noetherian down and golf them.

• Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.

• Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.

• Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.

• Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.

• Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').

• Combine isIntegral_trans_aux into isIntegral_trans and golf.

• Add Algebra namespace to isIntegral_sup.

• rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

• Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans

• Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -44,9 +44,9 @@ theorem discr_zeta_eq_discr_zeta_sub_one (hζ : IsPrimitiveRoot ζ n) :
     fun i j => toMatrix_isIntegral H₂ _ _ _ _
   · exact hζ.isIntegral n.pos
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' (K := ℚ) (hζ.isIntegral n.pos)
-  · exact IsIntegral.sub (hζ.isIntegral n.pos) isIntegral_one
+  · exact (hζ.isIntegral n.pos).sub isIntegral_one
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' (K := ℚ) _
-    exact IsIntegral.sub (hζ.isIntegral n.pos) isIntegral_one
+    exact (hζ.isIntegral n.pos).sub isIntegral_one
 #align is_primitive_root.discr_zeta_eq_discr_zeta_sub_one IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one
 
 end IsPrimitiveRoot

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
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

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>

@@ -23,8 +23,6 @@ We compute the discriminant of a `p ^ n`-th cyclotomic extension.
 
 universe u v
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open Algebra Polynomial Nat IsPrimitiveRoot PowerBasis
 
 open scoped Polynomial Cyclotomic
@@ -92,7 +90,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       obtain ⟨a, ha⟩ := (hp.out.even_sub_one hp2).two_dvd
       rw [ha, mul_left_comm, mul_assoc, Nat.mul_div_cancel_left _ two_pos,
         Nat.mul_div_cancel_left _ two_pos, mul_right_comm, pow_mul, (hpo.pow.mul _).neg_one_pow,
-        pow_mul, hpo.pow.neg_one_pow]; · norm_cast
+        pow_mul, hpo.pow.neg_one_pow]
       refine' Nat.Even.sub_odd _ (even_two_mul _) odd_one
       rw [mul_left_comm, ← ha]
       exact one_le_mul (one_le_pow _ _ hp.1.pos) (succ_le_iff.2 <| tsub_pos_of_lt hp.1.one_lt)
@@ -176,7 +174,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       simp only [discr, traceMatrix_apply, Matrix.det_unique, Fin.default_eq_zero, Fin.val_zero,
         _root_.pow_zero, traceForm_apply, mul_one]
       rw [← (algebraMap K L).map_one, trace_algebraMap, finrank _ hirr, hp, hk]; norm_num
-      simp [← coe_two]
+      simp [← coe_two, Even.neg_pow (by decide : Even (1 / 2))]
     · exact discr_prime_pow_ne_two hζ hirr hk
 #align is_cyclotomic_extension.discr_prime_pow IsCyclotomicExtension.discr_prime_pow
 
@@ -203,7 +201,7 @@ theorem discr_odd_prime [IsCyclotomicExtension {p} K L] [hp : Fact (p : ℕ).Pri
   have : IsCyclotomicExtension {p ^ (0 + 1)} K L := by
     rw [zero_add, pow_one]
     infer_instance
-  have hζ' : IsPrimitiveRoot ζ ↑(p ^ (0 + 1)) := by simpa using hζ
+  have hζ' : IsPrimitiveRoot ζ (p ^ (0 + 1) :) := by simpa using hζ
   convert discr_prime_pow_ne_two hζ' (by simpa [hirr]) (by simp [hodd]) using 2
   · rw [zero_add, pow_one, totient_prime hp.out]
   · rw [_root_.pow_zero, one_mul, zero_add, mul_one, Nat.sub_sub]

This PR tests a string-based tool for renaming declarations.

Inspired by this Zulip thread, I am trying to reduce the diff of #8406.

This PR makes the following renames:

| From | To |

@@ -46,9 +46,9 @@ theorem discr_zeta_eq_discr_zeta_sub_one (hζ : IsPrimitiveRoot ζ n) :
     fun i j => toMatrix_isIntegral H₂ _ _ _ _
   · exact hζ.isIntegral n.pos
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' (K := ℚ) (hζ.isIntegral n.pos)
-  · exact isIntegral_sub (hζ.isIntegral n.pos) isIntegral_one
+  · exact IsIntegral.sub (hζ.isIntegral n.pos) isIntegral_one
   · refine' minpoly.isIntegrallyClosed_eq_field_fractions' (K := ℚ) _
-    exact isIntegral_sub (hζ.isIntegral n.pos) isIntegral_one
+    exact IsIntegral.sub (hζ.isIntegral n.pos) isIntegral_one
 #align is_primitive_root.discr_zeta_eq_discr_zeta_sub_one IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one
 
 end IsPrimitiveRoot

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

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

@@ -101,7 +101,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
       derivative_sub, derivative_one, sub_zero, derivative_X_pow, C_eq_nat_cast, ← PNat.pow_coe,
       hζ.minpoly_eq_cyclotomic_of_irreducible hirr] at H
     replace H := congr_arg (fun P => aeval ζ P) H
-    simp only [aeval_add, aeval_mul, minpoly.aeval, MulZeroClass.zero_mul, add_zero, aeval_nat_cast,
+    simp only [aeval_add, aeval_mul, minpoly.aeval, zero_mul, add_zero, aeval_nat_cast,
       _root_.map_sub, aeval_one, aeval_X_pow] at H
     replace H := congr_arg (Algebra.norm K) H
     have hnorm : (norm K) (ζ ^ (p : ℕ) ^ k - 1) = (p : K) ^ (p : ℕ) ^ k := by

@@ -153,7 +153,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       minpoly.eq_X_sub_C_of_algebraMap_inj _ (algebraMap K L).injective, natDegree_X_sub_C]
     simp only [traceMatrix, map_one, one_pow, Matrix.det_unique, traceForm_apply, mul_one]
     rw [← (algebraMap K L).map_one, trace_algebraMap, finrank _ hirr]
-    simp; norm_num
+    norm_num
   · by_cases hk : p ^ (k + 1) = 2
     · have coe_two : 2 = ((2 : ℕ+) : ℕ) := rfl
       have hp : p = 2 := by
@@ -167,7 +167,6 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
       rw [add_left_eq_self] at hk
       rw [hp, hk] at hζ; norm_num at hζ; rw [← coe_two] at hζ
       rw [coe_basis, powerBasis_gen]; simp only [hp, hk]; norm_num
-      rw [← coe_two, totient_two, show 1 / 2 = 0 by rfl, _root_.pow_zero]
       -- Porting note: the goal at this point is `(discr K fun i ↦ ζ ^ ↑i) = 1`.
       -- This `simp_rw` is needed so the next `rw` can rewrite the type of `i` from
       -- `Fin (natDegree (minpoly K ζ))` to `Fin 1`

@@ -23,7 +23,7 @@ We compute the discriminant of a `p ^ n`-th cyclotomic extension.
 
 universe u v
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open Algebra Polynomial Nat IsPrimitiveRoot PowerBasis
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.discriminant
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
 import Mathlib.RingTheory.Discriminant
 
+#align_import number_theory.cyclotomic.discriminant from "leanprover-community/mathlib"@"3e068ece210655b7b9a9477c3aff38a492400aa1"
+
 /-!
 # Discriminant of cyclotomic fields
 We compute the discriminant of a `p ^ n`-th cyclotomic extension.

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -149,7 +149,7 @@ theorem discr_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} K L] [hp : Fact (
     discr K (hζ.powerBasis K).basis =
       (-1) ^ ((p ^ k : ℕ).totient / 2) * p ^ ((p : ℕ) ^ (k - 1) * ((p - 1) * k - 1)) := by
   cases' k with k k
-  · simp only [coe_basis, _root_.pow_zero, powerBasis_gen, totient_one, mul_zero, mul_one,
+  · simp only [coe_basis, _root_.pow_zero, powerBasis_gen _ hζ, totient_one, mul_zero, mul_one,
       show 1 / 2 = 0 by rfl, discr, traceMatrix]
     have hζone : ζ = 1 := by simpa using hζ
     rw [hζ.powerBasis_dim _, hζone, ← (algebraMap K L).map_one,

@@ -69,7 +69,7 @@ theorem discr_prime_pow_ne_two [IsCyclotomicExtension {p ^ (k + 1)} K L] [hp : F
     (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1))) (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K))
     (hk : p ^ (k + 1) ≠ 2) : discr K (hζ.powerBasis K).basis =
       (-1) ^ ((p ^ (k + 1) : ℕ).totient / 2) * p ^ ((p : ℕ) ^ k * ((p - 1) * (k + 1) - 1)) := by
-  haveI hne := IsCyclotomicExtension.ne_zero' (p ^ (k + 1)) K L
+  haveI hne := IsCyclotomicExtension.neZero' (p ^ (k + 1)) K L
   -- Porting note: these two instances are not automatically synthesised and must be constructed
   haveI mf : Module.Finite K L := finiteDimensional {p ^ (k + 1)} K L
   haveI se : IsSeparable K L := (isGalois (p ^ (k + 1)) K L).to_isSeparable