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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
 -/
-import Data.Pnat.Prime
+import Data.PNat.Prime
 import Algebra.IsPrimePow
 import NumberTheory.Cyclotomic.Basic
 import RingTheory.Adjoin.PowerBasis
@@ -397,7 +397,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           exact Subalgebra.add_mem _ (subset_adjoin (mem_singleton η)) (Subalgebra.one_mem _)
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
-          nth_rw 1 [← add_sub_cancel η 1]
+          nth_rw 1 [← add_sub_cancel_right η 1]
           refine' Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
       rw [H] at this
       exact this
@@ -413,7 +413,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   rw [norm_eq_norm_adjoin K]
   · have H := hη.sub_one_norm_is_prime_pow _ hirr₁ htwo
     swap; · rw [PNat.pow_coe]; exact hpri.1.IsPrimePow.pow (Nat.succ_ne_zero _)
-    rw [add_sub_cancel] at H
+    rw [add_sub_cancel_right] at H
     rw [H, coe_coe]
     congr
     · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]; exact Nat.succ_ne_zero _
@@ -539,8 +539,8 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
     haveI := hcycl
     obtain ⟨k₁, hk₁⟩ := Nat.exists_eq_succ_of_ne_zero hk
     rw [hζ.pow_sub_one_norm_two hirr]
-    rw [hk₁, pow_succ, pow_mul, neg_eq_neg_one_mul, mul_pow, neg_one_sq, one_mul, ← pow_mul, ←
-      pow_succ]
+    rw [hk₁, pow_succ', pow_mul, neg_eq_neg_one_mul, mul_pow, neg_one_sq, one_mul, ← pow_mul, ←
+      pow_succ']
   · exact hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_primitive_root.pow_sub_one_norm_prime_pow_of_ne_zero IsPrimitiveRoot.pow_sub_one_norm_prime_pow_of_ne_zero
 -/

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

@@ -243,7 +243,7 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
   by
   haveI := IsCyclotomicExtension.neZero' n K L
   by_cases h1 : n = 1
-  · rw [h1, one_coe, one_right_iff] at hζ 
+  · rw [h1, one_coe, one_right_iff] at hζ
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
   · replace h1 : 2 ≤ n
     · by_contra! h
@@ -261,7 +261,7 @@ theorem norm_eq_one_of_linearly_ordered {K : Type _} [LinearOrderedField K] [Alg
     (hodd : Odd (n : ℕ)) : norm K ζ = 1 :=
   by
   have hz := congr_arg (norm K) ((IsPrimitiveRoot.iff_def _ n).1 hζ).1
-  rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz 
+  rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz
   exact StrictMono.injective hodd.strict_mono_pow hz
 #align is_primitive_root.norm_eq_one_of_linearly_ordered IsPrimitiveRoot.norm_eq_one_of_linearly_ordered
 -/
@@ -377,7 +377,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   by
   have hirr₁ : Irreducible (cyclotomic (p ^ (k - s + 1)) K) :=
     cyclotomic_irreducible_pow_of_irreducible_pow hpri.1 (by linarith) hirr
-  rw [← PNat.pow_coe] at hirr₁ 
+  rw [← PNat.pow_coe] at hirr₁
   let η := ζ ^ (p : ℕ) ^ s - 1
   let η₁ : K⟮⟯ := IntermediateField.AdjoinSimple.gen K η
   have hη : IsPrimitiveRoot (η + 1) (p ^ (k + 1 - s)) :=
@@ -399,7 +399,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           nth_rw 1 [← add_sub_cancel η 1]
           refine' Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
-      rw [H] at this 
+      rw [H] at this
       exact this
     rw [IntermediateField.adjoin_simple_toSubalgebra_of_integral
         (IsCyclotomicExtension.integral {p ^ (k + 1)} K L _)]
@@ -413,7 +413,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   rw [norm_eq_norm_adjoin K]
   · have H := hη.sub_one_norm_is_prime_pow _ hirr₁ htwo
     swap; · rw [PNat.pow_coe]; exact hpri.1.IsPrimePow.pow (Nat.succ_ne_zero _)
-    rw [add_sub_cancel] at H 
+    rw [add_sub_cancel] at H
     rw [H, coe_coe]
     congr
     · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]; exact Nat.succ_ne_zero _
@@ -421,13 +421,13 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
     rw [IsCyclotomicExtension.finrank L hirr, IsCyclotomicExtension.finrank K⟮⟯ hirr₁, PNat.pow_coe,
       PNat.pow_coe, Nat.totient_prime_pow hpri.out (k - s).succ_pos,
       Nat.totient_prime_pow hpri.out k.succ_pos, mul_comm _ (↑p - 1), mul_assoc,
-      mul_comm (↑p ^ (k.succ - 1))] at this 
+      mul_comm (↑p ^ (k.succ - 1))] at this
     replace this := mul_left_cancel₀ (tsub_pos_iff_lt.2 hpri.out.one_lt).ne' this
     have Hex : k.succ - 1 = (k - s).succ - 1 + s :=
       by
       simp only [Nat.succ_sub_succ_eq_sub, tsub_zero]
       exact (Nat.sub_add_cancel hs).symm
-    rw [Hex, pow_add] at this 
+    rw [Hex, pow_add] at this
     exact mul_left_cancel₀ (pow_ne_zero _ hpri.out.ne_zero) this
   all_goals infer_instance
 #align is_primitive_root.pow_sub_one_norm_prime_pow_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_pow_ne_two
@@ -442,10 +442,10 @@ theorem pow_sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p
     norm K (ζ ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s :=
   by
   refine' hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs fun h => _
-  rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at h 
+  rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at h
   replace h :=
     eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (k - s).succ_pos h
-  rw [← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj] at h 
+  rw [← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj] at h
   exact hodd h
 #align is_primitive_root.pow_sub_one_norm_prime_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_ne_two
 -/
@@ -482,7 +482,7 @@ theorem pow_sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ (k + 1)))
     norm K (ζ ^ 2 ^ k - 1) = (-2) ^ 2 ^ k :=
   by
   have := hζ.pow_of_dvd (fun h => two_ne_zero (pow_eq_zero h)) (pow_dvd_pow 2 (le_succ k))
-  rw [Nat.pow_div (le_succ k) zero_lt_two, Nat.succ_sub (le_refl k), Nat.sub_self, pow_one] at this 
+  rw [Nat.pow_div (le_succ k) zero_lt_two, Nat.succ_sub (le_refl k), Nat.sub_self, pow_one] at this
   have H : (-1 : L) - (1 : L) = algebraMap K L (-2) :=
     by
     simp only [_root_.map_neg, map_bit0, _root_.map_one]
@@ -524,15 +524,15 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
   by_cases htwo : p ^ (k - s + 1) = 2
   · have hp : p = 2 :=
       by
-      rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at htwo 
+      rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at htwo
       replace htwo :=
         eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (succ_pos _) htwo
-      rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at htwo 
+      rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at htwo
     replace hs : s = k
-    · rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at htwo 
-      nth_rw 2 [← pow_one 2] at htwo 
+    · rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at htwo
+      nth_rw 2 [← pow_one 2] at htwo
       replace htwo := Nat.pow_right_injective rfl.le htwo
-      rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo 
+      rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo
       refine' le_antisymm hs htwo
     simp only [hs, hp, PNat.coe_bit0, one_coe, coe_coe, cast_bit0, cast_one, pow_coe] at hζ hirr
       hcycl ⊢

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

@@ -246,7 +246,7 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
   · rw [h1, one_coe, one_right_iff] at hζ 
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
   · replace h1 : 2 ≤ n
-    · by_contra' h
+    · by_contra! h
       exact h1 (PNat.eq_one_of_lt_two h)
     rw [← hζ.power_basis_gen K, power_basis.norm_gen_eq_coeff_zero_minpoly, hζ.power_basis_gen K, ←
       hζ.minpoly_eq_cyclotomic_of_irreducible hirr, cyclotomic_coeff_zero _ h1, mul_one,

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

@@ -153,7 +153,7 @@ theorem powerBasis_gen_mem_adjoin_zeta_sub_one :
 @[simps]
 noncomputable def subOnePowerBasis : PowerBasis K L :=
   (hζ.PowerBasis K).ofGenMemAdjoin
-    (isIntegral_sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
+    (IsIntegral.sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
     (hζ.powerBasis_gen_mem_adjoin_zeta_sub_one _)
 #align is_primitive_root.sub_one_power_basis IsPrimitiveRoot.subOnePowerBasis
 -/

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

@@ -3,13 +3,13 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
 -/
-import Mathbin.Data.Pnat.Prime
-import Mathbin.Algebra.IsPrimePow
-import Mathbin.NumberTheory.Cyclotomic.Basic
-import Mathbin.RingTheory.Adjoin.PowerBasis
-import Mathbin.RingTheory.Polynomial.Cyclotomic.Eval
-import Mathbin.RingTheory.Norm
-import Mathbin.RingTheory.Polynomial.Cyclotomic.Expand
+import Data.Pnat.Prime
+import Algebra.IsPrimePow
+import NumberTheory.Cyclotomic.Basic
+import RingTheory.Adjoin.PowerBasis
+import RingTheory.Polynomial.Cyclotomic.Eval
+import RingTheory.Norm
+import RingTheory.Polynomial.Cyclotomic.Expand
 
 #align_import number_theory.cyclotomic.primitive_roots from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -294,7 +294,7 @@ theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 <
     (hirr : Irreducible (cyclotomic n K)) : norm K (ζ - 1) = ↑(eval 1 (cyclotomic n ℤ)) :=
   by
   haveI := IsCyclotomicExtension.neZero' n K L
-  let E := AlgebraicClosure L
+  let E := AlgebraicClosureAux L
   obtain ⟨z, hz⟩ := IsAlgClosed.exists_root _ (degree_cyclotomic_pos n E n.pos).Ne.symm
   apply (algebraMap K E).Injective
   letI := FiniteDimensional {n} K L

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.primitive_roots
-! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Pnat.Prime
 import Mathbin.Algebra.IsPrimePow
@@ -16,6 +11,8 @@ import Mathbin.RingTheory.Polynomial.Cyclotomic.Eval
 import Mathbin.RingTheory.Norm
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Expand
 
+#align_import number_theory.cyclotomic.primitive_roots from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
+
 /-!
 # Primitive roots in cyclotomic fields
 

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

@@ -170,7 +170,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
     (hirr : Irreducible (cyclotomic n K)) : (L →ₐ[K] C) ≃ primitiveRoots n C :=
   (hζ.PowerBasis K).liftEquiv.trans
     { toFun := fun x => by
-        haveI := IsCyclotomicExtension.ne_zero' n K L
+        haveI := IsCyclotomicExtension.neZero' n K L
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
@@ -178,7 +178,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
           map_cyclotomic _ (algebraMap K C), hζ.minpoly_eq_cyclotomic_of_irreducible hirr, ←
           eval₂_eq_eval_map, ← aeval_def]
       invFun := fun x => by
-        haveI := IsCyclotomicExtension.ne_zero' n K L
+        haveI := IsCyclotomicExtension.neZero' n K L
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
@@ -210,7 +210,7 @@ variable {K} (L)
 cyclotomic extension is `n.totient`. -/
 theorem finrank (hirr : Irreducible (cyclotomic n K)) : finrank K L = (n : ℕ).totient :=
   by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   rw [((zeta_spec n K L).PowerBasis K).finrank, IsPrimitiveRoot.powerBasis_dim, ←
     (zeta_spec n K L).minpoly_eq_cyclotomic_of_irreducible hirr, nat_degree_cyclotomic]
 #align is_cyclotomic_extension.finrank IsCyclotomicExtension.finrank
@@ -244,7 +244,7 @@ theorem norm_eq_neg_one_pow (hζ : IsPrimitiveRoot ζ 2) [IsDomain L] :
 theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
     (hirr : Irreducible (cyclotomic n K)) : norm K ζ = 1 :=
   by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   by_cases h1 : n = 1
   · rw [h1, one_coe, one_right_iff] at hζ 
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
@@ -296,7 +296,7 @@ variable {K} [Field K] [Algebra K L]
 theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 < (n : ℕ))
     (hirr : Irreducible (cyclotomic n K)) : norm K (ζ - 1) = ↑(eval 1 (cyclotomic n ℤ)) :=
   by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   let E := AlgebraicClosure L
   obtain ⟨z, hz⟩ := IsAlgClosed.exists_root _ (degree_cyclotomic_pos n E n.pos).Ne.symm
   apply (algebraMap K E).Injective
@@ -352,7 +352,7 @@ theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
     (h : Irreducible (Polynomial.cyclotomic n K)) :
     minpoly K (ζ - 1) = (cyclotomic n K).comp (X + 1) :=
   by
-  haveI := IsCyclotomicExtension.ne_zero' n K A
+  haveI := IsCyclotomicExtension.neZero' n K A
   rw [show ζ - 1 = ζ + algebraMap K A (-1) by simp [sub_eq_add_neg],
     minpoly.add_algebraMap (IsCyclotomicExtension.integral {n} K A ζ),
     hζ.minpoly_eq_cyclotomic_of_irreducible h]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.primitive_roots
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
+! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.RingTheory.Polynomial.Cyclotomic.Expand
 
 /-!
 # Primitive roots in cyclotomic fields
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 If `is_cyclotomic_extension {n} A B`, we define an element `zeta n A B : B` that is a primitive
 `n`th-root of unity in `B` and we study its properties. We also prove related theorems under the
 more general assumption of just being a primitive root, for reasons described in the implementation

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -80,31 +80,41 @@ namespace IsCyclotomicExtension
 
 variable (n)
 
+#print IsCyclotomicExtension.zeta /-
 /-- If `B` is a `n`-th cyclotomic extension of `A`, then `zeta n A B` is a primitive root of
 unity in `B`. -/
 noncomputable def zeta : B :=
   (exists_prim_root A <| Set.mem_singleton n : ∃ r : B, IsPrimitiveRoot r n).some
 #align is_cyclotomic_extension.zeta IsCyclotomicExtension.zeta
+-/
 
+#print IsCyclotomicExtension.zeta_spec /-
 /-- `zeta n A B` is a primitive `n`-th root of unity. -/
 @[simp]
 theorem zeta_spec : IsPrimitiveRoot (zeta n A B) n :=
   Classical.choose_spec (exists_prim_root A (Set.mem_singleton n) : ∃ r : B, IsPrimitiveRoot r n)
 #align is_cyclotomic_extension.zeta_spec IsCyclotomicExtension.zeta_spec
+-/
 
+#print IsCyclotomicExtension.aeval_zeta /-
 theorem aeval_zeta [IsDomain B] [NeZero ((n : ℕ) : B)] : aeval (zeta n A B) (cyclotomic n A) = 0 :=
   by
   rw [aeval_def, ← eval_map, ← is_root.def, map_cyclotomic, is_root_cyclotomic_iff]
   exact zeta_spec n A B
 #align is_cyclotomic_extension.aeval_zeta IsCyclotomicExtension.aeval_zeta
+-/
 
+#print IsCyclotomicExtension.zeta_isRoot /-
 theorem zeta_isRoot [IsDomain B] [NeZero ((n : ℕ) : B)] : IsRoot (cyclotomic n B) (zeta n A B) := by
   convert aeval_zeta n A B; rw [is_root.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
 #align is_cyclotomic_extension.zeta_is_root IsCyclotomicExtension.zeta_isRoot
+-/
 
+#print IsCyclotomicExtension.zeta_pow /-
 theorem zeta_pow : zeta n A B ^ (n : ℕ) = 1 :=
   (zeta_spec n A B).pow_eq_one
 #align is_cyclotomic_extension.zeta_pow IsCyclotomicExtension.zeta_pow
+-/
 
 end IsCyclotomicExtension
 
@@ -119,6 +129,7 @@ namespace IsPrimitiveRoot
 
 variable {C}
 
+#print IsPrimitiveRoot.powerBasis /-
 /-- The `power_basis` given by a primitive root `η`. -/
 @[simps]
 protected noncomputable def powerBasis : PowerBasis K L :=
@@ -126,14 +137,18 @@ protected noncomputable def powerBasis : PowerBasis K L :=
     (Subalgebra.equivOfEq _ _ (IsCyclotomicExtension.adjoin_primitive_root_eq_top hζ)).trans
       Subalgebra.topEquiv
 #align is_primitive_root.power_basis IsPrimitiveRoot.powerBasis
+-/
 
+#print IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one /-
 theorem powerBasis_gen_mem_adjoin_zeta_sub_one :
     (hζ.PowerBasis K).gen ∈ adjoin K ({ζ - 1} : Set L) :=
   by
   rw [power_basis_gen, adjoin_singleton_eq_range_aeval, AlgHom.mem_range]
   exact ⟨X + 1, by simp⟩
 #align is_primitive_root.power_basis_gen_mem_adjoin_zeta_sub_one IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one
+-/
 
+#print IsPrimitiveRoot.subOnePowerBasis /-
 /-- The `power_basis` given by `η - 1`. -/
 @[simps]
 noncomputable def subOnePowerBasis : PowerBasis K L :=
@@ -141,9 +156,11 @@ noncomputable def subOnePowerBasis : PowerBasis K L :=
     (isIntegral_sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
     (hζ.powerBasis_gen_mem_adjoin_zeta_sub_one _)
 #align is_primitive_root.sub_one_power_basis IsPrimitiveRoot.subOnePowerBasis
+-/
 
 variable {K} (C)
 
+#print IsPrimitiveRoot.embeddingsEquivPrimitiveRoots /-
 -- We are not using @[simps] to avoid a timeout.
 /-- The equivalence between `L →ₐ[K] C` and `primitive_roots n C` given by a primitive root `ζ`. -/
 noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDomain C] [Algebra K C]
@@ -168,13 +185,16 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
       left_inv := fun x => Subtype.ext rfl
       right_inv := fun x => Subtype.ext rfl }
 #align is_primitive_root.embeddings_equiv_primitive_roots IsPrimitiveRoot.embeddingsEquivPrimitiveRoots
+-/
 
+#print IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe /-
 @[simp]
 theorem embeddingsEquivPrimitiveRoots_apply_coe (C : Type _) [CommRing C] [IsDomain C] [Algebra K C]
     (hirr : Irreducible (cyclotomic n K)) (φ : L →ₐ[K] C) :
     (hζ.embeddingsEquivPrimitiveRoots C hirr φ : C) = φ ζ :=
   rfl
 #align is_primitive_root.embeddings_equiv_primitive_roots_apply_coe IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe
+-/
 
 end IsPrimitiveRoot
 
@@ -182,6 +202,7 @@ namespace IsCyclotomicExtension
 
 variable {K} (L)
 
+#print IsCyclotomicExtension.finrank /-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), then the `finrank` of a
 cyclotomic extension is `n.totient`. -/
 theorem finrank (hirr : Irreducible (cyclotomic n K)) : finrank K L = (n : ℕ).totient :=
@@ -190,6 +211,7 @@ theorem finrank (hirr : Irreducible (cyclotomic n K)) : finrank K L = (n : ℕ).
   rw [((zeta_spec n K L).PowerBasis K).finrank, IsPrimitiveRoot.powerBasis_dim, ←
     (zeta_spec n K L).minpoly_eq_cyclotomic_of_irreducible hirr, nat_degree_cyclotomic]
 #align is_cyclotomic_extension.finrank IsCyclotomicExtension.finrank
+-/
 
 end IsCyclotomicExtension
 
@@ -205,12 +227,15 @@ variable [CommRing L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
 
 variable {K} [Field K] [Algebra K L]
 
+#print IsPrimitiveRoot.norm_eq_neg_one_pow /-
 /-- This mathematically trivial result is complementary to `norm_eq_one` below. -/
 theorem norm_eq_neg_one_pow (hζ : IsPrimitiveRoot ζ 2) [IsDomain L] :
     norm K ζ = (-1) ^ finrank K L := by
   rw [hζ.eq_neg_one_of_two_right, show -1 = algebraMap K L (-1) by simp, Algebra.norm_algebraMap]
 #align is_primitive_root.norm_eq_neg_one_pow IsPrimitiveRoot.norm_eq_neg_one_pow
+-/
 
+#print IsPrimitiveRoot.norm_eq_one /-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), the norm of a primitive root is
 `1` if `n ≠ 2`. -/
 theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
@@ -228,7 +253,9 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
       hζ.power_basis_dim K, ← hζ.minpoly_eq_cyclotomic_of_irreducible hirr, nat_degree_cyclotomic]
     exact (totient_even <| h1.lt_of_ne hn.symm).neg_one_pow
 #align is_primitive_root.norm_eq_one IsPrimitiveRoot.norm_eq_one
+-/
 
+#print IsPrimitiveRoot.norm_eq_one_of_linearly_ordered /-
 /-- If `K` is linearly ordered, the norm of a primitive root is `1` if `n` is odd. -/
 theorem norm_eq_one_of_linearly_ordered {K : Type _} [LinearOrderedField K] [Algebra K L]
     (hodd : Odd (n : ℕ)) : norm K ζ = 1 :=
@@ -237,7 +264,9 @@ theorem norm_eq_one_of_linearly_ordered {K : Type _} [LinearOrderedField K] [Alg
   rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz 
   exact StrictMono.injective hodd.strict_mono_pow hz
 #align is_primitive_root.norm_eq_one_of_linearly_ordered IsPrimitiveRoot.norm_eq_one_of_linearly_ordered
+-/
 
+#print IsPrimitiveRoot.norm_of_cyclotomic_irreducible /-
 theorem norm_of_cyclotomic_irreducible [IsDomain L] [IsCyclotomicExtension {n} K L]
     (hirr : Irreducible (cyclotomic n K)) : norm K ζ = ite (n = 2) (-1) 1 :=
   by
@@ -248,6 +277,7 @@ theorem norm_of_cyclotomic_irreducible [IsDomain L] [IsCyclotomicExtension {n} K
     all_goals infer_instance
   · exact hζ.norm_eq_one hn hirr
 #align is_primitive_root.norm_of_cyclotomic_irreducible IsPrimitiveRoot.norm_of_cyclotomic_irreducible
+-/
 
 end CommRing
 
@@ -257,6 +287,7 @@ variable [Field L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
 
 variable {K} [Field K] [Algebra K L]
 
+#print IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic /-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), then the norm of
 `ζ - 1` is `eval 1 (cyclotomic n ℤ)`. -/
 theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 < (n : ℕ))
@@ -286,7 +317,9 @@ theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 <
     map_cyclotomic_int, _root_.map_int_cast, ← Int.cast_one, eval_int_cast_map, eq_intCast,
     Int.cast_id]
 #align is_primitive_root.sub_one_norm_eq_eval_cyclotomic IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic
+-/
 
+#print IsPrimitiveRoot.sub_one_norm_isPrimePow /-
 /-- If `is_prime_pow (n : ℕ)`, `n ≠ 2` and `irreducible (cyclotomic n K)` (in particular for
 `K = ℚ`), then the norm of `ζ - 1` is `(n : ℕ).min_fac`. -/
 theorem sub_one_norm_isPrimePow (hn : IsPrimePow (n : ℕ)) [IsCyclotomicExtension {n} K L]
@@ -306,9 +339,11 @@ theorem sub_one_norm_isPrimePow (hn : IsPrimePow (n : ℕ)) [IsCyclotomicExtensi
           (mem_factors (IsPrimePow.ne_zero hn)).2 ⟨hprime.out, min_fac_dvd _⟩)
   simp [hk, sub_one_norm_eq_eval_cyclotomic hζ this hirr]
 #align is_primitive_root.sub_one_norm_is_prime_pow IsPrimitiveRoot.sub_one_norm_isPrimePow
+-/
 
 variable {A}
 
+#print IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp /-
 theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
     [IsCyclotomicExtension {n} K A] (hζ : IsPrimitiveRoot ζ n)
     (h : Irreducible (Polynomial.cyclotomic n K)) :
@@ -320,6 +355,7 @@ theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
     hζ.minpoly_eq_cyclotomic_of_irreducible h]
   simp
 #align is_primitive_root.minpoly_sub_one_eq_cyclotomic_comp IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp
+-/
 
 open scoped Cyclotomic
 
@@ -330,6 +366,7 @@ open scoped Cyclotomic
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/
+#print IsPrimitiveRoot.pow_sub_one_norm_prime_pow_ne_two /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
 then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `p ^ (k - s + 1) ≠ 2`. See the next lemmas
 for similar results. -/
@@ -394,7 +431,9 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
     exact mul_left_cancel₀ (pow_ne_zero _ hpri.out.ne_zero) this
   all_goals infer_instance
 #align is_primitive_root.pow_sub_one_norm_prime_pow_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_pow_ne_two
+-/
 
+#print IsPrimitiveRoot.pow_sub_one_norm_prime_ne_two /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
 then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `p ≠ 2`. -/
 theorem pow_sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
@@ -409,7 +448,9 @@ theorem pow_sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p
   rw [← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj] at h 
   exact hodd h
 #align is_primitive_root.pow_sub_one_norm_prime_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_ne_two
+-/
 
+#print IsPrimitiveRoot.sub_one_norm_prime_ne_two /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is an odd
 prime, then the norm of `ζ - 1` is `p`. -/
 theorem sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
@@ -417,7 +458,9 @@ theorem sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k
     (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K)) (h : p ≠ 2) : norm K (ζ - 1) = p := by
   simpa using hζ.pow_sub_one_norm_prime_ne_two hirr k.zero_le h
 #align is_primitive_root.sub_one_norm_prime_ne_two IsPrimitiveRoot.sub_one_norm_prime_ne_two
+-/
 
+#print IsPrimitiveRoot.sub_one_norm_prime /-
 /-- If `irreducible (cyclotomic p K)` (in particular for `K = ℚ`) and `p` is an odd prime,
 then the norm of `ζ - 1` is `p`. -/
 theorem sub_one_norm_prime [hpri : Fact (p : ℕ).Prime] [hcyc : IsCyclotomicExtension {p} K L]
@@ -429,7 +472,9 @@ theorem sub_one_norm_prime [hpri : Fact (p : ℕ).Prime] [hcyc : IsCyclotomicExt
   haveI : IsCyclotomicExtension {p ^ (0 + 1)} K L := by simp [hcyc]
   simpa using sub_one_norm_prime_ne_two hζ hirr h
 #align is_primitive_root.sub_one_norm_prime IsPrimitiveRoot.sub_one_norm_prime
+-/
 
+#print IsPrimitiveRoot.pow_sub_one_norm_two /-
 /-- If `irreducible (cyclotomic (2 ^ (k + 1)) K)` (in particular for `K = ℚ`), then the norm of
 `ζ ^ (2 ^ k) - 1` is `(-2) ^ (2 ^ k)`. -/
 theorem pow_sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ (k + 1)))
@@ -447,7 +492,9 @@ theorem pow_sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ (k + 1)))
     IsCyclotomicExtension.finrank L hirr, pow_coe, PNat.coe_bit0, one_coe,
     totient_prime_pow Nat.prime_two (zero_lt_succ k), succ_sub_succ_eq_sub, tsub_zero, mul_one]
 #align is_primitive_root.pow_sub_one_norm_two IsPrimitiveRoot.pow_sub_one_norm_two
+-/
 
+#print IsPrimitiveRoot.sub_one_norm_two /-
 /-- If `irreducible (cyclotomic (2 ^ k) K)` (in particular for `K = ℚ`) and `k` is at least `2`,
 then the norm of `ζ - 1` is `2`. -/
 theorem sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ k)) (hk : 2 ≤ k)
@@ -464,7 +511,9 @@ theorem sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ k)) (hk : 2 
   obtain ⟨k₁, hk₁⟩ := exists_eq_succ_of_ne_zero (lt_of_lt_of_le zero_lt_two hk).Ne.symm
   simpa [hk₁] using sub_one_norm_eq_eval_cyclotomic hζ this hirr
 #align is_primitive_root.sub_one_norm_two IsPrimitiveRoot.sub_one_norm_two
+-/
 
+#print IsPrimitiveRoot.pow_sub_one_norm_prime_pow_of_ne_zero /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
 then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `k ≠ 0` and `s ≤ k`. -/
 theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
@@ -494,6 +543,7 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       pow_succ]
   · exact hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_primitive_root.pow_sub_one_norm_prime_pow_of_ne_zero IsPrimitiveRoot.pow_sub_one_norm_prime_pow_of_ne_zero
+-/
 
 end Field
 
@@ -505,13 +555,16 @@ open IsPrimitiveRoot
 
 variable {K} (L) [Field K] [Field L] [Algebra K L]
 
+#print IsCyclotomicExtension.norm_zeta_eq_one /-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), the norm of `zeta n K L` is `1`
 if `n` is odd. -/
 theorem norm_zeta_eq_one [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
     (hirr : Irreducible (cyclotomic n K)) : norm K (zeta n K L) = 1 :=
   (zeta_spec n K L).norm_eq_one hn hirr
 #align is_cyclotomic_extension.norm_zeta_eq_one IsCyclotomicExtension.norm_zeta_eq_one
+-/
 
+#print IsCyclotomicExtension.isPrimePow_norm_zeta_sub_one /-
 /-- If `is_prime_pow (n : ℕ)`, `n ≠ 2` and `irreducible (cyclotomic n K)` (in particular for
 `K = ℚ`), then the norm of `zeta n K L - 1` is `(n : ℕ).min_fac`. -/
 theorem isPrimePow_norm_zeta_sub_one (hn : IsPrimePow (n : ℕ)) [IsCyclotomicExtension {n} K L]
@@ -519,7 +572,9 @@ theorem isPrimePow_norm_zeta_sub_one (hn : IsPrimePow (n : ℕ)) [IsCyclotomicEx
     norm K (zeta n K L - 1) = (n : ℕ).minFac :=
   (zeta_spec n K L).sub_one_norm_isPrimePow hn hirr h
 #align is_cyclotomic_extension.is_prime_pow_norm_zeta_sub_one IsCyclotomicExtension.isPrimePow_norm_zeta_sub_one
+-/
 
+#print IsCyclotomicExtension.prime_ne_two_pow_norm_zeta_pow_sub_one /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
 then the norm of `(zeta (p ^ (k + 1)) K L) ^ (p ^ s) - 1` is `p ^ (p ^ s)`
 if `p ^ (k - s + 1) ≠ 2`. -/
@@ -530,7 +585,9 @@ theorem prime_ne_two_pow_norm_zeta_pow_sub_one {k : ℕ} [hpri : Fact (p : ℕ).
     norm K (zeta (p ^ (k + 1)) K L ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s :=
   (zeta_spec _ K L).pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_cyclotomic_extension.prime_ne_two_pow_norm_zeta_pow_sub_one IsCyclotomicExtension.prime_ne_two_pow_norm_zeta_pow_sub_one
+-/
 
+#print IsCyclotomicExtension.prime_ne_two_pow_norm_zeta_sub_one /-
 /-- If `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is an odd
 prime, then the norm of `zeta (p ^ (k + 1)) K L - 1` is `p`. -/
 theorem prime_ne_two_pow_norm_zeta_sub_one {k : ℕ} [hpri : Fact (p : ℕ).Prime]
@@ -539,7 +596,9 @@ theorem prime_ne_two_pow_norm_zeta_sub_one {k : ℕ} [hpri : Fact (p : ℕ).Prim
     norm K (zeta (p ^ (k + 1)) K L - 1) = p :=
   (zeta_spec _ K L).sub_one_norm_prime_ne_two hirr h
 #align is_cyclotomic_extension.prime_ne_two_pow_norm_zeta_sub_one IsCyclotomicExtension.prime_ne_two_pow_norm_zeta_sub_one
+-/
 
+#print IsCyclotomicExtension.prime_ne_two_norm_zeta_sub_one /-
 /-- If `irreducible (cyclotomic p K)` (in particular for `K = ℚ`) and `p` is an odd prime,
 then the norm of `zeta p K L - 1` is `p`. -/
 theorem prime_ne_two_norm_zeta_sub_one [hpri : Fact (p : ℕ).Prime]
@@ -547,13 +606,16 @@ theorem prime_ne_two_norm_zeta_sub_one [hpri : Fact (p : ℕ).Prime]
     norm K (zeta p K L - 1) = p :=
   (zeta_spec _ K L).sub_one_norm_prime hirr h
 #align is_cyclotomic_extension.prime_ne_two_norm_zeta_sub_one IsCyclotomicExtension.prime_ne_two_norm_zeta_sub_one
+-/
 
+#print IsCyclotomicExtension.two_pow_norm_zeta_sub_one /-
 /-- If `irreducible (cyclotomic (2 ^ k) K)` (in particular for `K = ℚ`) and `k` is at least `2`,
 then the norm of `zeta (2 ^ k) K L - 1` is `2`. -/
 theorem two_pow_norm_zeta_sub_one {k : ℕ} (hk : 2 ≤ k) [IsCyclotomicExtension {2 ^ k} K L]
     (hirr : Irreducible (cyclotomic (2 ^ k) K)) : norm K (zeta (2 ^ k) K L - 1) = 2 :=
   sub_one_norm_two (zeta_spec (2 ^ k) K L) hk hirr
 #align is_cyclotomic_extension.two_pow_norm_zeta_sub_one IsCyclotomicExtension.two_pow_norm_zeta_sub_one
+-/
 
 end IsCyclotomicExtension
 

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

@@ -211,8 +211,6 @@ theorem norm_eq_neg_one_pow (hζ : IsPrimitiveRoot ζ 2) [IsDomain L] :
   rw [hζ.eq_neg_one_of_two_right, show -1 = algebraMap K L (-1) by simp, Algebra.norm_algebraMap]
 #align is_primitive_root.norm_eq_neg_one_pow IsPrimitiveRoot.norm_eq_neg_one_pow
 
-include hζ
-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), the norm of a primitive root is
 `1` if `n ≠ 2`. -/
 theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
@@ -259,8 +257,6 @@ variable [Field L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
 
 variable {K} [Field K] [Algebra K L]
 
-include hζ
-
 /-- If `irreducible (cyclotomic n K)` (in particular for `K = ℚ`), then the norm of
 `ζ - 1` is `eval 1 (cyclotomic n ℤ)`. -/
 theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 < (n : ℕ))
@@ -311,8 +307,6 @@ theorem sub_one_norm_isPrimePow (hn : IsPrimePow (n : ℕ)) [IsCyclotomicExtensi
   simp [hk, sub_one_norm_eq_eval_cyclotomic hζ this hirr]
 #align is_primitive_root.sub_one_norm_is_prime_pow IsPrimitiveRoot.sub_one_norm_isPrimePow
 
-omit hζ
-
 variable {A}
 
 theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}

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

@@ -220,7 +220,7 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
   by
   haveI := IsCyclotomicExtension.ne_zero' n K L
   by_cases h1 : n = 1
-  · rw [h1, one_coe, one_right_iff] at hζ
+  · rw [h1, one_coe, one_right_iff] at hζ 
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
   · replace h1 : 2 ≤ n
     · by_contra' h
@@ -236,7 +236,7 @@ theorem norm_eq_one_of_linearly_ordered {K : Type _} [LinearOrderedField K] [Alg
     (hodd : Odd (n : ℕ)) : norm K ζ = 1 :=
   by
   have hz := congr_arg (norm K) ((IsPrimitiveRoot.iff_def _ n).1 hζ).1
-  rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz
+  rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz 
   exact StrictMono.injective hodd.strict_mono_pow hz
 #align is_primitive_root.norm_eq_one_of_linearly_ordered IsPrimitiveRoot.norm_eq_one_of_linearly_ordered
 
@@ -346,7 +346,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   by
   have hirr₁ : Irreducible (cyclotomic (p ^ (k - s + 1)) K) :=
     cyclotomic_irreducible_pow_of_irreducible_pow hpri.1 (by linarith) hirr
-  rw [← PNat.pow_coe] at hirr₁
+  rw [← PNat.pow_coe] at hirr₁ 
   let η := ζ ^ (p : ℕ) ^ s - 1
   let η₁ : K⟮⟯ := IntermediateField.AdjoinSimple.gen K η
   have hη : IsPrimitiveRoot (η + 1) (p ^ (k + 1 - s)) :=
@@ -368,7 +368,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           nth_rw 1 [← add_sub_cancel η 1]
           refine' Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
-      rw [H] at this
+      rw [H] at this 
       exact this
     rw [IntermediateField.adjoin_simple_toSubalgebra_of_integral
         (IsCyclotomicExtension.integral {p ^ (k + 1)} K L _)]
@@ -382,7 +382,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   rw [norm_eq_norm_adjoin K]
   · have H := hη.sub_one_norm_is_prime_pow _ hirr₁ htwo
     swap; · rw [PNat.pow_coe]; exact hpri.1.IsPrimePow.pow (Nat.succ_ne_zero _)
-    rw [add_sub_cancel] at H
+    rw [add_sub_cancel] at H 
     rw [H, coe_coe]
     congr
     · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]; exact Nat.succ_ne_zero _
@@ -390,13 +390,13 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
     rw [IsCyclotomicExtension.finrank L hirr, IsCyclotomicExtension.finrank K⟮⟯ hirr₁, PNat.pow_coe,
       PNat.pow_coe, Nat.totient_prime_pow hpri.out (k - s).succ_pos,
       Nat.totient_prime_pow hpri.out k.succ_pos, mul_comm _ (↑p - 1), mul_assoc,
-      mul_comm (↑p ^ (k.succ - 1))] at this
+      mul_comm (↑p ^ (k.succ - 1))] at this 
     replace this := mul_left_cancel₀ (tsub_pos_iff_lt.2 hpri.out.one_lt).ne' this
     have Hex : k.succ - 1 = (k - s).succ - 1 + s :=
       by
       simp only [Nat.succ_sub_succ_eq_sub, tsub_zero]
       exact (Nat.sub_add_cancel hs).symm
-    rw [Hex, pow_add] at this
+    rw [Hex, pow_add] at this 
     exact mul_left_cancel₀ (pow_ne_zero _ hpri.out.ne_zero) this
   all_goals infer_instance
 #align is_primitive_root.pow_sub_one_norm_prime_pow_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_pow_ne_two
@@ -409,10 +409,10 @@ theorem pow_sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p
     norm K (ζ ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s :=
   by
   refine' hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs fun h => _
-  rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at h
+  rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at h 
   replace h :=
     eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (k - s).succ_pos h
-  rw [← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj] at h
+  rw [← PNat.one_coe, ← PNat.coe_bit0, PNat.coe_inj] at h 
   exact hodd h
 #align is_primitive_root.pow_sub_one_norm_prime_ne_two IsPrimitiveRoot.pow_sub_one_norm_prime_ne_two
 
@@ -443,7 +443,7 @@ theorem pow_sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ (k + 1)))
     norm K (ζ ^ 2 ^ k - 1) = (-2) ^ 2 ^ k :=
   by
   have := hζ.pow_of_dvd (fun h => two_ne_zero (pow_eq_zero h)) (pow_dvd_pow 2 (le_succ k))
-  rw [Nat.pow_div (le_succ k) zero_lt_two, Nat.succ_sub (le_refl k), Nat.sub_self, pow_one] at this
+  rw [Nat.pow_div (le_succ k) zero_lt_two, Nat.succ_sub (le_refl k), Nat.sub_self, pow_one] at this 
   have H : (-1 : L) - (1 : L) = algebraMap K L (-2) :=
     by
     simp only [_root_.map_neg, map_bit0, _root_.map_one]
@@ -481,18 +481,18 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
   by_cases htwo : p ^ (k - s + 1) = 2
   · have hp : p = 2 :=
       by
-      rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at htwo
+      rw [← PNat.coe_inj, PNat.coe_bit0, PNat.one_coe, PNat.pow_coe, ← pow_one 2] at htwo 
       replace htwo :=
         eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (succ_pos _) htwo
-      rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at htwo
+      rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at htwo 
     replace hs : s = k
-    · rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at htwo
-      nth_rw 2 [← pow_one 2] at htwo
+    · rw [hp, ← PNat.coe_inj, PNat.pow_coe, PNat.coe_bit0, PNat.one_coe] at htwo 
+      nth_rw 2 [← pow_one 2] at htwo 
       replace htwo := Nat.pow_right_injective rfl.le htwo
-      rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo
+      rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo 
       refine' le_antisymm hs htwo
-    simp only [hs, hp, PNat.coe_bit0, one_coe, coe_coe, cast_bit0, cast_one, pow_coe] at
-      hζ hirr hcycl⊢
+    simp only [hs, hp, PNat.coe_bit0, one_coe, coe_coe, cast_bit0, cast_one, pow_coe] at hζ hirr
+      hcycl ⊢
     haveI := hcycl
     obtain ⟨k₁, hk₁⟩ := Nat.exists_eq_succ_of_ne_zero hk
     rw [hζ.pow_sub_one_norm_two hirr]

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

@@ -327,7 +327,7 @@ theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
   simp
 #align is_primitive_root.minpoly_sub_one_eq_cyclotomic_comp IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp
 
-open Cyclotomic
+open scoped Cyclotomic
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/

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

@@ -98,10 +98,8 @@ theorem aeval_zeta [IsDomain B] [NeZero ((n : ℕ) : B)] : aeval (zeta n A B) (c
   exact zeta_spec n A B
 #align is_cyclotomic_extension.aeval_zeta IsCyclotomicExtension.aeval_zeta
 
-theorem zeta_isRoot [IsDomain B] [NeZero ((n : ℕ) : B)] : IsRoot (cyclotomic n B) (zeta n A B) :=
-  by
-  convert aeval_zeta n A B
-  rw [is_root.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
+theorem zeta_isRoot [IsDomain B] [NeZero ((n : ℕ) : B)] : IsRoot (cyclotomic n B) (zeta n A B) := by
+  convert aeval_zeta n A B; rw [is_root.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
 #align is_cyclotomic_extension.zeta_is_root IsCyclotomicExtension.zeta_isRoot
 
 theorem zeta_pow : zeta n A B ^ (n : ℕ) = 1 :=
@@ -383,14 +381,11 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
     rw [Nat.sub_add_comm hs, pow_coe]
   rw [norm_eq_norm_adjoin K]
   · have H := hη.sub_one_norm_is_prime_pow _ hirr₁ htwo
-    swap
-    · rw [PNat.pow_coe]
-      exact hpri.1.IsPrimePow.pow (Nat.succ_ne_zero _)
+    swap; · rw [PNat.pow_coe]; exact hpri.1.IsPrimePow.pow (Nat.succ_ne_zero _)
     rw [add_sub_cancel] at H
     rw [H, coe_coe]
     congr
-    · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]
-      exact Nat.succ_ne_zero _
+    · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]; exact Nat.succ_ne_zero _
     have := FiniteDimensional.finrank_mul_finrank K K⟮⟯ L
     rw [IsCyclotomicExtension.finrank L hirr, IsCyclotomicExtension.finrank K⟮⟯ hirr₁, PNat.pow_coe,
       PNat.pow_coe, Nat.totient_prime_pow hpri.out (k - s).succ_pos,

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.primitive_roots
-! leanprover-community/mathlib commit b602702a58f74f5317862a24893693e80bee6d41
+! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,7 @@ import Mathbin.NumberTheory.Cyclotomic.Basic
 import Mathbin.RingTheory.Adjoin.PowerBasis
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Eval
 import Mathbin.RingTheory.Norm
+import Mathbin.RingTheory.Polynomial.Cyclotomic.Expand
 
 /-!
 # Primitive roots in cyclotomic fields

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.primitive_roots
-! leanprover-community/mathlib commit 8631e2d5ea77f6c13054d9151d82b83069680cb1
+! leanprover-community/mathlib commit b602702a58f74f5317862a24893693e80bee6d41
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,14 +17,14 @@ import Mathbin.RingTheory.Norm
 
 /-!
 # Primitive roots in cyclotomic fields
-If `is_cyclotomic_extension {n} A B`, we define an element `zeta n A B : B` that is (under certain
-assumptions) a primitive `n`-root of unity in `B` and we study its properties. We also prove related
-theorems under the more general assumption of just being a primitive root, for reasons described
-in the implementation details section.
+If `is_cyclotomic_extension {n} A B`, we define an element `zeta n A B : B` that is a primitive
+`n`th-root of unity in `B` and we study its properties. We also prove related theorems under the
+more general assumption of just being a primitive root, for reasons described in the implementation
+details section.
 
 ## Main definitions
 * `is_cyclotomic_extension.zeta n A B`: if `is_cyclotomic_extension {n} A B`, than `zeta n A B`
-  is an element of `B` that plays the role of a primitive `n`-th root of unity.
+  is a primitive `n`-th root of unity in `B`.
 * `is_primitive_root.power_basis`: if `K` and `L` are fields such that
   `is_cyclotomic_extension {n} K L`, then `is_primitive_root.power_basis`
   gives a K-power basis for L given a primitive root `ζ`.
@@ -39,7 +39,7 @@ in the implementation details section.
   the norm of a primitive root is `1` if `n ≠ 2`.
 * `is_primitive_root.sub_one_norm_eq_eval_cyclotomic`: if `irreducible (cyclotomic n K)`
   (in particular for `K = ℚ`), then the norm of `ζ - 1` is `eval 1 (cyclotomic n ℤ)`, for a
-  primitive root ζ. We also prove the analogous of this result for `zeta`.
+  primitive root `ζ`. We also prove the analogous of this result for `zeta`.
 * `is_primitive_root.pow_sub_one_norm_prime_pow_ne_two` : if
   `irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
   then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` `p ^ (k - s + 1) ≠ 2`. See the following
@@ -51,9 +51,9 @@ in the implementation details section.
   and `primitive_roots n A` given by the choice of `ζ`.
 
 ## Implementation details
-`zeta n A B` is defined as any primitive root of unity in `B`, that exists by definition. It is not
-true in general that it is a root of `cyclotomic n B`, but this holds if `is_domain B` and
-`ne_zero (↑n : B)`.
+`zeta n A B` is defined as any primitive root of unity in `B`, - this must exist, by definition of
+`is_cyclotomic_extension`. It is not true in general that it is a root of `cyclotomic n B`,
+but this holds if `is_domain B` and `ne_zero (↑n : B)`.
 
 `zeta n A B` is defined using `exists.some`, which means we cannot control it.
 For example, in normal mathematics, we can demand that `(zeta p ℤ ℤ[ζₚ] : ℚ(ζₚ))` is equal to
@@ -328,9 +328,7 @@ theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
   simp
 #align is_primitive_root.minpoly_sub_one_eq_cyclotomic_comp IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp
 
-attribute [local instance] IsCyclotomicExtension.finiteDimensional
-
-attribute [local instance] IsCyclotomicExtension.isGalois
+open Cyclotomic
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:192:11: unsupported (impossible) -/

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

@@ -319,7 +319,7 @@ variable {A}
 theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
     [IsCyclotomicExtension {n} K A] (hζ : IsPrimitiveRoot ζ n)
     (h : Irreducible (Polynomial.cyclotomic n K)) :
-    minpoly K (ζ - 1) = (cyclotomic n K).comp (x + 1) :=
+    minpoly K (ζ - 1) = (cyclotomic n K).comp (X + 1) :=
   by
   haveI := IsCyclotomicExtension.ne_zero' n K A
   rw [show ζ - 1 = ζ + algebraMap K A (-1) by simp [sub_eq_add_neg],

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

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.

@@ -358,7 +358,7 @@ theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 <
     simp
   haveI : NeZero ((n : ℕ) : E) := NeZero.of_noZeroSMulDivisors K _ (n : ℕ)
   rw [Hprod, cyclotomic', ← cyclotomic_eq_prod_X_sub_primitiveRoots (isRoot_cyclotomic_iff.1 hz),
-    ← map_cyclotomic_int, _root_.map_intCast, ← Int.cast_one, eval_int_cast_map, eq_intCast,
+    ← map_cyclotomic_int, _root_.map_intCast, ← Int.cast_one, eval_intCast_map, eq_intCast,
     Int.cast_id]
 #align is_primitive_root.sub_one_norm_eq_eval_cyclotomic IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic
 

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

@@ -91,13 +91,13 @@ theorem zeta_spec : IsPrimitiveRoot (zeta n A B) n :=
 
 theorem aeval_zeta [IsDomain B] [NeZero ((n : ℕ) : B)] :
     aeval (zeta n A B) (cyclotomic n A) = 0 := by
-  rw [aeval_def, ← eval_map, ← IsRoot.definition, map_cyclotomic, isRoot_cyclotomic_iff]
+  rw [aeval_def, ← eval_map, ← IsRoot.def, map_cyclotomic, isRoot_cyclotomic_iff]
   exact zeta_spec n A B
 #align is_cyclotomic_extension.aeval_zeta IsCyclotomicExtension.aeval_zeta
 
 theorem zeta_isRoot [IsDomain B] [NeZero ((n : ℕ) : B)] : IsRoot (cyclotomic n B) (zeta n A B) := by
   convert aeval_zeta n A B using 0
-  rw [IsRoot.definition, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
+  rw [IsRoot.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
 #align is_cyclotomic_extension.zeta_is_root IsCyclotomicExtension.zeta_isRoot
 
 theorem zeta_pow : zeta n A B ^ (n : ℕ) = 1 :=
@@ -151,7 +151,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type*) [CommRing C] [IsDoma
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
-        rwa [mem_primitiveRoots n.pos, ← isRoot_cyclotomic_iff, IsRoot.definition,
+        rwa [mem_primitiveRoots n.pos, ← isRoot_cyclotomic_iff, IsRoot.def,
           ← map_cyclotomic _ (algebraMap K C), hζ.minpoly_eq_cyclotomic_of_irreducible hirr,
           ← eval₂_eq_eval_map, ← aeval_def]
       invFun := fun x => by
@@ -160,7 +160,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type*) [CommRing C] [IsDoma
         refine' ⟨x.1, _⟩
         cases x
         rwa [aeval_def, eval₂_eq_eval_map, hζ.powerBasis_gen K, ←
-          hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_cyclotomic, ← IsRoot.definition,
+          hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_cyclotomic, ← IsRoot.def,
           isRoot_cyclotomic_iff, ← mem_primitiveRoots n.pos]
       left_inv := fun x => Subtype.ext rfl
       right_inv := fun x => Subtype.ext rfl }

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.

@@ -559,8 +559,8 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       at hζ hirr hcycl ⊢
     obtain ⟨k₁, hk₁⟩ := Nat.exists_eq_succ_of_ne_zero hk
 -- Porting note: the proof is slightly different because of coercions.
-    rw [hζ.pow_sub_one_norm_two hirr, hk₁, _root_.pow_succ, pow_mul, neg_eq_neg_one_mul, mul_pow,
-      neg_one_sq, one_mul, ← pow_mul, ← _root_.pow_succ]
+    rw [hζ.pow_sub_one_norm_two hirr, hk₁, _root_.pow_succ', pow_mul, neg_eq_neg_one_mul, mul_pow,
+      neg_one_sq, one_mul, ← pow_mul, ← _root_.pow_succ']
     simp
   · exact hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_primitive_root.pow_sub_one_norm_prime_pow_of_ne_zero IsPrimitiveRoot.pow_sub_one_norm_prime_pow_of_ne_zero

We add IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder: If x is a root of unity (spelled as IsOfFinOrder x) in an n-th cyclotomic extension of ℚ, where n is odd, and ζ is a primitive n-th root of unity, then there exists r < n such that x = ζ^r or x = -ζ^r.

From flt-regular

• depends on: #11235

@@ -188,6 +188,26 @@ theorem finrank (hirr : Irreducible (cyclotomic n K)) : finrank K L = (n : ℕ).
     (zeta_spec n K L).minpoly_eq_cyclotomic_of_irreducible hirr, natDegree_cyclotomic]
 #align is_cyclotomic_extension.finrank IsCyclotomicExtension.finrank
 
+variable {L} in
+/-- If `L` contains both a primitive `p`-th root of unity and `q`-th root of unity, and
+`Irreducible (cyclotomic (lcm p q) K)` (in particular for `K = ℚ`), then the `finrank K L` is at
+least `(lcm p q).totient`. -/
+theorem _root_.IsPrimitiveRoot.lcm_totient_le_finrank [FiniteDimensional K L] {p q : ℕ} {x y : L}
+    (hx : IsPrimitiveRoot x p) (hy : IsPrimitiveRoot y q)
+    (hirr : Irreducible (cyclotomic (Nat.lcm p q) K)) :
+    (Nat.lcm p q).totient ≤ FiniteDimensional.finrank K L := by
+  rcases Nat.eq_zero_or_pos p with (rfl | hppos)
+  · simp
+  rcases Nat.eq_zero_or_pos q with (rfl | hqpos)
+  · simp
+  let z := x ^ (p / factorizationLCMLeft p q) * y ^ (q / factorizationLCMRight p q)
+  let k := PNat.lcm ⟨p, hppos⟩ ⟨q, hqpos⟩
+  have : IsPrimitiveRoot z k := hx.pow_mul_pow_lcm hy hppos.ne' hqpos.ne'
+  haveI := IsPrimitiveRoot.adjoin_isCyclotomicExtension K this
+  convert Submodule.finrank_le (Subalgebra.toSubmodule (adjoin K {z}))
+  rw [show Nat.lcm p q = (k : ℕ) from rfl] at hirr
+  simpa using (IsCyclotomicExtension.finrank (Algebra.adjoin K {z}) hirr).symm
+
 end IsCyclotomicExtension
 
 end NoOrder
@@ -196,6 +216,70 @@ section Norm
 
 namespace IsPrimitiveRoot
 
+section Field
+
+variable {K} [Field K] [NumberField K]
+
+variable (n) in
+/-- If a `n`-th cyclotomic extension of `ℚ` contains a primitive `l`-th root of unity, then
+`l ∣ 2 * n`. -/
+theorem dvd_of_isCyclotomicExtension [NumberField K] [IsCyclotomicExtension {n} ℚ K] {ζ : K}
+    {l : ℕ} (hζ : IsPrimitiveRoot ζ l) (hl : l ≠ 0) : l ∣ 2 * n := by
+  have hl : NeZero l := ⟨hl⟩
+  have hroot := IsCyclotomicExtension.zeta_spec n ℚ K
+  have key := IsPrimitiveRoot.lcm_totient_le_finrank hζ hroot
+    (cyclotomic.irreducible_rat <| Nat.lcm_pos (Nat.pos_of_ne_zero hl.1) n.2)
+  rw [IsCyclotomicExtension.finrank K (cyclotomic.irreducible_rat n.2)] at key
+  rcases _root_.dvd_lcm_right l n with ⟨r, hr⟩
+  have ineq := Nat.totient_super_multiplicative n r
+  rw [← hr] at ineq
+  replace key := (mul_le_iff_le_one_right (Nat.totient_pos n.2)).mp (le_trans ineq key)
+  have rpos : 0 < r := by
+    refine Nat.pos_of_ne_zero (fun h ↦ ?_)
+    simp only [h, mul_zero, _root_.lcm_eq_zero_iff, PNat.ne_zero, or_false] at hr
+    exact hl.1 hr
+  replace key := (Nat.dvd_prime Nat.prime_two).1 (Nat.dvd_two_of_totient_le_one rpos key)
+  rcases key with (key | key)
+  · rw [key, mul_one] at hr
+    rw [← hr]
+    exact dvd_mul_of_dvd_right (_root_.dvd_lcm_left l ↑n) 2
+  · rw [key, mul_comm] at hr
+    simpa [← hr] using _root_.dvd_lcm_left _ _
+
+/-- If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of
+`ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exist `r`
+such that `x = (-ζ)^r`. -/
+theorem exists_neg_pow_of_isOfFinOrder [NumberField K] [IsCyclotomicExtension {n} ℚ K]
+    (hno : Odd (n : ℕ)) {ζ x : K} (hζ : IsPrimitiveRoot ζ n) (hx : IsOfFinOrder x) :
+    ∃ r : ℕ, x = (-ζ) ^ r :=  by
+  have hnegζ : IsPrimitiveRoot (-ζ) (2 * n) := by
+    convert IsPrimitiveRoot.orderOf (-ζ)
+    rw [neg_eq_neg_one_mul, (Commute.all _ _).orderOf_mul_eq_mul_orderOf_of_coprime]
+    · simp [hζ.eq_orderOf]
+    · simp [← hζ.eq_orderOf, Nat.odd_iff_not_even.1 hno]
+  obtain ⟨k, hkpos, hkn⟩ := isOfFinOrder_iff_pow_eq_one.1 hx
+  obtain ⟨l, hl, hlroot⟩ := (isRoot_of_unity_iff hkpos _).1 hkn
+  have hlzero : NeZero l := ⟨fun h ↦ by simp [h] at hl⟩
+  have : NeZero (l : K) := ⟨NeZero.natCast_ne l K⟩
+  rw [isRoot_cyclotomic_iff] at hlroot
+  obtain ⟨a, ha⟩ := hlroot.dvd_of_isCyclotomicExtension n hlzero.1
+  replace hlroot : x ^ (2 * (n : ℕ)) = 1 := by rw [ha, pow_mul, hlroot.pow_eq_one, one_pow]
+  obtain ⟨s, -, hs⟩ := hnegζ.eq_pow_of_pow_eq_one hlroot (by simp)
+  exact ⟨s, hs.symm⟩
+
+/-- If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of
+`ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n`
+such that `x = ζ^r` or `x = -ζ^r`. -/
+theorem exists_pow_or_neg_mul_pow_of_isOfFinOrder [NumberField K] [IsCyclotomicExtension {n} ℚ K]
+    (hno : Odd (n : ℕ)) {ζ x : K} (hζ : IsPrimitiveRoot ζ n) (hx : IsOfFinOrder x) :
+    ∃ r : ℕ, r < n ∧ (x = ζ ^ r ∨ x = -ζ ^ r) :=  by
+  obtain ⟨r, hr⟩ := hζ.exists_neg_pow_of_isOfFinOrder hno hx
+  refine ⟨r % n, Nat.mod_lt _ n.2, ?_⟩
+  rw [show ζ ^ (r % ↑n) = ζ ^ r from (IsPrimitiveRoot.eq_orderOf hζ).symm ▸ pow_mod_orderOf .., hr]
+  rcases Nat.even_or_odd r with (h | h) <;> simp [neg_pow, h.neg_one_pow]
+
+end Field
+
 section CommRing
 
 variable [CommRing L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)

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

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

| Statement | New name | Old name | |

@@ -338,7 +338,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           exact Subalgebra.add_mem _ (subset_adjoin (mem_singleton η)) (Subalgebra.one_mem _)
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
-          nth_rw 1 [← add_sub_cancel η 1]
+          nth_rw 1 [← add_sub_cancel_right η 1]
           exact Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
 -- Porting note: the previous proof was `rw [H] at this; exact this` but it now fails.
       exact IsCyclotomicExtension.equiv _ _ _ (Subalgebra.equivOfEq _ _ H)
@@ -361,7 +361,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   rw [norm_eq_norm_adjoin K]
   · have H := hη.sub_one_norm_isPrimePow ?_ hirr₁ htwo
     swap; · rw [PNat.pow_coe]; exact hpri.1.isPrimePow.pow (Nat.succ_ne_zero _)
-    rw [add_sub_cancel] at H
+    rw [add_sub_cancel_right] at H
     rw [H]
     congr
     · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -91,13 +91,13 @@ theorem zeta_spec : IsPrimitiveRoot (zeta n A B) n :=
 
 theorem aeval_zeta [IsDomain B] [NeZero ((n : ℕ) : B)] :
     aeval (zeta n A B) (cyclotomic n A) = 0 := by
-  rw [aeval_def, ← eval_map, ← IsRoot.def, map_cyclotomic, isRoot_cyclotomic_iff]
+  rw [aeval_def, ← eval_map, ← IsRoot.definition, map_cyclotomic, isRoot_cyclotomic_iff]
   exact zeta_spec n A B
 #align is_cyclotomic_extension.aeval_zeta IsCyclotomicExtension.aeval_zeta
 
 theorem zeta_isRoot [IsDomain B] [NeZero ((n : ℕ) : B)] : IsRoot (cyclotomic n B) (zeta n A B) := by
   convert aeval_zeta n A B using 0
-  rw [IsRoot.def, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
+  rw [IsRoot.definition, aeval_def, eval₂_eq_eval_map, map_cyclotomic]
 #align is_cyclotomic_extension.zeta_is_root IsCyclotomicExtension.zeta_isRoot
 
 theorem zeta_pow : zeta n A B ^ (n : ℕ) = 1 :=
@@ -151,16 +151,16 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type*) [CommRing C] [IsDoma
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
-        rwa [mem_primitiveRoots n.pos, ← isRoot_cyclotomic_iff, IsRoot.def, ←
-          map_cyclotomic _ (algebraMap K C), hζ.minpoly_eq_cyclotomic_of_irreducible hirr, ←
-          eval₂_eq_eval_map, ← aeval_def]
+        rwa [mem_primitiveRoots n.pos, ← isRoot_cyclotomic_iff, IsRoot.definition,
+          ← map_cyclotomic _ (algebraMap K C), hζ.minpoly_eq_cyclotomic_of_irreducible hirr,
+          ← eval₂_eq_eval_map, ← aeval_def]
       invFun := fun x => by
         haveI := IsCyclotomicExtension.neZero' n K L
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
         rwa [aeval_def, eval₂_eq_eval_map, hζ.powerBasis_gen K, ←
-          hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_cyclotomic, ← IsRoot.def,
+          hζ.minpoly_eq_cyclotomic_of_irreducible hirr, map_cyclotomic, ← IsRoot.definition,
           isRoot_cyclotomic_iff, ← mem_primitiveRoots n.pos]
       left_inv := fun x => Subtype.ext rfl
       right_inv := fun x => Subtype.ext rfl }

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)

@@ -69,7 +69,6 @@ open scoped IntermediateField
 universe u v w z
 
 variable {p n : ℕ+} (A : Type w) (B : Type z) (K : Type u) {L : Type v} (C : Type w)
-
 variable [CommRing A] [CommRing B] [Algebra A B] [IsCyclotomicExtension {n} A B]
 
 section Zeta
@@ -200,7 +199,6 @@ namespace IsPrimitiveRoot
 section CommRing
 
 variable [CommRing L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
-
 variable {K} [Field K] [Algebra K L]
 
 /-- This mathematically trivial result is complementary to `norm_eq_one` below. -/
@@ -250,7 +248,6 @@ end CommRing
 section Field
 
 variable [Field L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
-
 variable {K} [Field K] [Algebra K L]
 
 /-- If `Irreducible (cyclotomic n K)` (in particular for `K = ℚ`), then the norm of

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>

@@ -326,7 +326,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   have hirr₁ : Irreducible (cyclotomic ((p : ℕ) ^ (k - s + 1)) K) :=
     cyclotomic_irreducible_pow_of_irreducible_pow hpri.1 (by simp) hirr
   rw [← PNat.pow_coe] at hirr₁
-  set η := ζ ^ (p : ℕ) ^ s - 1 with ηdef
+  set η := ζ ^ (p : ℕ) ^ s - 1
   let η₁ : K⟮η⟯ := IntermediateField.AdjoinSimple.gen K η
   have hη : IsPrimitiveRoot (η + 1) ((p : ℕ) ^ (k + 1 - s)) := by
     rw [sub_add_cancel]
@@ -340,8 +340,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
         refine' Subalgebra.ext fun x => ⟨fun hx => adjoin_le _ hx, fun hx => adjoin_le _ hx⟩
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           exact Subalgebra.add_mem _ (subset_adjoin (mem_singleton η)) (Subalgebra.one_mem _)
--- Porting note `ηdef` was not needed.
-        · simp only [Set.singleton_subset_iff, SetLike.mem_coe, ← ηdef]
+        · simp only [Set.singleton_subset_iff, SetLike.mem_coe]
           nth_rw 1 [← add_sub_cancel η 1]
           exact Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
 -- Porting note: the previous proof was `rw [H] at this; exact this` but it now fails.

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -343,7 +343,7 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
 -- Porting note `ηdef` was not needed.
         · simp only [Set.singleton_subset_iff, SetLike.mem_coe, ← ηdef]
           nth_rw 1 [← add_sub_cancel η 1]
-          refine' Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
+          exact Subalgebra.sub_mem _ (subset_adjoin (mem_singleton _)) (Subalgebra.one_mem _)
 -- Porting note: the previous proof was `rw [H] at this; exact this` but it now fails.
       exact IsCyclotomicExtension.equiv _ _ _ (Subalgebra.equivOfEq _ _ H)
 -- Porting note: the next `refine` was `rw [H]`, abusing defeq, and it now fails.
@@ -474,7 +474,7 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       nth_rw 2 [← pow_one 2] at htwo
       replace htwo := Nat.pow_right_injective rfl.le htwo
       rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo
-      refine' le_antisymm hs htwo
+      exact le_antisymm hs htwo
     simp only [hs, hp, one_coe, cast_one, pow_coe, show ((2 : ℕ+) : ℕ) = 2 from rfl]
       at hζ hirr hcycl ⊢
     obtain ⟨k₁, hk₁⟩ := Nat.exists_eq_succ_of_ne_zero hk

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>

@@ -217,8 +217,8 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
   by_cases h1 : n = 1
   · rw [h1, one_coe, one_right_iff] at hζ
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
-  · replace h1 : 2 ≤ n
-    · by_contra! h
+  · replace h1 : 2 ≤ n := by
+      by_contra! h
       exact h1 (PNat.eq_one_of_lt_two h)
 -- Porting note: specyfing the type of `cyclotomic_coeff_zero K h1` was not needed.
     rw [← hζ.powerBasis_gen K, PowerBasis.norm_gen_eq_coeff_zero_minpoly, hζ.powerBasis_gen K, ←
@@ -354,8 +354,8 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
 -- Porting note: `using 1` was not needed.
     convert hη'.adjoin_isCyclotomicExtension K using 1
     rw [Nat.sub_add_comm hs]
-  replace hη : IsPrimitiveRoot (η₁ + 1) ↑(p ^ (k - s + 1))
-  · apply coe_submonoidClass_iff.1
+  replace hη : IsPrimitiveRoot (η₁ + 1) ↑(p ^ (k - s + 1)) := by
+    apply coe_submonoidClass_iff.1
     convert hη using 1
     rw [Nat.sub_add_comm hs, pow_coe]
 -- Porting note: the following `haveI` were not needed because the locale `cyclotomic` set them
@@ -469,8 +469,8 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       replace htwo :=
         eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (succ_pos _) htwo
       rwa [show 2 = ((2 : ℕ+) : ℕ) by decide, PNat.coe_inj] at htwo
-    replace hs : s = k
-    · rw [hp, ← PNat.coe_inj, PNat.pow_coe] at htwo
+    replace hs : s = k := by
+      rw [hp, ← PNat.coe_inj, PNat.pow_coe] at htwo
       nth_rw 2 [← pow_one 2] at htwo
       replace htwo := Nat.pow_right_injective rfl.le htwo
       rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -447,7 +447,7 @@ theorem sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ k)) (hk : 2 
   have : 2 < (2 : ℕ+) ^ k := by
     simp only [← coe_lt_coe, one_coe, pow_coe]
     nth_rw 1 [← pow_one 2]
-    exact pow_lt_pow one_lt_two (lt_of_lt_of_le one_lt_two hk)
+    exact pow_lt_pow_right one_lt_two (lt_of_lt_of_le one_lt_two hk)
 -- Porting note: `simpa using hirr` was `simp [hirr]`_
   replace hirr : Irreducible (cyclotomic ((2 : ℕ+) ^ k : ℕ+) K) := by simpa using hirr
 -- Porting note: `simpa using hζ` was `simp [hζ]`_

To fit with the "please try harder" convention of ! tactics.

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

@@ -218,7 +218,7 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
   · rw [h1, one_coe, one_right_iff] at hζ
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
   · replace h1 : 2 ≤ n
-    · by_contra' h
+    · by_contra! h
       exact h1 (PNat.eq_one_of_lt_two h)
 -- Porting note: specyfing the type of `cyclotomic_coeff_zero K h1` was not needed.
     rw [← hζ.powerBasis_gen K, PowerBasis.norm_gen_eq_coeff_zero_minpoly, hζ.powerBasis_gen K, ←

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>

@@ -136,7 +136,7 @@ theorem powerBasis_gen_mem_adjoin_zeta_sub_one :
 @[simps!]
 noncomputable def subOnePowerBasis : PowerBasis K L :=
   (hζ.powerBasis K).ofGenMemAdjoin
-    (IsIntegral.sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
+    ((IsCyclotomicExtension.integral {n} K L ζ).sub isIntegral_one)
     (hζ.powerBasis_gen_mem_adjoin_zeta_sub_one _)
 #align is_primitive_root.sub_one_power_basis IsPrimitiveRoot.subOnePowerBasis
 

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>

@@ -72,7 +72,6 @@ variable {p n : ℕ+} (A : Type w) (B : Type z) (K : Type u) {L : Type v} (C : T
 
 variable [CommRing A] [CommRing B] [Algebra A B] [IsCyclotomicExtension {n} A B]
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 section Zeta
 
 namespace IsCyclotomicExtension
@@ -413,8 +412,8 @@ then the norm of `ζ - 1` is `p`. -/
 theorem sub_one_norm_prime [hpri : Fact (p : ℕ).Prime] [hcyc : IsCyclotomicExtension {p} K L]
     (hζ : IsPrimitiveRoot ζ p) (hirr : Irreducible (cyclotomic p K)) (h : p ≠ 2) :
     norm K (ζ - 1) = p := by
-  replace hirr : Irreducible (cyclotomic (↑(p ^ (0 + 1)) : ℕ) K) := by simp [hirr]
-  replace hζ : IsPrimitiveRoot ζ (↑(p ^ (0 + 1)) : ℕ) := by simp [hζ]
+  replace hirr : Irreducible (cyclotomic (p ^ (0 + 1) : ℕ) K) := by simp [hirr]
+  replace hζ : IsPrimitiveRoot ζ (p ^ (0 + 1) : ℕ) := by simp [hζ]
   haveI : IsCyclotomicExtension {p ^ (0 + 1)} K L := by simp [hcyc]
   simpa using sub_one_norm_prime_ne_two hζ hirr h
 #align is_primitive_root.sub_one_norm_prime IsPrimitiveRoot.sub_one_norm_prime
@@ -452,7 +451,7 @@ theorem sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ k)) (hk : 2 
 -- Porting note: `simpa using hirr` was `simp [hirr]`_
   replace hirr : Irreducible (cyclotomic ((2 : ℕ+) ^ k : ℕ+) K) := by simpa using hirr
 -- Porting note: `simpa using hζ` was `simp [hζ]`_
-  replace hζ : IsPrimitiveRoot ζ ((2 : ℕ+) ^ k) := by simpa using hζ
+  replace hζ : IsPrimitiveRoot ζ (2 ^ k : ℕ+) := by simpa using hζ
   obtain ⟨k₁, hk₁⟩ := exists_eq_succ_of_ne_zero (lt_of_lt_of_le zero_lt_two hk).ne.symm
 -- Porting note: the proof is slightly different because of coercions.
   simpa [hk₁, show ((2 : ℕ+) : ℕ) = 2 from rfl] using sub_one_norm_eq_eval_cyclotomic hζ this hirr
@@ -469,7 +468,7 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       rw [← PNat.coe_inj, PNat.pow_coe, ← pow_one 2] at htwo
       replace htwo :=
         eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (succ_pos _) htwo
-      rwa [show 2 = ((2 : ℕ+) : ℕ) by simp, PNat.coe_inj] at htwo
+      rwa [show 2 = ((2 : ℕ+) : ℕ) by decide, PNat.coe_inj] at htwo
     replace hs : s = k
     · rw [hp, ← PNat.coe_inj, PNat.pow_coe] at htwo
       nth_rw 2 [← pow_one 2] at htwo

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 |

@@ -137,7 +137,7 @@ theorem powerBasis_gen_mem_adjoin_zeta_sub_one :
 @[simps!]
 noncomputable def subOnePowerBasis : PowerBasis K L :=
   (hζ.powerBasis K).ofGenMemAdjoin
-    (isIntegral_sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
+    (IsIntegral.sub (IsCyclotomicExtension.integral {n} K L ζ) isIntegral_one)
     (hζ.powerBasis_gen_mem_adjoin_zeta_sub_one _)
 #align is_primitive_root.sub_one_power_basis IsPrimitiveRoot.subOnePowerBasis
 

mathlib can't make up its mind on whether to spell "the prime factors of n" as n.factors.toFinset or n.factorization.support, even though those two are defeq. This PR proposes to unify everything to a new definition Nat.primeFactors, and streamline the existing scattered API about n.factors.toFinset and n.factorization.support to Nat.primeFactors. We also get to write a bit more API that didn't make sense before, eg primeFactors_mono.

@@ -296,7 +296,7 @@ theorem sub_one_norm_isPrimePow (hn : IsPrimePow (n : ℕ)) [IsCyclotomicExtensi
   obtain ⟨k, hk⟩ : ∃ k, (n : ℕ).factorization (n : ℕ).minFac = k + 1 :=
     exists_eq_succ_of_ne_zero
       (((n : ℕ).factorization.mem_support_toFun (n : ℕ).minFac).1 <|
-        factor_iff_mem_factorization.2 <|
+        mem_primeFactors_iff_mem_factors.2 <|
           (mem_factors (IsPrimePow.ne_zero hn)).2 ⟨hprime.out, minFac_dvd _⟩)
   simp [hk, sub_one_norm_eq_eval_cyclotomic hζ this hirr]
 #align is_primitive_root.sub_one_norm_is_prime_pow IsPrimitiveRoot.sub_one_norm_isPrimePow

@@ -64,6 +64,7 @@ and only at the "final step", when we need to provide an "explicit" primitive ro
 
 
 open Polynomial Algebra Finset FiniteDimensional IsCyclotomicExtension Nat PNat Set
+open scoped IntermediateField
 
 universe u v w z
 

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

This has nice performance benefits.

@@ -144,7 +144,7 @@ variable {K} (C)
 
 -- We are not using @[simps] to avoid a timeout.
 /-- The equivalence between `L →ₐ[K] C` and `primitiveRoots n C` given by a primitive root `ζ`. -/
-noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDomain C] [Algebra K C]
+noncomputable def embeddingsEquivPrimitiveRoots (C : Type*) [CommRing C] [IsDomain C] [Algebra K C]
     (hirr : Irreducible (cyclotomic n K)) : (L →ₐ[K] C) ≃ primitiveRoots n C :=
   (hζ.powerBasis K).liftEquiv.trans
     { toFun := fun x => by
@@ -169,7 +169,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
 
 -- Porting note: renamed argument `φ`: "expected '_' or identifier"
 @[simp]
-theorem embeddingsEquivPrimitiveRoots_apply_coe (C : Type _) [CommRing C] [IsDomain C] [Algebra K C]
+theorem embeddingsEquivPrimitiveRoots_apply_coe (C : Type*) [CommRing C] [IsDomain C] [Algebra K C]
     (hirr : Irreducible (cyclotomic n K)) (φ' : L →ₐ[K] C) :
     (hζ.embeddingsEquivPrimitiveRoots C hirr φ' : C) = φ' ζ :=
   rfl
@@ -229,7 +229,7 @@ theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
 #align is_primitive_root.norm_eq_one IsPrimitiveRoot.norm_eq_one
 
 /-- If `K` is linearly ordered, the norm of a primitive root is `1` if `n` is odd. -/
-theorem norm_eq_one_of_linearly_ordered {K : Type _} [LinearOrderedField K] [Algebra K L]
+theorem norm_eq_one_of_linearly_ordered {K : Type*} [LinearOrderedField K] [Algebra K L]
     (hodd : Odd (n : ℕ)) : norm K ζ = 1 := by
   have hz := congr_arg (norm K) ((IsPrimitiveRoot.iff_def _ n).1 hζ).1
   rw [← (algebraMap K L).map_one, Algebra.norm_algebraMap, one_pow, map_pow, ← one_pow ↑n] at hz

@@ -71,7 +71,7 @@ variable {p n : ℕ+} (A : Type w) (B : Type z) (K : Type u) {L : Type v} (C : T
 
 variable [CommRing A] [CommRing B] [Algebra A B] [IsCyclotomicExtension {n} A B]
 
-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
 section Zeta
 
 namespace IsCyclotomicExtension

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.primitive_roots
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.PNat.Prime
 import Mathlib.Algebra.IsPrimePow
@@ -16,6 +11,8 @@ import Mathlib.RingTheory.Polynomial.Cyclotomic.Eval
 import Mathlib.RingTheory.Norm
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Expand
 
+#align_import number_theory.cyclotomic.primitive_roots from "leanprover-community/mathlib"@"5bfbcca0a7ffdd21cf1682e59106d6c942434a32"
+
 /-!
 # Primitive roots in cyclotomic fields
 If `IsCyclotomicExtension {n} A B`, we define an element `zeta n A B : B` that is a primitive

@@ -81,7 +81,7 @@ namespace IsCyclotomicExtension
 
 variable (n)
 
-/-- If `B` is a `n`-th cyclotomic extension of `A`, then `zeta n A B` is a primitive root of
+/-- If `B` is an `n`-th cyclotomic extension of `A`, then `zeta n A B` is a primitive root of
 unity in `B`. -/
 noncomputable def zeta : B :=
   (exists_prim_root A <| Set.mem_singleton n : ∃ r : B, IsPrimitiveRoot r n).choose

@@ -151,7 +151,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
     (hirr : Irreducible (cyclotomic n K)) : (L →ₐ[K] C) ≃ primitiveRoots n C :=
   (hζ.powerBasis K).liftEquiv.trans
     { toFun := fun x => by
-        haveI := IsCyclotomicExtension.ne_zero' n K L
+        haveI := IsCyclotomicExtension.neZero' n K L
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
@@ -159,7 +159,7 @@ noncomputable def embeddingsEquivPrimitiveRoots (C : Type _) [CommRing C] [IsDom
           map_cyclotomic _ (algebraMap K C), hζ.minpoly_eq_cyclotomic_of_irreducible hirr, ←
           eval₂_eq_eval_map, ← aeval_def]
       invFun := fun x => by
-        haveI := IsCyclotomicExtension.ne_zero' n K L
+        haveI := IsCyclotomicExtension.neZero' n K L
         haveI hn := NeZero.of_noZeroSMulDivisors K C n
         refine' ⟨x.1, _⟩
         cases x
@@ -187,7 +187,7 @@ variable {K} (L)
 /-- If `Irreducible (cyclotomic n K)` (in particular for `K = ℚ`), then the `finrank` of a
 cyclotomic extension is `n.totient`. -/
 theorem finrank (hirr : Irreducible (cyclotomic n K)) : finrank K L = (n : ℕ).totient := by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   rw [((zeta_spec n K L).powerBasis K).finrank, IsPrimitiveRoot.powerBasis_dim, ←
     (zeta_spec n K L).minpoly_eq_cyclotomic_of_irreducible hirr, natDegree_cyclotomic]
 #align is_cyclotomic_extension.finrank IsCyclotomicExtension.finrank
@@ -208,17 +208,15 @@ variable {K} [Field K] [Algebra K L]
 
 /-- This mathematically trivial result is complementary to `norm_eq_one` below. -/
 theorem norm_eq_neg_one_pow (hζ : IsPrimitiveRoot ζ 2) [IsDomain L] :
-    norm K ζ = (-1) ^ finrank K L := by
+    norm K ζ = (-1 : K) ^ finrank K L := by
   rw [hζ.eq_neg_one_of_two_right, show -1 = algebraMap K L (-1) by simp, Algebra.norm_algebraMap]
--- Porting note: the following `simp` is not needed without `local macro_rules...`.
-  simp
 #align is_primitive_root.norm_eq_neg_one_pow IsPrimitiveRoot.norm_eq_neg_one_pow
 
 /-- If `Irreducible (cyclotomic n K)` (in particular for `K = ℚ`), the norm of a primitive root is
 `1` if `n ≠ 2`. -/
 theorem norm_eq_one [IsDomain L] [IsCyclotomicExtension {n} K L] (hn : n ≠ 2)
     (hirr : Irreducible (cyclotomic n K)) : norm K ζ = 1 := by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   by_cases h1 : n = 1
   · rw [h1, one_coe, one_right_iff] at hζ
     rw [hζ, show 1 = algebraMap K L 1 by simp, Algebra.norm_algebraMap, one_pow]
@@ -247,14 +245,11 @@ theorem norm_of_cyclotomic_irreducible [IsDomain L] [IsCyclotomicExtension {n} K
   · subst hn
     convert norm_eq_neg_one_pow (K := K) hζ
     erw [IsCyclotomicExtension.finrank _ hirr, totient_two, pow_one]
--- Porting note: the following `simp` is not needed without `local macro_rules...`.
-    simp
   · exact hζ.norm_eq_one hn hirr
 #align is_primitive_root.norm_of_cyclotomic_irreducible IsPrimitiveRoot.norm_of_cyclotomic_irreducible
 
 end CommRing
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
 section Field
 
 variable [Field L] {ζ : L} (hζ : IsPrimitiveRoot ζ n)
@@ -265,7 +260,7 @@ variable {K} [Field K] [Algebra K L]
 `ζ - 1` is `eval 1 (cyclotomic n ℤ)`. -/
 theorem sub_one_norm_eq_eval_cyclotomic [IsCyclotomicExtension {n} K L] (h : 2 < (n : ℕ))
     (hirr : Irreducible (cyclotomic n K)) : norm K (ζ - 1) = ↑(eval 1 (cyclotomic n ℤ)) := by
-  haveI := IsCyclotomicExtension.ne_zero' n K L
+  haveI := IsCyclotomicExtension.neZero' n K L
   let E := AlgebraicClosure L
   obtain ⟨z, hz⟩ := IsAlgClosed.exists_root _ (degree_cyclotomic_pos n E n.pos).ne.symm
   apply (algebraMap K E).injective
@@ -314,7 +309,7 @@ theorem minpoly_sub_one_eq_cyclotomic_comp [Algebra K A] [IsDomain A] {ζ : A}
     [IsCyclotomicExtension {n} K A] (hζ : IsPrimitiveRoot ζ n)
     (h : Irreducible (Polynomial.cyclotomic n K)) :
     minpoly K (ζ - 1) = (cyclotomic n K).comp (X + 1) := by
-  haveI := IsCyclotomicExtension.ne_zero' n K A
+  haveI := IsCyclotomicExtension.neZero' n K A
   rw [show ζ - 1 = ζ + algebraMap K A (-1) by simp [sub_eq_add_neg],
     minpoly.add_algebraMap (IsCyclotomicExtension.integral {n} K A ζ),
     hζ.minpoly_eq_cyclotomic_of_irreducible h]
@@ -329,18 +324,17 @@ for similar results. -/
 theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
     [hpri : Fact (p : ℕ).Prime] [IsCyclotomicExtension {p ^ (k + 1)} K L]
     (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K)) (hs : s ≤ k)
-    (htwo : p ^ (k - s + 1) ≠ 2) : norm K (ζ ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s := by
+    (htwo : p ^ (k - s + 1) ≠ 2) : norm K (ζ ^ (p : ℕ) ^ s - 1) = (p : K) ^ (p : ℕ) ^ s := by
 -- Porting note: `by simp` was `by linarith` that now fails.
-  have hirr₁ : Irreducible (cyclotomic (p ^ (k - s + 1)) K) :=
+  have hirr₁ : Irreducible (cyclotomic ((p : ℕ) ^ (k - s + 1)) K) :=
     cyclotomic_irreducible_pow_of_irreducible_pow hpri.1 (by simp) hirr
--- Porting note: there was a `rw [← PNat.pow_coe] at hirr₁` that is now useless.
+  rw [← PNat.pow_coe] at hirr₁
   set η := ζ ^ (p : ℕ) ^ s - 1 with ηdef
   let η₁ : K⟮η⟯ := IntermediateField.AdjoinSimple.gen K η
-  have hη : IsPrimitiveRoot (η + 1) (p ^ (k + 1 - s)) := by
+  have hη : IsPrimitiveRoot (η + 1) ((p : ℕ) ^ (k + 1 - s)) := by
     rw [sub_add_cancel]
     refine' IsPrimitiveRoot.pow (p ^ (k + 1)).pos hζ _
-    rw [PNat.pow_coe, PNat.pow_coe, ← pow_add, add_comm s, Nat.sub_add_cancel
-      (le_trans hs (Nat.le_succ k))]
+    rw [PNat.pow_coe, ← pow_add, add_comm s, Nat.sub_add_cancel (le_trans hs (Nat.le_succ k))]
   have : IsCyclotomicExtension {p ^ (k - s + 1)} K K⟮η⟯ := by
     suffices IsCyclotomicExtension {p ^ (k - s + 1)} K K⟮η + 1⟯.toSubalgebra by
       have H : K⟮η + 1⟯.toSubalgebra = K⟮η⟯.toSubalgebra := by
@@ -375,11 +369,10 @@ theorem pow_sub_one_norm_prime_pow_ne_two {k s : ℕ} (hζ : IsPrimitiveRoot ζ
   · have H := hη.sub_one_norm_isPrimePow ?_ hirr₁ htwo
     swap; · rw [PNat.pow_coe]; exact hpri.1.isPrimePow.pow (Nat.succ_ne_zero _)
     rw [add_sub_cancel] at H
--- Porting note: the proof is slightly different because of coercions.
-    rw [H, PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]
-    swap; · exact Nat.succ_ne_zero _
-    simp only [pow_coe, cast_pow]
+    rw [H]
     congr
+    · rw [PNat.pow_coe, Nat.pow_minFac, hpri.1.minFac_eq]
+      exact Nat.succ_ne_zero _
     have := FiniteDimensional.finrank_mul_finrank K K⟮η⟯ L
     rw [IsCyclotomicExtension.finrank L hirr, IsCyclotomicExtension.finrank K⟮η⟯ hirr₁,
       PNat.pow_coe, PNat.pow_coe, Nat.totient_prime_pow hpri.out (k - s).succ_pos,
@@ -398,11 +391,12 @@ then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `p ≠ 2`. -/
 theorem pow_sub_one_norm_prime_ne_two {k : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
     [hpri : Fact (p : ℕ).Prime] [IsCyclotomicExtension {p ^ (k + 1)} K L]
     (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K)) {s : ℕ} (hs : s ≤ k) (hodd : p ≠ 2) :
-    norm K (ζ ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s := by
+    norm K (ζ ^ (p : ℕ) ^ s - 1) = (p : K) ^ (p : ℕ) ^ s := by
   refine' hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs fun h => _
-  rw [← PNat.coe_inj, PNat.pow_coe, ← pow_one 2] at h
+  have coe_two : ((2 : ℕ+) : ℕ) = 2 := by norm_cast
+  rw [← PNat.coe_inj, coe_two, PNat.pow_coe, ← pow_one 2] at h
 -- Porting note: the proof is slightly different because of coercions.
-  replace h : (p : ℕ) = ((2 : ℕ+) : ℕ) :=
+  replace h :=
     eq_of_prime_pow_eq (prime_iff.1 hpri.out) (prime_iff.1 Nat.prime_two) (k - s).succ_pos h
   exact hodd (PNat.coe_injective h)
 
@@ -432,7 +426,8 @@ theorem sub_one_norm_prime [hpri : Fact (p : ℕ).Prime] [hcyc : IsCyclotomicExt
 -- Porting note: writing `(2 : ℕ+)` was not needed (similarly everywhere).
 theorem pow_sub_one_norm_two {k : ℕ} (hζ : IsPrimitiveRoot ζ (2 ^ (k + 1)))
     [IsCyclotomicExtension {(2 : ℕ+) ^ (k + 1)} K L]
-    (hirr : Irreducible (cyclotomic (2 ^ (k + 1)) K)) : norm K (ζ ^ 2 ^ k - 1) = (-2) ^ 2 ^ k := by
+    (hirr : Irreducible (cyclotomic (2 ^ (k + 1)) K)) :
+    norm K (ζ ^ 2 ^ k - 1) = (-2 : K) ^ 2 ^ k := by
   have := hζ.pow_of_dvd (fun h => two_ne_zero (pow_eq_zero h)) (pow_dvd_pow 2 (le_succ k))
   rw [Nat.pow_div (le_succ k) zero_lt_two, Nat.succ_sub (le_refl k), Nat.sub_self, pow_one] at this
   have H : (-1 : L) - (1 : L) = algebraMap K L (-2) := by
@@ -470,7 +465,7 @@ then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `k ≠ 0` and `s ≤ k`.
 theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1)))
     [hpri : Fact (p : ℕ).Prime] [hcycl : IsCyclotomicExtension {p ^ (k + 1)} K L]
     (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K)) (hs : s ≤ k) (hk : k ≠ 0) :
-    norm K (ζ ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s := by
+    norm K (ζ ^ (p : ℕ) ^ s - 1) = (p : K) ^ (p : ℕ) ^ s := by
   by_cases htwo : p ^ (k - s + 1) = 2
   · have hp : p = 2 := by
       rw [← PNat.coe_inj, PNat.pow_coe, ← pow_one 2] at htwo
@@ -483,13 +478,12 @@ theorem pow_sub_one_norm_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot
       replace htwo := Nat.pow_right_injective rfl.le htwo
       rw [add_left_eq_self, Nat.sub_eq_zero_iff_le] at htwo
       refine' le_antisymm hs htwo
-    simp only [hs, hp, one_coe, cast_one, pow_coe] at hζ hirr hcycl ⊢
-    haveI := hcycl
+    simp only [hs, hp, one_coe, cast_one, pow_coe, show ((2 : ℕ+) : ℕ) = 2 from rfl]
+      at hζ hirr hcycl ⊢
     obtain ⟨k₁, hk₁⟩ := Nat.exists_eq_succ_of_ne_zero hk
 -- Porting note: the proof is slightly different because of coercions.
-    simp only [show ((2 : ℕ+) : ℕ) = 2 from rfl]
     rw [hζ.pow_sub_one_norm_two hirr, hk₁, _root_.pow_succ, pow_mul, neg_eq_neg_one_mul, mul_pow,
-      pow_mul, neg_one_sq, one_pow, one_mul, ← pow_mul, ← _root_.pow_succ]
+      neg_one_sq, one_mul, ← pow_mul, ← _root_.pow_succ]
     simp
   · exact hζ.pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_primitive_root.pow_sub_one_norm_prime_pow_of_ne_zero IsPrimitiveRoot.pow_sub_one_norm_prime_pow_of_ne_zero
@@ -526,7 +520,7 @@ theorem prime_ne_two_pow_norm_zeta_pow_sub_one {k : ℕ} [Fact (p : ℕ).Prime]
     [IsCyclotomicExtension {p ^ (k + 1)} K L]
     (hirr : Irreducible (cyclotomic (↑(p ^ (k + 1)) : ℕ) K)) {s : ℕ} (hs : s ≤ k)
     (htwo : p ^ (k - s + 1) ≠ 2) :
-    norm K (zeta (p ^ (k + 1)) K L ^ (p : ℕ) ^ s - 1) = p ^ (p : ℕ) ^ s :=
+    norm K (zeta (p ^ (k + 1)) K L ^ (p : ℕ) ^ s - 1) = (p : K) ^ (p : ℕ) ^ s :=
   (zeta_spec _ K L).pow_sub_one_norm_prime_pow_ne_two hirr hs htwo
 #align is_cyclotomic_extension.prime_ne_two_pow_norm_zeta_pow_sub_one IsCyclotomicExtension.prime_ne_two_pow_norm_zeta_pow_sub_one
 

Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>