number_theory.ramification_inertia ⟷ Mathlib.NumberTheory.RamificationInertia

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

@@ -681,7 +681,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
       Submodule.coe_sub]
     refine' ⟨⟨_, Ideal.mem_map_of_mem _ (Submodule.neg_mem _ hz)⟩, _⟩
     rw [pow_quot_succ_inclusion_apply_coe, Subtype.coe_mk, Ideal.Quotient.mk_eq_mk, map_add,
-      mul_comm y a, sub_add_cancel', map_neg]
+      mul_comm y a, sub_add_cancel_left, map_neg]
   letI := Classical.decEq (Ideal S)
   rw [sup_eq_prod_inf_factors _ (pow_ne_zero _ hP0), normalized_factors_pow,
     normalized_factors_irreducible ((Ideal.prime_iff_isPrime hP0).mpr hP).Irreducible, normalize_eq,
@@ -735,7 +735,7 @@ theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime
       (e - i) • Module.rank (R ⧸ p) (S ⧸ P) :=
   by
   refine' @Nat.decreasingInduction' _ i e (fun j lt_e le_j ih => _) hi _
-  · rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul, Nat.sub_succ, ← Nat.succ_eq_add_one,
+  · rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul', Nat.sub_succ, ← Nat.succ_eq_add_one,
       Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt lt_e)]
     assumption
   · rw [Nat.sub_self, zero_nsmul, map_quotient_self]

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

@@ -319,7 +319,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   -- Because `R/I` is nontrivial, we can lift `g` to a nontrivial linear dependence in `S`.
   have hgI : algebraMap R S (g' j) ≠ 0 :=
     by
-    simp only [FractionalIdeal.mem_coeIdeal, not_exists, not_and'] at hgI 
+    simp only [FractionalIdeal.mem_coeIdeal, not_exists, not_and'] at hgI
     exact hgI _ (hg' j hjs)
   refine' ⟨fun i => algebraMap R S (g' i), _, j, hjs, hgI⟩
   have eq : f (∑ i in s, g' i • b i) = 0 :=
@@ -406,7 +406,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   have span_d : (Submodule.span S ({algebraMap R S A.det} : Set S)).restrictScalars R ≤ M :=
     by
     intro x hx
-    rw [Submodule.restrictScalars_mem] at hx 
+    rw [Submodule.restrictScalars_mem] at hx
     obtain ⟨x', rfl⟩ := submodule.mem_span_singleton.mp hx
     rw [smul_eq_mul, mul_comm, ← Algebra.smul_def] at hx ⊢
     rw [← Submodule.Quotient.mk_eq_zero, Submodule.Quotient.mk_smul]
@@ -445,7 +445,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       rfl
   -- And we conclude `L = span L {det A} ≤ span K b`, so `span K b` spans everything.
   · intro x hx
-    rw [Submodule.restrictScalars_mem, IsScalarTower.algebraMap_apply R S L] at hx 
+    rw [Submodule.restrictScalars_mem, IsScalarTower.algebraMap_apply R S L] at hx
     refine' IsFractionRing.ideal_span_singleton_map_subset R _ hRL span_d hx
     haveI : NoZeroSMulDivisors R L := NoZeroSMulDivisors.of_algebraMap_injective hRL
     rw [← IsFractionRing.isAlgebraic_iff' R S]
@@ -495,13 +495,13 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
       b.mem_span _
     rw [← @Submodule.restrictScalars_mem R,
       Submodule.restrictScalars_span R (R ⧸ p) Ideal.Quotient.mk_surjective, b_eq_b',
-      Set.range_comp, ← Submodule.map_span] at mem_span_b 
+      Set.range_comp, ← Submodule.map_span] at mem_span_b
     obtain ⟨y, y_mem, y_eq⟩ := submodule.mem_map.mp mem_span_b
     suffices y + -(y - x) ∈ _ by simpa
     rw [LinearMap.restrictScalars_apply, Submodule.mkQ_apply, Submodule.mkQ_apply,
-      Submodule.Quotient.eq] at y_eq 
+      Submodule.Quotient.eq] at y_eq
     exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
-  · have := b.linear_independent; rw [b_eq_b'] at this 
+  · have := b.linear_independent; rw [b_eq_b'] at this
     convert
       finrank_quotient_map.linear_independent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
@@ -575,7 +575,7 @@ theorem powQuotSuccInclusion_injective (i : ℕ) :
   rw [← LinearMap.ker_eq_bot, LinearMap.ker_eq_bot']
   rintro ⟨x, hx⟩ hx0
   rw [Subtype.ext_iff] at hx0 ⊢
-  rwa [pow_quot_succ_inclusion_apply_coe] at hx0 
+  rwa [pow_quot_succ_inclusion_apply_coe] at hx0
 #align ideal.pow_quot_succ_inclusion_injective Ideal.powQuotSuccInclusion_injective
 -/
 
@@ -651,9 +651,9 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
         Submodule.coe_sub] at h ⊢
       rcases h with ⟨⟨⟨z⟩, hz⟩, h⟩
       rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
-        sup_eq_left.mpr Pe_le_Pi1] at hz 
+        sup_eq_left.mpr Pe_le_Pi1] at hz
       rw [pow_quot_succ_inclusion_apply_coe, Subtype.coe_mk, Submodule.Quotient.quot_mk_eq_mk,
-        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← sub_mul] at h 
+        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← sub_mul] at h
       exact
         (Ideal.IsPrime.mul_mem_pow _
               ((Submodule.sub_mem_iff_right _ hz).mp (Pe_le_Pi1 h))).resolve_right
@@ -671,7 +671,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
   have Pe_le_Pi : P ^ e ≤ P ^ i := Ideal.pow_le_pow hi.le
   have Pe_le_Pi1 : P ^ e ≤ P ^ (i + 1) := Ideal.pow_le_pow hi
   rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
-    sup_eq_left.mpr Pe_le_Pi] at hx 
+    sup_eq_left.mpr Pe_le_Pi] at hx
   suffices hx' : x ∈ Ideal.span {a} ⊔ P ^ (i + 1)
   · obtain ⟨y', hy', z, hz, rfl⟩ := submodule.mem_sup.mp hx'
     obtain ⟨y, rfl⟩ := ideal.mem_span_singleton.mp hy'
@@ -686,10 +686,10 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
   rw [sup_eq_prod_inf_factors _ (pow_ne_zero _ hP0), normalized_factors_pow,
     normalized_factors_irreducible ((Ideal.prime_iff_isPrime hP0).mpr hP).Irreducible, normalize_eq,
     Multiset.nsmul_singleton, Multiset.inter_replicate, Multiset.prod_replicate]
-  rw [← Submodule.span_singleton_le_iff_mem, Ideal.submodule_span_eq] at a_mem a_not_mem 
+  rw [← Submodule.span_singleton_le_iff_mem, Ideal.submodule_span_eq] at a_mem a_not_mem
   rwa [Ideal.count_normalizedFactors_eq a_mem a_not_mem, min_eq_left i.le_succ]
   · intro ha
-    rw [ideal.span_singleton_eq_bot.mp ha] at a_not_mem 
+    rw [ideal.span_singleton_eq_bot.mp ha] at a_not_mem
     have := (P ^ (i + 1)).zero_mem
     contradiction
 #align ideal.quotient_to_quotient_range_pow_quot_succ_surjective Ideal.quotientToQuotientRangePowQuotSucc_surjective
@@ -756,7 +756,7 @@ theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMa
   by
   letI : NeZero e := ⟨he⟩
   have := rank_pow_quot f p P hP0 0 (Nat.zero_le e)
-  rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this 
+  rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this
   exact (rank_top (R ⧸ p) _).symm.trans this
 #align ideal.rank_prime_pow_ramification_idx Ideal.rank_prime_pow_ramificationIdx
 -/

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

@@ -871,7 +871,7 @@ instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) :
     FiniteDimensional (R ⧸ p) (S ⧸ (P : Ideal S) ^ ramificationIdx (algebraMap R S) p P) :=
   by
-  refine' FiniteDimensional.finiteDimensional_of_finrank _
+  refine' FiniteDimensional.of_finrank_pos _
   rw [pos_iff_ne_zero, factors.finrank_pow_ramification_idx]
   exact mul_ne_zero (factors.ramification_idx_ne_zero p P) (factors.inertia_deg_ne_zero p P)
 #align ideal.factors.finite_dimensional_quotient_pow Ideal.Factors.finiteDimensional_quotient_pow

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

@@ -704,7 +704,7 @@ noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekin
   by
   choose a a_mem a_not_mem using
     SetLike.exists_of_lt
-      (Ideal.strictAnti_pow P hP (Ideal.IsPrime.ne_top inferInstance) (le_refl i.succ))
+      (Ideal.pow_right_strictAnti P hP (Ideal.IsPrime.ne_top inferInstance) (le_refl i.succ))
   refine' (LinearEquiv.ofBijective _ ⟨_, _⟩).symm
   · exact quotient_to_quotient_range_pow_quot_succ f p P a_mem
   · exact quotient_to_quotient_range_pow_quot_succ_injective f p P hi a_mem a_not_mem

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -307,7 +307,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   -- then we can find a linear dependence with coefficients `I.quotient.mk g'` in `R/I`,
   -- where `I = ker (algebra_map R S)`.
   -- We make use of the same principle but stay in `R` everywhere.
-  simp only [linearIndependent_iff', not_forall] at hb ⊢
+  simp only [linearIndependent_iff', Classical.not_forall] at hb ⊢
   obtain ⟨s, g, eq, j', hj's, hj'g⟩ := hb
   use s
   obtain ⟨a, hag, j, hjs, hgI⟩ := Ideal.exist_integer_multiples_not_mem hRS s g hj's hj'g

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

@@ -324,11 +324,11 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   refine' ⟨fun i => algebraMap R S (g' i), _, j, hjs, hgI⟩
   have eq : f (∑ i in s, g' i • b i) = 0 :=
     by
-    rw [LinearMap.map_sum, ← smul_zero a, ← Eq, Finset.smul_sum, Finset.sum_congr rfl]
+    rw [map_sum, ← smul_zero a, ← Eq, Finset.smul_sum, Finset.sum_congr rfl]
     intro i hi
     rw [LinearMap.map_smul, ← IsScalarTower.algebraMap_smul K, hg' i hi, ← smul_assoc, smul_eq_mul]
     infer_instance
-  simp only [IsScalarTower.algebraMap_smul, ← LinearMap.map_smul, ← LinearMap.map_sum,
+  simp only [IsScalarTower.algebraMap_smul, ← LinearMap.map_smul, ← map_sum,
     (f.map_eq_zero_iff hf).mp Eq, LinearMap.map_zero]
 #align ideal.finrank_quotient_map.linear_independent_of_nontrivial Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.LinearAlgebra.FreeModule.Finite.Rank
-import Mathbin.RingTheory.DedekindDomain.Ideal
+import LinearAlgebra.FreeModule.Finite.Rank
+import RingTheory.DedekindDomain.Ideal
 
 #align_import number_theory.ramification_inertia from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 

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

@@ -521,7 +521,7 @@ local notation "e" => ramificationIdx f p P
 /-- `R / p` has a canonical map to `S / (P ^ e)`, where `e` is the ramification index
 of `P` over `p`. -/
 noncomputable instance Quotient.algebraQuotientPowRamificationIdx : Algebra (R ⧸ p) (S ⧸ P ^ e) :=
-  Quotient.algebraQuotientOfLeComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)
+  Quotient.algebraQuotientOfLEComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)
 #align ideal.quotient.algebra_quotient_pow_ramification_idx Ideal.Quotient.algebraQuotientPowRamificationIdx
 -/
 
@@ -541,7 +541,7 @@ variable [hfp : NeZero (ramificationIdx f p P)]
 This can't be an instance since the map `f : R → S` is generally not inferrable.
 -/
 def Quotient.algebraQuotientOfRamificationIdxNeZero : Algebra (R ⧸ p) (S ⧸ P) :=
-  Quotient.algebraQuotientOfLeComap (le_comap_of_ramificationIdx_ne_zero hfp.out)
+  Quotient.algebraQuotientOfLEComap (le_comap_of_ramificationIdx_ne_zero hfp.out)
 #align ideal.quotient.algebra_quotient_of_ramification_idx_ne_zero Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -722,7 +722,7 @@ theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsP
         Module.rank (R ⧸ p) (Ideal.map (P ^ e).Quotient.mk (P ^ (i + 1))) :=
   by
   letI : Field (R ⧸ p) := Ideal.Quotient.field _
-  rw [rank_eq_of_injective _ (pow_quot_succ_inclusion_injective f p P i),
+  rw [rank_range_of_injective _ (pow_quot_succ_inclusion_injective f p P i),
     (quotient_range_pow_quot_succ_inclusion_equiv f p P hP0 hi).symm.rank_eq]
   exact (rank_quotient_add_rank (LinearMap.range (pow_quot_succ_inclusion f p P i))).symm
 #align ideal.rank_pow_quot_aux Ideal.rank_pow_quot_aux

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.ramification_inertia
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FreeModule.Finite.Rank
 import Mathbin.RingTheory.DedekindDomain.Ideal
 
+#align_import number_theory.ramification_inertia from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # Ramification index and inertia degree
 

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

@@ -81,16 +81,21 @@ noncomputable def ramificationIdx : ℕ :=
 
 variable {f p P}
 
+#print Ideal.ramificationIdx_eq_find /-
 theorem ramificationIdx_eq_find (h : ∃ n, ∀ k, map f p ≤ P ^ k → k ≤ n) :
     ramificationIdx f p P = Nat.find h :=
   Nat.sSup_def h
 #align ideal.ramification_idx_eq_find Ideal.ramificationIdx_eq_find
+-/
 
+#print Ideal.ramificationIdx_eq_zero /-
 theorem ramificationIdx_eq_zero (h : ∀ n : ℕ, ∃ k, map f p ≤ P ^ k ∧ n < k) :
     ramificationIdx f p P = 0 :=
   dif_neg (by push_neg <;> exact h)
 #align ideal.ramification_idx_eq_zero Ideal.ramificationIdx_eq_zero
+-/
 
+#print Ideal.ramificationIdx_spec /-
 theorem ramificationIdx_spec {n : ℕ} (hle : map f p ≤ P ^ n) (hgt : ¬map f p ≤ P ^ (n + 1)) :
     ramificationIdx f p P = n :=
   by
@@ -103,7 +108,9 @@ theorem ramificationIdx_spec {n : ℕ} (hle : map f p ≤ P ^ n) (hgt : ¬map f
     obtain this' := Nat.find_spec ⟨n, this⟩
     exact h.not_le (this' _ hle)
 #align ideal.ramification_idx_spec Ideal.ramificationIdx_spec
+-/
 
+#print Ideal.ramificationIdx_lt /-
 theorem ramificationIdx_lt {n : ℕ} (hgt : ¬map f p ≤ P ^ n) : ramificationIdx f p P < n :=
   by
   cases n
@@ -116,44 +123,60 @@ theorem ramificationIdx_lt {n : ℕ} (hgt : ¬map f p ≤ P ^ n) : ramificationI
   rw [ramification_idx_eq_find ⟨n, this⟩]
   exact Nat.find_min' ⟨n, this⟩ this
 #align ideal.ramification_idx_lt Ideal.ramificationIdx_lt
+-/
 
+#print Ideal.ramificationIdx_bot /-
 @[simp]
 theorem ramificationIdx_bot : ramificationIdx f ⊥ P = 0 :=
   dif_neg <| not_exists.mpr fun n hn => n.lt_succ_self.not_le (hn _ (by simp))
 #align ideal.ramification_idx_bot Ideal.ramificationIdx_bot
+-/
 
+#print Ideal.ramificationIdx_of_not_le /-
 @[simp]
 theorem ramificationIdx_of_not_le (h : ¬map f p ≤ P) : ramificationIdx f p P = 0 :=
   ramificationIdx_spec (by simp) (by simpa using h)
 #align ideal.ramification_idx_of_not_le Ideal.ramificationIdx_of_not_le
+-/
 
+#print Ideal.ramificationIdx_ne_zero /-
 theorem ramificationIdx_ne_zero {e : ℕ} (he : e ≠ 0) (hle : map f p ≤ P ^ e)
     (hnle : ¬map f p ≤ P ^ (e + 1)) : ramificationIdx f p P ≠ 0 := by
   rwa [ramification_idx_spec hle hnle]
 #align ideal.ramification_idx_ne_zero Ideal.ramificationIdx_ne_zero
+-/
 
+#print Ideal.le_pow_of_le_ramificationIdx /-
 theorem le_pow_of_le_ramificationIdx {n : ℕ} (hn : n ≤ ramificationIdx f p P) : map f p ≤ P ^ n :=
   by
   contrapose! hn
   exact ramification_idx_lt hn
 #align ideal.le_pow_of_le_ramification_idx Ideal.le_pow_of_le_ramificationIdx
+-/
 
+#print Ideal.le_pow_ramificationIdx /-
 theorem le_pow_ramificationIdx : map f p ≤ P ^ ramificationIdx f p P :=
   le_pow_of_le_ramificationIdx (le_refl _)
 #align ideal.le_pow_ramification_idx Ideal.le_pow_ramificationIdx
+-/
 
+#print Ideal.le_comap_pow_ramificationIdx /-
 theorem le_comap_pow_ramificationIdx : p ≤ comap f (P ^ ramificationIdx f p P) :=
   map_le_iff_le_comap.mp le_pow_ramificationIdx
 #align ideal.le_comap_pow_ramification_idx Ideal.le_comap_pow_ramificationIdx
+-/
 
+#print Ideal.le_comap_of_ramificationIdx_ne_zero /-
 theorem le_comap_of_ramificationIdx_ne_zero (h : ramificationIdx f p P ≠ 0) : p ≤ comap f P :=
   Ideal.map_le_iff_le_comap.mp <| le_pow_ramificationIdx.trans <| Ideal.pow_le_self <| h
 #align ideal.le_comap_of_ramification_idx_ne_zero Ideal.le_comap_of_ramificationIdx_ne_zero
+-/
 
 namespace IsDedekindDomain
 
 variable [IsDomain S] [IsDedekindDomain S]
 
+#print Ideal.IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count /-
 theorem ramificationIdx_eq_normalizedFactors_count (hp0 : map f p ≠ ⊥) (hP : P.IsPrime)
     (hP0 : P ≠ ⊥) : ramificationIdx f p P = (normalizedFactors (map f p)).count P :=
   by
@@ -164,13 +187,17 @@ theorem ramificationIdx_eq_normalizedFactors_count (hp0 : map f p ≠ ⊥) (hP :
       Multiset.nsmul_singleton, ← Multiset.le_count_iff_replicate_le]
   · exact (Nat.lt_succ_self _).not_le
 #align ideal.is_dedekind_domain.ramification_idx_eq_normalized_factors_count Ideal.IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count
+-/
 
+#print Ideal.IsDedekindDomain.ramificationIdx_eq_factors_count /-
 theorem ramificationIdx_eq_factors_count (hp0 : map f p ≠ ⊥) (hP : P.IsPrime) (hP0 : P ≠ ⊥) :
     ramificationIdx f p P = (factors (map f p)).count P := by
   rw [is_dedekind_domain.ramification_idx_eq_normalized_factors_count hp0 hP hP0,
     factors_eq_normalized_factors]
 #align ideal.is_dedekind_domain.ramification_idx_eq_factors_count Ideal.IsDedekindDomain.ramificationIdx_eq_factors_count
+-/
 
+#print Ideal.IsDedekindDomain.ramificationIdx_ne_zero /-
 theorem ramificationIdx_ne_zero (hp0 : map f p ≠ ⊥) (hP : P.IsPrime) (le : map f p ≤ P) :
     ramificationIdx f p P ≠ 0 :=
   by
@@ -184,6 +211,7 @@ theorem ramificationIdx_ne_zero (hp0 : map f p ≠ ⊥) (hP : P.IsPrime) (le : m
     exists_mem_normalized_factors_of_dvd hp0 hPirr (ideal.dvd_iff_le.mpr le)
   rwa [Multiset.count_ne_zero, associated_iff_eq.mp P'_eq]
 #align ideal.is_dedekind_domain.ramification_idx_ne_zero Ideal.IsDedekindDomain.ramificationIdx_ne_zero
+-/
 
 end IsDedekindDomain
 
@@ -264,8 +292,7 @@ variable [AddCommGroup V''] [Module R V'']
 
 variable (K)
 
-include hRK
-
+#print Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial /-
 /-- Let `V` be a vector space over `K = Frac(R)`, `S / R` a ring extension
 and `V'` a module over `S`. If `b`, in the intersection `V''` of `V` and `V'`,
 is linear independent over `S` in `V'`, then it is linear independent over `R` in `V`.
@@ -307,13 +334,13 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   simp only [IsScalarTower.algebraMap_smul, ← LinearMap.map_smul, ← LinearMap.map_sum,
     (f.map_eq_zero_iff hf).mp Eq, LinearMap.map_zero]
 #align ideal.finrank_quotient_map.linear_independent_of_nontrivial Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial
+-/
 
 open scoped Matrix
 
 variable {K}
 
-omit hRK
-
+#print Ideal.FinrankQuotientMap.span_eq_top /-
 /-- If `b` mod `p` spans `S/p` as `R/p`-space, then `b` itself spans `Frac(S)` as `K`-space.
 
 Here,
@@ -428,11 +455,11 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
     intro x
     exact IsIntegral.isAlgebraic _ (isIntegral_of_noetherian inferInstance _)
 #align ideal.finrank_quotient_map.span_eq_top Ideal.FinrankQuotientMap.span_eq_top
-
-include hRK
+-/
 
 variable (K L)
 
+#print Ideal.finrank_quotient_map /-
 /-- If `p` is a maximal ideal of `R`, and `S` is the integral closure of `R` in `L`,
 then the dimension `[S/pS : R/p]` is equal to `[Frac(S) : Frac(R)]`. -/
 theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Algebra K L]
@@ -485,12 +512,12 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
       exact hp.ne_top
     · exact IsFractionRing.injective S L
 #align ideal.finrank_quotient_map Ideal.finrank_quotient_map
+-/
 
 end FinrankQuotientMap
 
 section FactLeComap
 
--- mathport name: expre
 local notation "e" => ramificationIdx f p P
 
 #print Ideal.Quotient.algebraQuotientPowRamificationIdx /-
@@ -501,16 +528,16 @@ noncomputable instance Quotient.algebraQuotientPowRamificationIdx : Algebra (R 
 #align ideal.quotient.algebra_quotient_pow_ramification_idx Ideal.Quotient.algebraQuotientPowRamificationIdx
 -/
 
+#print Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx /-
 @[simp]
 theorem Quotient.algebraMap_quotient_pow_ramificationIdx (x : R) :
     algebraMap (R ⧸ p) (S ⧸ P ^ e) (Ideal.Quotient.mk p x) = Ideal.Quotient.mk _ (f x) :=
   rfl
 #align ideal.quotient.algebra_map_quotient_pow_ramification_idx Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx
+-/
 
 variable [hfp : NeZero (ramificationIdx f p P)]
 
-include hfp
-
 #print Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero /-
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`.
 
@@ -524,14 +551,15 @@ def Quotient.algebraQuotientOfRamificationIdxNeZero : Algebra (R ⧸ p) (S ⧸ P
 -- In this file, the value for `f` can be inferred.
 attribute [local instance] Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero
 
+#print Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero /-
 @[simp]
 theorem Quotient.algebraMap_quotient_of_ramificationIdx_neZero (x : R) :
     algebraMap (R ⧸ p) (S ⧸ P) (Ideal.Quotient.mk p x) = Ideal.Quotient.mk _ (f x) :=
   rfl
 #align ideal.quotient.algebra_map_quotient_of_ramification_idx_ne_zero Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero
+-/
 
-omit hfp
-
+#print Ideal.powQuotSuccInclusion /-
 /-- The inclusion `(P^(i + 1) / P^e) ⊂ (P^i / P^e)`. -/
 @[simps]
 def powQuotSuccInclusion (i : ℕ) :
@@ -541,7 +569,9 @@ def powQuotSuccInclusion (i : ℕ) :
   map_add' x y := rfl
   map_smul' c x := rfl
 #align ideal.pow_quot_succ_inclusion Ideal.powQuotSuccInclusion
+-/
 
+#print Ideal.powQuotSuccInclusion_injective /-
 theorem powQuotSuccInclusion_injective (i : ℕ) :
     Function.Injective (powQuotSuccInclusion f p P i) :=
   by
@@ -550,6 +580,7 @@ theorem powQuotSuccInclusion_injective (i : ℕ) :
   rw [Subtype.ext_iff] at hx0 ⊢
   rwa [pow_quot_succ_inclusion_apply_coe] at hx0 
 #align ideal.pow_quot_succ_inclusion_injective Ideal.powQuotSuccInclusion_injective
+-/
 
 #print Ideal.quotientToQuotientRangePowQuotSuccAux /-
 /-- `S ⧸ P` embeds into the quotient by `P^(i+1) ⧸ P^e` as a subspace of `P^i ⧸ P^e`.
@@ -577,8 +608,6 @@ theorem quotientToQuotientRangePowQuotSuccAux_mk {i : ℕ} {a : S} (a_mem : a 
 #align ideal.quotient_to_quotient_range_pow_quot_succ_aux_mk Ideal.quotientToQuotientRangePowQuotSuccAux_mk
 -/
 
-include hfp
-
 #print Ideal.quotientToQuotientRangePowQuotSucc /-
 /-- `S ⧸ P` embeds into the quotient by `P^(i+1) ⧸ P^e` as a subspace of `P^i ⧸ P^e`. -/
 noncomputable def quotientToQuotientRangePowQuotSucc {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) :
@@ -635,6 +664,7 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
 #align ideal.quotient_to_quotient_range_pow_quot_succ_injective Ideal.quotientToQuotientRangePowQuotSucc_injective
 -/
 
+#print Ideal.quotientToQuotientRangePowQuotSucc_surjective /-
 theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDomain S]
     (hP0 : P ≠ ⊥) [hP : P.IsPrime] {i : ℕ} (hi : i < e) {a : S} (a_mem : a ∈ P ^ i)
     (a_not_mem : a ∉ P ^ (i + 1)) :
@@ -666,7 +696,9 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
     have := (P ^ (i + 1)).zero_mem
     contradiction
 #align ideal.quotient_to_quotient_range_pow_quot_succ_surjective Ideal.quotientToQuotientRangePowQuotSucc_surjective
+-/
 
+#print Ideal.quotientRangePowQuotSuccInclusionEquiv /-
 /-- Quotienting `P^i / P^e` by its subspace `P^(i+1) ⧸ P^e` is
 `R ⧸ p`-linearly isomorphic to `S ⧸ P`. -/
 noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekindDomain S]
@@ -681,7 +713,9 @@ noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekin
   · exact quotient_to_quotient_range_pow_quot_succ_injective f p P hi a_mem a_not_mem
   · exact quotient_to_quotient_range_pow_quot_succ_surjective f p P hP hi a_mem a_not_mem
 #align ideal.quotient_range_pow_quot_succ_inclusion_equiv Ideal.quotientRangePowQuotSuccInclusionEquiv
+-/
 
+#print Ideal.rank_pow_quot_aux /-
 /-- Since the inclusion `(P^(i + 1) / P^e) ⊂ (P^i / P^e)` has a kernel isomorphic to `P / S`,
 `[P^i / P^e : R / p] = [P^(i+1) / P^e : R / p] + [P / S : R / p]` -/
 theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
@@ -695,7 +729,9 @@ theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsP
     (quotient_range_pow_quot_succ_inclusion_equiv f p P hP0 hi).symm.rank_eq]
   exact (rank_quotient_add_rank (LinearMap.range (pow_quot_succ_inclusion f p P i))).symm
 #align ideal.rank_pow_quot_aux Ideal.rank_pow_quot_aux
+-/
 
+#print Ideal.rank_pow_quot /-
 theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
     (i : ℕ) (hi : i ≤ e) :
     Module.rank (R ⧸ p) (Ideal.map (P ^ e).Quotient.mk (P ^ i)) =
@@ -708,9 +744,9 @@ theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime
   · rw [Nat.sub_self, zero_nsmul, map_quotient_self]
     exact rank_bot (R ⧸ p) (S ⧸ P ^ e)
 #align ideal.rank_pow_quot Ideal.rank_pow_quot
+-/
 
-omit hfp
-
+#print Ideal.rank_prime_pow_ramificationIdx /-
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]` is equal to `e * [S/P : R/p]`. -/
 theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime]
@@ -726,7 +762,9 @@ theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMa
   rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this 
   exact (rank_top (R ⧸ p) _).symm.trans this
 #align ideal.rank_prime_pow_ramification_idx Ideal.rank_prime_pow_ramificationIdx
+-/
 
+#print Ideal.finrank_prime_pow_ramificationIdx /-
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]`, as a natural number, is equal to `e * [S/P : R/p]`. -/
 theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0 : P ≠ ⊥)
@@ -750,6 +788,7 @@ theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0
   simp only [finrank_of_infinite_dimensional hP, finrank_of_infinite_dimensional hPe,
     MulZeroClass.mul_zero]
 #align ideal.finrank_prime_pow_ramification_idx Ideal.finrank_prime_pow_ramificationIdx
+-/
 
 end FactLeComap
 
@@ -843,6 +882,7 @@ instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]
 
 universe w
 
+#print Ideal.Factors.piQuotientEquiv /-
 /-- **Chinese remainder theorem** for a ring of integers: if the prime ideal `p : ideal R`
 factors in `S` as `∏ i, P i ^ e i`, then `S ⧸ I` factors as `Π i, R ⧸ (P i ^ e i)`. -/
 noncomputable def Factors.piQuotientEquiv (p : Ideal R) (hp : map (algebraMap R S) p ≠ ⊥) :
@@ -858,22 +898,28 @@ noncomputable def Factors.piQuotientEquiv (p : Ideal R) (hp : map (algebraMap R
         rw [is_dedekind_domain.ramification_idx_eq_factors_count hp (factors.is_prime p P)
             (factors.ne_bot p P)]
 #align ideal.factors.pi_quotient_equiv Ideal.Factors.piQuotientEquiv
+-/
 
+#print Ideal.Factors.piQuotientEquiv_mk /-
 @[simp]
 theorem Factors.piQuotientEquiv_mk (p : Ideal R) (hp : map (algebraMap R S) p ≠ ⊥) (x : S) :
     Factors.piQuotientEquiv p hp (Ideal.Quotient.mk _ x) = fun P => Ideal.Quotient.mk _ x :=
   rfl
 #align ideal.factors.pi_quotient_equiv_mk Ideal.Factors.piQuotientEquiv_mk
+-/
 
+#print Ideal.Factors.piQuotientEquiv_map /-
 @[simp]
 theorem Factors.piQuotientEquiv_map (p : Ideal R) (hp : map (algebraMap R S) p ≠ ⊥) (x : R) :
     Factors.piQuotientEquiv p hp (algebraMap _ _ x) = fun P =>
       Ideal.Quotient.mk _ (algebraMap _ _ x) :=
   rfl
 #align ideal.factors.pi_quotient_equiv_map Ideal.Factors.piQuotientEquiv_map
+-/
 
 variable (S)
 
+#print Ideal.Factors.piQuotientLinearEquiv /-
 /-- **Chinese remainder theorem** for a ring of integers: if the prime ideal `p : ideal R`
 factors in `S` as `∏ i, P i ^ e i`,
 then `S ⧸ I` factors `R ⧸ I`-linearly as `Π i, R ⧸ (P i ^ e i)`. -/
@@ -890,11 +936,13 @@ noncomputable def Factors.piQuotientLinearEquiv (p : Ideal R) (hp : map (algebra
         Ideal.Quotient.mk_eq_mk, Algebra.smul_def, _root_.map_mul, RingHomCompTriple.comp_apply]
       congr }
 #align ideal.factors.pi_quotient_linear_equiv Ideal.Factors.piQuotientLinearEquiv
+-/
 
 variable {S}
 
 open scoped BigOperators
 
+#print Ideal.sum_ramification_inertia /-
 /-- The **fundamental identity** of ramification index `e` and inertia degree `f`:
 for `P` ranging over the primes lying over `p`, `∑ P, e P * f P = [Frac(S) : Frac(R)]`;
 here `S` is a finite `R`-module (and thus `Frac(S) : Frac(R)` is a finite extension) and `p`
@@ -938,6 +986,7 @@ theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
       le_bot_iff]
   · exact finrank_quotient_map p K L
 #align ideal.sum_ramification_inertia Ideal.sum_ramification_inertia
+-/
 
 end FactorsMap
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -347,7 +347,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
         rw [Submodule.map_smul'', Submodule.map_top, M.range_mkq]
       _ = ⊤ := by rw [Ideal.smul_top_eq_map, (Submodule.map_mkQ_eq_top M _).mpr hb']
   -- we can write the elements of `a` as `p`-linear combinations of other elements of `a`.
-  have exists_sum : ∀ x : S ⧸ M, ∃ a' : Fin n → R, (∀ i, a' i ∈ p) ∧ (∑ i, a' i • a i) = x :=
+  have exists_sum : ∀ x : S ⧸ M, ∃ a' : Fin n → R, (∀ i, a' i ∈ p) ∧ ∑ i, a' i • a i = x :=
     by
     intro x
     obtain ⟨a'', ha'', hx⟩ := (Submodule.mem_ideal_smul_span_iff_exists_sum p a x).1 _
@@ -360,7 +360,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   -- This gives us a(n invertible) matrix `A` such that `det A ∈ (M = span R b)`,
   let A : Matrix (Fin n) (Fin n) R := A' - 1
   let B := A.adjugate
-  have A_smul : ∀ i, (∑ j, A i j • a j) = 0 := by
+  have A_smul : ∀ i, ∑ j, A i j • a j = 0 := by
     intros
     simp only [A, Pi.sub_apply, sub_smul, Finset.sum_sub_distrib, hA', Matrix.one_apply, ite_smul,
       one_smul, zero_smul, Finset.sum_ite_eq, Finset.mem_univ, if_true, sub_self]
@@ -904,8 +904,8 @@ theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
     [IsDedekindDomain R] [Algebra R K] [IsFractionRing R K] [Algebra S L] [IsFractionRing S L]
     [Algebra K L] [Algebra R L] [IsScalarTower R S L] [IsScalarTower R K L] [IsNoetherian R S]
     [IsIntegralClosure S R L] [p.IsMaximal] (hp0 : p ≠ ⊥) :
-    (∑ P in (factors (map (algebraMap R S) p)).toFinset,
-        ramificationIdx (algebraMap R S) p P * inertiaDeg (algebraMap R S) p P) =
+    ∑ P in (factors (map (algebraMap R S) p)).toFinset,
+        ramificationIdx (algebraMap R S) p P * inertiaDeg (algebraMap R S) p P =
       finrank K L :=
   by
   set e := ramification_idx (algebraMap R S) p
@@ -920,7 +920,7 @@ theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
     rw [← RingHom.coe_comp, ← IsScalarTower.algebraMap_eq]
     exact inj_RL
   calc
-    (∑ P in (factors (map (algebraMap R S) p)).toFinset, e P * f P) =
+    ∑ P in (factors (map (algebraMap R S) p)).toFinset, e P * f P =
         ∑ P in (factors (map (algebraMap R S) p)).toFinset.attach,
           finrank (R ⧸ p) (S ⧸ (P : Ideal S) ^ e P) :=
       _

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.ramification_inertia
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.DedekindDomain.Ideal
 /-!
 # Ramification index and inertia degree
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given `P : ideal S` lying over `p : ideal R` for the ring extension `f : R →+* S`
 (assuming `P` and `p` are prime or maximal where needed),
 the **ramification index** `ideal.ramification_idx f p P` is the multiplicity of `P` in `map f p`,

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

@@ -343,7 +343,6 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       p • ⊤ = Submodule.map M.mkq (p • ⊤) := by
         rw [Submodule.map_smul'', Submodule.map_top, M.range_mkq]
       _ = ⊤ := by rw [Ideal.smul_top_eq_map, (Submodule.map_mkQ_eq_top M _).mpr hb']
-      
   -- we can write the elements of `a` as `p`-linear combinations of other elements of `a`.
   have exists_sum : ∀ x : S ⧸ M, ∃ a' : Fin n → R, (∀ i, a' i ∈ p) ∧ (∑ i, a' i • a i) = x :=
     by
@@ -369,7 +368,6 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       A.det • a i = ∑ j, (B ⬝ A) i j • a j := _
       _ = ∑ k, B i k • ∑ j, A k j • a j := _
       _ = 0 := Finset.sum_eq_zero fun k _ => _
-      
     ·
       simp only [Matrix.adjugate_mul, Pi.smul_apply, Matrix.one_apply, mul_ite, ite_smul,
         smul_eq_mul, mul_one, MulZeroClass.mul_zero, one_smul, zero_smul, Finset.sum_ite_eq,
@@ -393,8 +391,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
     top_le_iff.mp
       (calc
         ⊤ = (Ideal.span {algebraMap R L A.det}).restrictScalars K := _
-        _ ≤ Submodule.span K (algebraMap S L '' b) := _
-        )
+        _ ≤ Submodule.span K (algebraMap S L '' b) := _)
   -- Because `det A ≠ 0`, we have `span L {det A} = ⊤`.
   · rw [eq_comm, Submodule.restrictScalars_eq_top_iff, Ideal.span_singleton_eq_top]
     refine'
@@ -413,7 +410,6 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       _ = Matrix.det (-1 : Matrix (Fin n) (Fin n) (R ⧸ p)) := _
       _ = (-1 : R ⧸ p) ^ n := by rw [Matrix.det_neg, Fintype.card_fin, Matrix.det_one, mul_one]
       _ ≠ 0 := IsUnit.ne_zero (is_unit_one.neg.pow _)
-      
     · refine' congr_arg Matrix.det (Matrix.ext fun i j => _)
       rw [map_sub, RingHom.mapMatrix_apply, map_one]
       rfl
@@ -931,7 +927,6 @@ theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
       (finrank_pi_fintype (R ⧸ p)).symm
     _ = finrank (R ⧸ p) (S ⧸ map (algebraMap R S) p) := _
     _ = finrank K L := _
-    
   · rw [← Finset.sum_attach]
     refine' Finset.sum_congr rfl fun P _ => _
     rw [factors.finrank_pow_ramification_idx]

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -62,6 +62,7 @@ section DecEq
 
 open scoped Classical
 
+#print Ideal.ramificationIdx /-
 /-- The ramification index of `P` over `p` is the largest exponent `n` such that
 `p` is contained in `P^n`.
 
@@ -73,6 +74,7 @@ defined to be 0.
 noncomputable def ramificationIdx : ℕ :=
   sSup {n | map f p ≤ P ^ n}
 #align ideal.ramification_idx Ideal.ramificationIdx
+-/
 
 variable {f p P}
 
@@ -186,6 +188,7 @@ variable (f p P)
 
 attribute [local instance] Ideal.Quotient.field
 
+#print Ideal.inertiaDeg /-
 /-- The inertia degree of `P : ideal S` lying over `p : ideal R` is the degree of the
 extension `(S / P) : (R / p)`.
 
@@ -203,7 +206,9 @@ noncomputable def inertiaDeg [hp : p.IsMaximal] : ℕ :=
             Quotient.eq_zero_iff_mem.mpr <| mem_comap.mp <| hPp.symm ▸ ha
   else 0
 #align ideal.inertia_deg Ideal.inertiaDeg
+-/
 
+#print Ideal.inertiaDeg_of_subsingleton /-
 -- Useful for the `nontriviality` tactic using `comap_eq_of_scalar_tower_quotient`.
 @[simp]
 theorem inertiaDeg_of_subsingleton [hp : p.IsMaximal] [hQ : Subsingleton (S ⧸ P)] :
@@ -213,7 +218,9 @@ theorem inertiaDeg_of_subsingleton [hp : p.IsMaximal] [hQ : Subsingleton (S ⧸
   subst this
   exact dif_neg fun h => hp.ne_top <| h.symm.trans comap_top
 #align ideal.inertia_deg_of_subsingleton Ideal.inertiaDeg_of_subsingleton
+-/
 
+#print Ideal.inertiaDeg_algebraMap /-
 @[simp]
 theorem inertiaDeg_algebraMap [Algebra R S] [Algebra (R ⧸ p) (S ⧸ P)]
     [IsScalarTower R (R ⧸ p) (S ⧸ P)] [hp : p.IsMaximal] :
@@ -228,6 +235,7 @@ theorem inertiaDeg_algebraMap [Algebra R S] [Algebra (R ⧸ p) (S ⧸ P)]
   rw [Ideal.Quotient.lift_mk, ← Ideal.Quotient.algebraMap_eq, ← IsScalarTower.algebraMap_eq, ←
     Ideal.Quotient.algebraMap_eq, ← IsScalarTower.algebraMap_apply]
 #align ideal.inertia_deg_algebra_map Ideal.inertiaDeg_algebraMap
+-/
 
 end DecEq
 
@@ -486,11 +494,13 @@ section FactLeComap
 -- mathport name: expre
 local notation "e" => ramificationIdx f p P
 
+#print Ideal.Quotient.algebraQuotientPowRamificationIdx /-
 /-- `R / p` has a canonical map to `S / (P ^ e)`, where `e` is the ramification index
 of `P` over `p`. -/
 noncomputable instance Quotient.algebraQuotientPowRamificationIdx : Algebra (R ⧸ p) (S ⧸ P ^ e) :=
   Quotient.algebraQuotientOfLeComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)
 #align ideal.quotient.algebra_quotient_pow_ramification_idx Ideal.Quotient.algebraQuotientPowRamificationIdx
+-/
 
 @[simp]
 theorem Quotient.algebraMap_quotient_pow_ramificationIdx (x : R) :
@@ -502,6 +512,7 @@ variable [hfp : NeZero (ramificationIdx f p P)]
 
 include hfp
 
+#print Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero /-
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`.
 
 This can't be an instance since the map `f : R → S` is generally not inferrable.
@@ -509,6 +520,7 @@ This can't be an instance since the map `f : R → S` is generally not inferrabl
 def Quotient.algebraQuotientOfRamificationIdxNeZero : Algebra (R ⧸ p) (S ⧸ P) :=
   Quotient.algebraQuotientOfLeComap (le_comap_of_ramificationIdx_ne_zero hfp.out)
 #align ideal.quotient.algebra_quotient_of_ramification_idx_ne_zero Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero
+-/
 
 -- In this file, the value for `f` can be inferred.
 attribute [local instance] Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero
@@ -540,6 +552,7 @@ theorem powQuotSuccInclusion_injective (i : ℕ) :
   rwa [pow_quot_succ_inclusion_apply_coe] at hx0 
 #align ideal.pow_quot_succ_inclusion_injective Ideal.powQuotSuccInclusion_injective
 
+#print Ideal.quotientToQuotientRangePowQuotSuccAux /-
 /-- `S ⧸ P` embeds into the quotient by `P^(i+1) ⧸ P^e` as a subspace of `P^i ⧸ P^e`.
 See `quotient_to_quotient_range_pow_quot_succ` for this as a linear map,
 and `quotient_range_pow_quot_succ_inclusion_equiv` for this as a linear equivalence.
@@ -555,15 +568,19 @@ noncomputable def quotientToQuotientRangePowQuotSuccAux {i : ℕ} {a : S} (a_mem
     rw [pow_quot_succ_inclusion_apply_coe, Subtype.coe_mk, Submodule.coe_sub, Subtype.coe_mk,
       Subtype.coe_mk, _root_.map_mul, map_sub, sub_mul]
 #align ideal.quotient_to_quotient_range_pow_quot_succ_aux Ideal.quotientToQuotientRangePowQuotSuccAux
+-/
 
+#print Ideal.quotientToQuotientRangePowQuotSuccAux_mk /-
 theorem quotientToQuotientRangePowQuotSuccAux_mk {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) (x : S) :
     quotientToQuotientRangePowQuotSuccAux f p P a_mem (Submodule.Quotient.mk x) =
       Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩ :=
   by apply Quotient.map'_mk''
 #align ideal.quotient_to_quotient_range_pow_quot_succ_aux_mk Ideal.quotientToQuotientRangePowQuotSuccAux_mk
+-/
 
 include hfp
 
+#print Ideal.quotientToQuotientRangePowQuotSucc /-
 /-- `S ⧸ P` embeds into the quotient by `P^(i+1) ⧸ P^e` as a subspace of `P^i ⧸ P^e`. -/
 noncomputable def quotientToQuotientRangePowQuotSucc {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) :
     S ⧸ P →ₗ[R ⧸ p] (P ^ i).map (P ^ e).Quotient.mk ⧸ (powQuotSuccInclusion f p P i).range
@@ -586,13 +603,17 @@ noncomputable def quotientToQuotientRangePowQuotSucc {i : ℕ} {a : S} (a_mem :
       Ideal.Quotient.mk_eq_mk, Submodule.coe_smul_of_tower,
       Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx]
 #align ideal.quotient_to_quotient_range_pow_quot_succ Ideal.quotientToQuotientRangePowQuotSucc
+-/
 
+#print Ideal.quotientToQuotientRangePowQuotSucc_mk /-
 theorem quotientToQuotientRangePowQuotSucc_mk {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) (x : S) :
     quotientToQuotientRangePowQuotSucc f p P a_mem (Submodule.Quotient.mk x) =
       Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩ :=
   quotientToQuotientRangePowQuotSuccAux_mk f p P a_mem x
 #align ideal.quotient_to_quotient_range_pow_quot_succ_mk Ideal.quotientToQuotientRangePowQuotSucc_mk
+-/
 
+#print Ideal.quotientToQuotientRangePowQuotSucc_injective /-
 theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDomain S] [P.IsPrime]
     {i : ℕ} (hi : i < e) {a : S} (a_mem : a ∈ P ^ i) (a_not_mem : a ∉ P ^ (i + 1)) :
     Function.Injective (quotientToQuotientRangePowQuotSucc f p P a_mem) := fun x =>
@@ -613,6 +634,7 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
               ((Submodule.sub_mem_iff_right _ hz).mp (Pe_le_Pi1 h))).resolve_right
           a_not_mem
 #align ideal.quotient_to_quotient_range_pow_quot_succ_injective Ideal.quotientToQuotientRangePowQuotSucc_injective
+-/
 
 theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDomain S]
     (hP0 : P ≠ ⊥) [hP : P.IsPrime] {i : ℕ} (hi : i < e) {a : S} (a_mem : a ∈ P ^ i)
@@ -741,35 +763,46 @@ open scoped Classical
 
 variable [IsDomain S] [IsDedekindDomain S] [Algebra R S]
 
+#print Ideal.Factors.ne_bot /-
 theorem Factors.ne_bot (P : (factors (map (algebraMap R S) p)).toFinset) : (P : Ideal S) ≠ ⊥ :=
   (prime_of_factor _ (Multiset.mem_toFinset.mp P.2)).NeZero
 #align ideal.factors.ne_bot Ideal.Factors.ne_bot
+-/
 
+#print Ideal.Factors.isPrime /-
 instance Factors.isPrime (P : (factors (map (algebraMap R S) p)).toFinset) :
     IsPrime (P : Ideal S) :=
   Ideal.isPrime_of_prime (prime_of_factor _ (Multiset.mem_toFinset.mp P.2))
 #align ideal.factors.is_prime Ideal.Factors.isPrime
+-/
 
+#print Ideal.Factors.ramificationIdx_ne_zero /-
 theorem Factors.ramificationIdx_ne_zero (P : (factors (map (algebraMap R S) p)).toFinset) :
     ramificationIdx (algebraMap R S) p P ≠ 0 :=
   IsDedekindDomain.ramificationIdx_ne_zero (ne_zero_of_mem_factors (Multiset.mem_toFinset.mp P.2))
     (Factors.isPrime p P) (Ideal.le_of_dvd (dvd_of_mem_factors (Multiset.mem_toFinset.mp P.2)))
 #align ideal.factors.ramification_idx_ne_zero Ideal.Factors.ramificationIdx_ne_zero
+-/
 
+#print Ideal.Factors.fact_ramificationIdx_neZero /-
 instance Factors.fact_ramificationIdx_neZero (P : (factors (map (algebraMap R S) p)).toFinset) :
     NeZero (ramificationIdx (algebraMap R S) p P) :=
   ⟨Factors.ramificationIdx_ne_zero p P⟩
 #align ideal.factors.fact_ramification_idx_ne_zero Ideal.Factors.fact_ramificationIdx_neZero
+-/
 
 attribute [local instance] quotient.algebra_quotient_of_ramification_idx_ne_zero
 
+#print Ideal.Factors.isScalarTower /-
 instance Factors.isScalarTower (P : (factors (map (algebraMap R S) p)).toFinset) :
     IsScalarTower R (R ⧸ p) (S ⧸ (P : Ideal S)) :=
   IsScalarTower.of_algebraMap_eq fun x => by simp
 #align ideal.factors.is_scalar_tower Ideal.Factors.isScalarTower
+-/
 
 attribute [local instance] Ideal.Quotient.field
 
+#print Ideal.Factors.finrank_pow_ramificationIdx /-
 theorem Factors.finrank_pow_ramificationIdx [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) :
     finrank (R ⧸ p) (S ⧸ (P : Ideal S) ^ ramificationIdx (algebraMap R S) p P) =
@@ -778,7 +811,9 @@ theorem Factors.finrank_pow_ramificationIdx [p.IsMaximal]
   rw [finrank_prime_pow_ramification_idx, inertia_deg_algebra_map]
   exact factors.ne_bot p P
 #align ideal.factors.finrank_pow_ramification_idx Ideal.Factors.finrank_pow_ramificationIdx
+-/
 
+#print Ideal.Factors.finiteDimensional_quotient /-
 instance Factors.finiteDimensional_quotient [IsNoetherian R S] [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) :
     FiniteDimensional (R ⧸ p) (S ⧸ (P : Ideal S)) :=
@@ -787,12 +822,16 @@ instance Factors.finiteDimensional_quotient [IsNoetherian R S] [p.IsMaximal]
       isNoetherian_of_surjective S (Ideal.Quotient.mkₐ _ _).toLinearMap <|
         LinearMap.range_eq_top.mpr Ideal.Quotient.mk_surjective
 #align ideal.factors.finite_dimensional_quotient Ideal.Factors.finiteDimensional_quotient
+-/
 
+#print Ideal.Factors.inertiaDeg_ne_zero /-
 theorem Factors.inertiaDeg_ne_zero [IsNoetherian R S] [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) : inertiaDeg (algebraMap R S) p P ≠ 0 := by
   rw [inertia_deg_algebra_map]; exact (finite_dimensional.finrank_pos_iff.mpr inferInstance).ne'
 #align ideal.factors.inertia_deg_ne_zero Ideal.Factors.inertiaDeg_ne_zero
+-/
 
+#print Ideal.Factors.finiteDimensional_quotient_pow /-
 instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) :
     FiniteDimensional (R ⧸ p) (S ⧸ (P : Ideal S) ^ ramificationIdx (algebraMap R S) p P) :=
@@ -801,6 +840,7 @@ instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]
   rw [pos_iff_ne_zero, factors.finrank_pow_ramification_idx]
   exact mul_ne_zero (factors.ramification_idx_ne_zero p P) (factors.inertia_deg_ne_zero p P)
 #align ideal.factors.finite_dimensional_quotient_pow Ideal.Factors.finiteDimensional_quotient_pow
+-/
 
 universe w
 

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

@@ -71,7 +71,7 @@ If there is no largest such `n` (e.g. because `p = ⊥`), then `ramification_idx
 defined to be 0.
 -/
 noncomputable def ramificationIdx : ℕ :=
-  sSup { n | map f p ≤ P ^ n }
+  sSup {n | map f p ≤ P ^ n}
 #align ideal.ramification_idx Ideal.ramificationIdx
 
 variable {f p P}
@@ -471,7 +471,8 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
       Submodule.Quotient.eq] at y_eq 
     exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
   · have := b.linear_independent; rw [b_eq_b'] at this 
-    convert finrank_quotient_map.linear_independent_of_nontrivial K _
+    convert
+      finrank_quotient_map.linear_independent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
     · rw [quotient.algebra_map_eq, Ideal.mk_ker]
       exact hp.ne_top

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

@@ -272,7 +272,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   -- then we can find a linear dependence with coefficients `I.quotient.mk g'` in `R/I`,
   -- where `I = ker (algebra_map R S)`.
   -- We make use of the same principle but stay in `R` everywhere.
-  simp only [linearIndependent_iff', not_forall] at hb⊢
+  simp only [linearIndependent_iff', not_forall] at hb ⊢
   obtain ⟨s, g, eq, j', hj's, hj'g⟩ := hb
   use s
   obtain ⟨a, hag, j, hjs, hgI⟩ := Ideal.exist_integer_multiples_not_mem hRS s g hj's hj'g
@@ -284,7 +284,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   -- Because `R/I` is nontrivial, we can lift `g` to a nontrivial linear dependence in `S`.
   have hgI : algebraMap R S (g' j) ≠ 0 :=
     by
-    simp only [FractionalIdeal.mem_coeIdeal, not_exists, not_and'] at hgI
+    simp only [FractionalIdeal.mem_coeIdeal, not_exists, not_and'] at hgI 
     exact hgI _ (hg' j hjs)
   refine' ⟨fun i => algebraMap R S (g' i), _, j, hjs, hgI⟩
   have eq : f (∑ i in s, g' i • b i) = 0 :=
@@ -373,9 +373,9 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   have span_d : (Submodule.span S ({algebraMap R S A.det} : Set S)).restrictScalars R ≤ M :=
     by
     intro x hx
-    rw [Submodule.restrictScalars_mem] at hx
+    rw [Submodule.restrictScalars_mem] at hx 
     obtain ⟨x', rfl⟩ := submodule.mem_span_singleton.mp hx
-    rw [smul_eq_mul, mul_comm, ← Algebra.smul_def] at hx⊢
+    rw [smul_eq_mul, mul_comm, ← Algebra.smul_def] at hx ⊢
     rw [← Submodule.Quotient.mk_eq_zero, Submodule.Quotient.mk_smul]
     obtain ⟨a', _, quot_x_eq⟩ := exists_sum (Submodule.Quotient.mk x')
     simp_rw [← quot_x_eq, Finset.smul_sum, smul_comm A.det, d_smul, smul_zero,
@@ -414,7 +414,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       rfl
   -- And we conclude `L = span L {det A} ≤ span K b`, so `span K b` spans everything.
   · intro x hx
-    rw [Submodule.restrictScalars_mem, IsScalarTower.algebraMap_apply R S L] at hx
+    rw [Submodule.restrictScalars_mem, IsScalarTower.algebraMap_apply R S L] at hx 
     refine' IsFractionRing.ideal_span_singleton_map_subset R _ hRL span_d hx
     haveI : NoZeroSMulDivisors R L := NoZeroSMulDivisors.of_algebraMap_injective hRL
     rw [← IsFractionRing.isAlgebraic_iff' R S]
@@ -464,13 +464,13 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
       b.mem_span _
     rw [← @Submodule.restrictScalars_mem R,
       Submodule.restrictScalars_span R (R ⧸ p) Ideal.Quotient.mk_surjective, b_eq_b',
-      Set.range_comp, ← Submodule.map_span] at mem_span_b
+      Set.range_comp, ← Submodule.map_span] at mem_span_b 
     obtain ⟨y, y_mem, y_eq⟩ := submodule.mem_map.mp mem_span_b
     suffices y + -(y - x) ∈ _ by simpa
     rw [LinearMap.restrictScalars_apply, Submodule.mkQ_apply, Submodule.mkQ_apply,
-      Submodule.Quotient.eq] at y_eq
+      Submodule.Quotient.eq] at y_eq 
     exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
-  · have := b.linear_independent; rw [b_eq_b'] at this
+  · have := b.linear_independent; rw [b_eq_b'] at this 
     convert finrank_quotient_map.linear_independent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
     · rw [quotient.algebra_map_eq, Ideal.mk_ker]
@@ -535,8 +535,8 @@ theorem powQuotSuccInclusion_injective (i : ℕ) :
   by
   rw [← LinearMap.ker_eq_bot, LinearMap.ker_eq_bot']
   rintro ⟨x, hx⟩ hx0
-  rw [Subtype.ext_iff] at hx0⊢
-  rwa [pow_quot_succ_inclusion_apply_coe] at hx0
+  rw [Subtype.ext_iff] at hx0 ⊢
+  rwa [pow_quot_succ_inclusion_apply_coe] at hx0 
 #align ideal.pow_quot_succ_inclusion_injective Ideal.powQuotSuccInclusion_injective
 
 /-- `S ⧸ P` embeds into the quotient by `P^(i+1) ⧸ P^e` as a subspace of `P^i ⧸ P^e`.
@@ -547,7 +547,7 @@ noncomputable def quotientToQuotientRangePowQuotSuccAux {i : ℕ} {a : S} (a_mem
     S ⧸ P → (P ^ i).map (P ^ e).Quotient.mk ⧸ (powQuotSuccInclusion f p P i).range :=
   Quotient.map' (fun x : S => ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩)
     fun x y h => by
-    rw [Submodule.quotientRel_r_def] at h⊢
+    rw [Submodule.quotientRel_r_def] at h ⊢
     simp only [_root_.map_mul, LinearMap.mem_range]
     refine' ⟨⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_mul h a_mem)⟩, _⟩
     ext
@@ -601,12 +601,12 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
       have Pe_le_Pi1 : P ^ e ≤ P ^ (i + 1) := Ideal.pow_le_pow hi
       simp only [Submodule.Quotient.mk''_eq_mk, quotient_to_quotient_range_pow_quot_succ_mk,
         Submodule.Quotient.eq, LinearMap.mem_range, Subtype.ext_iff, Subtype.coe_mk,
-        Submodule.coe_sub] at h⊢
+        Submodule.coe_sub] at h ⊢
       rcases h with ⟨⟨⟨z⟩, hz⟩, h⟩
       rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
-        sup_eq_left.mpr Pe_le_Pi1] at hz
+        sup_eq_left.mpr Pe_le_Pi1] at hz 
       rw [pow_quot_succ_inclusion_apply_coe, Subtype.coe_mk, Submodule.Quotient.quot_mk_eq_mk,
-        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← sub_mul] at h
+        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← sub_mul] at h 
       exact
         (Ideal.IsPrime.mul_mem_pow _
               ((Submodule.sub_mem_iff_right _ hz).mp (Pe_le_Pi1 h))).resolve_right
@@ -622,7 +622,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
   have Pe_le_Pi : P ^ e ≤ P ^ i := Ideal.pow_le_pow hi.le
   have Pe_le_Pi1 : P ^ e ≤ P ^ (i + 1) := Ideal.pow_le_pow hi
   rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
-    sup_eq_left.mpr Pe_le_Pi] at hx
+    sup_eq_left.mpr Pe_le_Pi] at hx 
   suffices hx' : x ∈ Ideal.span {a} ⊔ P ^ (i + 1)
   · obtain ⟨y', hy', z, hz, rfl⟩ := submodule.mem_sup.mp hx'
     obtain ⟨y, rfl⟩ := ideal.mem_span_singleton.mp hy'
@@ -637,10 +637,10 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
   rw [sup_eq_prod_inf_factors _ (pow_ne_zero _ hP0), normalized_factors_pow,
     normalized_factors_irreducible ((Ideal.prime_iff_isPrime hP0).mpr hP).Irreducible, normalize_eq,
     Multiset.nsmul_singleton, Multiset.inter_replicate, Multiset.prod_replicate]
-  rw [← Submodule.span_singleton_le_iff_mem, Ideal.submodule_span_eq] at a_mem a_not_mem
+  rw [← Submodule.span_singleton_le_iff_mem, Ideal.submodule_span_eq] at a_mem a_not_mem 
   rwa [Ideal.count_normalizedFactors_eq a_mem a_not_mem, min_eq_left i.le_succ]
   · intro ha
-    rw [ideal.span_singleton_eq_bot.mp ha] at a_not_mem
+    rw [ideal.span_singleton_eq_bot.mp ha] at a_not_mem 
     have := (P ^ (i + 1)).zero_mem
     contradiction
 #align ideal.quotient_to_quotient_range_pow_quot_succ_surjective Ideal.quotientToQuotientRangePowQuotSucc_surjective
@@ -701,7 +701,7 @@ theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMa
   by
   letI : NeZero e := ⟨he⟩
   have := rank_pow_quot f p P hP0 0 (Nat.zero_le e)
-  rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this
+  rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this 
   exact (rank_top (R ⧸ p) _).symm.trans this
 #align ideal.rank_prime_pow_ramification_idx Ideal.rank_prime_pow_ramificationIdx
 

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

@@ -846,7 +846,7 @@ noncomputable def Factors.piQuotientLinearEquiv (p : Ideal R) (hp : map (algebra
       rintro ⟨c⟩ ⟨x⟩; ext P
       simp only [Ideal.Quotient.mk_algebraMap, factors.pi_quotient_equiv_mk,
         factors.pi_quotient_equiv_map, Submodule.Quotient.quot_mk_eq_mk, Pi.algebraMap_apply,
-        [anonymous], Pi.mul_apply, Ideal.Quotient.algebraMap_quotient_map_quotient,
+        RingEquiv.toFun_eq_coe, Pi.mul_apply, Ideal.Quotient.algebraMap_quotient_map_quotient,
         Ideal.Quotient.mk_eq_mk, Algebra.smul_def, _root_.map_mul, RingHomCompTriple.comp_apply]
       congr }
 #align ideal.factors.pi_quotient_linear_equiv Ideal.Factors.piQuotientLinearEquiv

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

@@ -60,7 +60,7 @@ open UniqueFactorizationMonoid
 
 section DecEq
 
-open Classical
+open scoped Classical
 
 /-- The ramification index of `P` over `p` is the largest exponent `n` such that
 `p` is contained in `P^n`.
@@ -233,9 +233,9 @@ end DecEq
 
 section FinrankQuotientMap
 
-open BigOperators
+open scoped BigOperators
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
 variable [Algebra R S]
 
@@ -297,7 +297,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
     (f.map_eq_zero_iff hf).mp Eq, LinearMap.map_zero]
 #align ideal.finrank_quotient_map.linear_independent_of_nontrivial Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial
 
-open Matrix
+open scoped Matrix
 
 variable {K}
 
@@ -733,7 +733,7 @@ end FactLeComap
 
 section FactorsMap
 
-open Classical
+open scoped Classical
 
 /-! ## Properties of the factors of `p.map (algebra_map R S)` -/
 
@@ -853,7 +853,7 @@ noncomputable def Factors.piQuotientLinearEquiv (p : Ideal R) (hp : map (algebra
 
 variable {S}
 
-open BigOperators
+open scoped BigOperators
 
 /-- The **fundamental identity** of ramification index `e` and inertia degree `f`:
 for `P` ranging over the primes lying over `p`, `∑ P, e P * f P = [Frac(S) : Frac(R)]`;

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

@@ -279,9 +279,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   choose g'' hg'' using hag
   letI := Classical.propDecidable
   let g' i := if h : i ∈ s then g'' i h else 0
-  have hg' : ∀ i ∈ s, algebraMap _ _ (g' i) = a * g i :=
-    by
-    intro i hi
+  have hg' : ∀ i ∈ s, algebraMap _ _ (g' i) = a * g i := by intro i hi;
     exact (congr_arg _ (dif_pos hi)).trans (hg'' i hi)
   -- Because `R/I` is nontrivial, we can lift `g` to a nontrivial linear dependence in `S`.
   have hgI : algebraMap R S (g' j) ≠ 0 :=
@@ -472,8 +470,7 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
     rw [LinearMap.restrictScalars_apply, Submodule.mkQ_apply, Submodule.mkQ_apply,
       Submodule.Quotient.eq] at y_eq
     exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
-  · have := b.linear_independent
-    rw [b_eq_b'] at this
+  · have := b.linear_independent; rw [b_eq_b'] at this
     convert finrank_quotient_map.linear_independent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
     · rw [quotient.algebra_map_eq, Ideal.mk_ker]
@@ -791,10 +788,8 @@ instance Factors.finiteDimensional_quotient [IsNoetherian R S] [p.IsMaximal]
 #align ideal.factors.finite_dimensional_quotient Ideal.Factors.finiteDimensional_quotient
 
 theorem Factors.inertiaDeg_ne_zero [IsNoetherian R S] [p.IsMaximal]
-    (P : (factors (map (algebraMap R S) p)).toFinset) : inertiaDeg (algebraMap R S) p P ≠ 0 :=
-  by
-  rw [inertia_deg_algebra_map]
-  exact (finite_dimensional.finrank_pos_iff.mpr inferInstance).ne'
+    (P : (factors (map (algebraMap R S) p)).toFinset) : inertiaDeg (algebraMap R S) p P ≠ 0 := by
+  rw [inertia_deg_algebra_map]; exact (finite_dimensional.finrank_pos_iff.mpr inferInstance).ne'
 #align ideal.factors.inertia_deg_ne_zero Ideal.Factors.inertiaDeg_ne_zero
 
 instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]

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

@@ -286,7 +286,7 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
   -- Because `R/I` is nontrivial, we can lift `g` to a nontrivial linear dependence in `S`.
   have hgI : algebraMap R S (g' j) ≠ 0 :=
     by
-    simp only [FractionalIdeal.mem_coe_ideal, not_exists, not_and'] at hgI
+    simp only [FractionalIdeal.mem_coeIdeal, not_exists, not_and'] at hgI
     exact hgI _ (hg' j hjs)
   refine' ⟨fun i => algebraMap R S (g' i), _, j, hjs, hgI⟩
   have eq : f (∑ i in s, g' i • b i) = 0 :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -71,14 +71,14 @@ If there is no largest such `n` (e.g. because `p = ⊥`), then `ramification_idx
 defined to be 0.
 -/
 noncomputable def ramificationIdx : ℕ :=
-  supₛ { n | map f p ≤ P ^ n }
+  sSup { n | map f p ≤ P ^ n }
 #align ideal.ramification_idx Ideal.ramificationIdx
 
 variable {f p P}
 
 theorem ramificationIdx_eq_find (h : ∃ n, ∀ k, map f p ≤ P ^ k → k ≤ n) :
     ramificationIdx f p P = Nat.find h :=
-  Nat.supₛ_def h
+  Nat.sSup_def h
 #align ideal.ramification_idx_eq_find Ideal.ramificationIdx_eq_find
 
 theorem ramificationIdx_eq_zero (h : ∀ n : ℕ, ∃ k, map f p ≤ P ^ k ∧ n < k) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.ramification_inertia
-! leanprover-community/mathlib commit 4cf7ca0e69e048b006674cf4499e5c7d296a89e0
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -665,36 +665,36 @@ noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekin
 
 /-- Since the inclusion `(P^(i + 1) / P^e) ⊂ (P^i / P^e)` has a kernel isomorphic to `P / S`,
 `[P^i / P^e : R / p] = [P^(i+1) / P^e : R / p] + [P / S : R / p]` -/
-theorem dim_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
+theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
     {i : ℕ} (hi : i < e) :
     Module.rank (R ⧸ p) (Ideal.map (P ^ e).Quotient.mk (P ^ i)) =
       Module.rank (R ⧸ p) (S ⧸ P) +
         Module.rank (R ⧸ p) (Ideal.map (P ^ e).Quotient.mk (P ^ (i + 1))) :=
   by
   letI : Field (R ⧸ p) := Ideal.Quotient.field _
-  rw [dim_eq_of_injective _ (pow_quot_succ_inclusion_injective f p P i),
-    (quotient_range_pow_quot_succ_inclusion_equiv f p P hP0 hi).symm.dim_eq]
-  exact (dim_quotient_add_dim (LinearMap.range (pow_quot_succ_inclusion f p P i))).symm
-#align ideal.dim_pow_quot_aux Ideal.dim_pow_quot_aux
+  rw [rank_eq_of_injective _ (pow_quot_succ_inclusion_injective f p P i),
+    (quotient_range_pow_quot_succ_inclusion_equiv f p P hP0 hi).symm.rank_eq]
+  exact (rank_quotient_add_rank (LinearMap.range (pow_quot_succ_inclusion f p P i))).symm
+#align ideal.rank_pow_quot_aux Ideal.rank_pow_quot_aux
 
-theorem dim_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
+theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
     (i : ℕ) (hi : i ≤ e) :
     Module.rank (R ⧸ p) (Ideal.map (P ^ e).Quotient.mk (P ^ i)) =
       (e - i) • Module.rank (R ⧸ p) (S ⧸ P) :=
   by
   refine' @Nat.decreasingInduction' _ i e (fun j lt_e le_j ih => _) hi _
-  · rw [dim_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul, Nat.sub_succ, ← Nat.succ_eq_add_one,
+  · rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul, Nat.sub_succ, ← Nat.succ_eq_add_one,
       Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt lt_e)]
     assumption
   · rw [Nat.sub_self, zero_nsmul, map_quotient_self]
-    exact dim_bot (R ⧸ p) (S ⧸ P ^ e)
-#align ideal.dim_pow_quot Ideal.dim_pow_quot
+    exact rank_bot (R ⧸ p) (S ⧸ P ^ e)
+#align ideal.rank_pow_quot Ideal.rank_pow_quot
 
 omit hfp
 
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]` is equal to `e * [S/P : R/p]`. -/
-theorem dim_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime]
+theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime]
     (hP0 : P ≠ ⊥) (he : e ≠ 0) :
     Module.rank (R ⧸ p) (S ⧸ P ^ e) =
       e •
@@ -703,10 +703,10 @@ theorem dim_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMax
             @Quotient.algebraQuotientOfRamificationIdxNeZero _ _ _ _ _ ⟨he⟩) :=
   by
   letI : NeZero e := ⟨he⟩
-  have := dim_pow_quot f p P hP0 0 (Nat.zero_le e)
+  have := rank_pow_quot f p P hP0 0 (Nat.zero_le e)
   rw [pow_zero, Nat.sub_zero, Ideal.one_eq_top, Ideal.map_top] at this
-  exact (dim_top (R ⧸ p) _).symm.trans this
-#align ideal.dim_prime_pow_ramification_idx Ideal.dim_prime_pow_ramificationIdx
+  exact (rank_top (R ⧸ p) _).symm.trans this
+#align ideal.rank_prime_pow_ramification_idx Ideal.rank_prime_pow_ramificationIdx
 
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]`, as a natural number, is equal to `e * [S/P : R/p]`. -/
@@ -721,12 +721,12 @@ theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0
   letI : NeZero e := ⟨he⟩
   letI : Algebra (R ⧸ p) (S ⧸ P) := quotient.algebra_quotient_of_ramification_idx_ne_zero f p P
   letI := Ideal.Quotient.field p
-  have hdim := dim_prime_pow_ramification_idx _ _ _ hP0 he
+  have hdim := rank_prime_pow_ramification_idx _ _ _ hP0 he
   by_cases hP : FiniteDimensional (R ⧸ p) (S ⧸ P)
   · haveI := hP
     haveI := (finite_dimensional_iff_of_rank_eq_nsmul he hdim).mpr hP
     refine' Cardinal.natCast_injective _
-    rw [finrank_eq_dim, Nat.cast_mul, finrank_eq_dim, hdim, nsmul_eq_mul]
+    rw [finrank_eq_rank', Nat.cast_mul, finrank_eq_rank', hdim, nsmul_eq_mul]
   have hPe := mt (finite_dimensional_iff_of_rank_eq_nsmul he hdim).mp hP
   simp only [finrank_of_infinite_dimensional hP, finrank_of_infinite_dimensional hPe,
     MulZeroClass.mul_zero]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.ramification_inertia
-! leanprover-community/mathlib commit 71150516f28d9826c7341f8815b31f7d8770c212
+! leanprover-community/mathlib commit 4cf7ca0e69e048b006674cf4499e5c7d296a89e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -892,7 +892,7 @@ theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
     _ =
         finrank (R ⧸ p)
           (∀ P : (factors (map (algebraMap R S) p)).toFinset, S ⧸ (P : Ideal S) ^ e P) :=
-      (Module.Free.finrank_pi_fintype (R ⧸ p)).symm
+      (finrank_pi_fintype (R ⧸ p)).symm
     _ = finrank (R ⧸ p) (S ⧸ map (algebraMap R S) p) := _
     _ = finrank K L := _
     

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

@@ -474,8 +474,7 @@ theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Alg
     exact add_mem (Submodule.mem_sup_left y_mem) (neg_mem <| Submodule.mem_sup_right y_eq)
   · have := b.linear_independent
     rw [b_eq_b'] at this
-    convert
-      finrank_quotient_map.linear_independent_of_nontrivial K _
+    convert finrank_quotient_map.linear_independent_of_nontrivial K _
         ((Algebra.linearMap S L).restrictScalars R) _ ((Submodule.mkQ _).restrictScalars R) this
     · rw [quotient.algebra_map_eq, Ideal.mk_ker]
       exact hp.ne_top

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

@@ -366,8 +366,8 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       
     ·
       simp only [Matrix.adjugate_mul, Pi.smul_apply, Matrix.one_apply, mul_ite, ite_smul,
-        smul_eq_mul, mul_one, mul_zero, one_smul, zero_smul, Finset.sum_ite_eq, Finset.mem_univ,
-        if_true]
+        smul_eq_mul, mul_one, MulZeroClass.mul_zero, one_smul, zero_smul, Finset.sum_ite_eq,
+        Finset.mem_univ, if_true]
     · simp only [Matrix.mul_apply, Finset.smul_sum, Finset.sum_smul, smul_smul]
       rw [Finset.sum_comm]
     · rw [A_smul, smul_zero]
@@ -729,7 +729,8 @@ theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0
     refine' Cardinal.natCast_injective _
     rw [finrank_eq_dim, Nat.cast_mul, finrank_eq_dim, hdim, nsmul_eq_mul]
   have hPe := mt (finite_dimensional_iff_of_rank_eq_nsmul he hdim).mp hP
-  simp only [finrank_of_infinite_dimensional hP, finrank_of_infinite_dimensional hPe, mul_zero]
+  simp only [finrank_of_infinite_dimensional hP, finrank_of_infinite_dimensional hPe,
+    MulZeroClass.mul_zero]
 #align ideal.finrank_prime_pow_ramification_idx Ideal.finrank_prime_pow_ramificationIdx
 
 end FactLeComap

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

Scatter the content of Data.Nat.Basic across:

• Data.Nat.Defs for the lemmas having no dependencies
• Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
• Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

• Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
• Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
• Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before

After

@@ -625,7 +625,7 @@ theorem rank_pow_quot [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P 
   let Q : ℕ → Prop :=
     fun i => Module.rank (R ⧸ p) { x // x ∈ map (Quotient.mk (P ^ e)) (P ^ i) }
       = (e - i) • Module.rank (R ⧸ p) (S ⧸ P)
-  refine @Nat.decreasingInduction' Q i e (fun j lt_e _le_j ih => ?_) hi ?_
+  refine Nat.decreasingInduction' (P := Q) (fun j lt_e _le_j ih => ?_) hi ?_
   · dsimp only [Q]
     rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul', Nat.sub_succ, ← Nat.succ_eq_add_one,
       Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt lt_e)]

@@ -830,7 +830,7 @@ theorem sum_ramification_inertia (K L : Type*) [Field K] [Field L] [IsDedekindDo
     refine Finset.sum_congr rfl fun P _ => ?_
     rw [Factors.finrank_pow_ramificationIdx]
   · refine LinearEquiv.finrank_eq (Factors.piQuotientLinearEquiv S p ?_).symm
-    rwa [Ne.def, Ideal.map_eq_bot_iff_le_ker, (RingHom.injective_iff_ker_eq_bot _).mp inj_RS,
+    rwa [Ne, Ideal.map_eq_bot_iff_le_ker, (RingHom.injective_iff_ker_eq_bot _).mp inj_RS,
       le_bot_iff]
   · exact finrank_quotient_map p K L
 #align ideal.sum_ramification_inertia Ideal.sum_ramification_inertia

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.

@@ -496,19 +496,19 @@ and `quotientRangePowQuotSuccInclusionEquiv` for this as a linear equivalence.
 noncomputable def quotientToQuotientRangePowQuotSuccAux {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) :
     S ⧸ P →
       (P ^ i).map (Ideal.Quotient.mk (P ^ e)) ⧸ LinearMap.range (powQuotSuccInclusion f p P i) :=
-  Quotient.map' (fun x : S => ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩)
+  Quotient.map' (fun x : S => ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_right x _ a_mem)⟩)
     fun x y h => by
     rw [Submodule.quotientRel_r_def] at h ⊢
     simp only [_root_.map_mul, LinearMap.mem_range]
-    refine' ⟨⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_mul h a_mem)⟩, _⟩
+    refine' ⟨⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_mul a_mem h)⟩, _⟩
     ext
     rw [powQuotSuccInclusion_apply_coe, Subtype.coe_mk, Submodule.coe_sub, Subtype.coe_mk,
-      Subtype.coe_mk, _root_.map_mul, map_sub, sub_mul]
+      Subtype.coe_mk, _root_.map_mul, map_sub, mul_sub]
 #align ideal.quotient_to_quotient_range_pow_quot_succ_aux Ideal.quotientToQuotientRangePowQuotSuccAux
 
 theorem quotientToQuotientRangePowQuotSuccAux_mk {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) (x : S) :
     quotientToQuotientRangePowQuotSuccAux f p P a_mem (Submodule.Quotient.mk x) =
-      Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩ :=
+      Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_right x _ a_mem)⟩ :=
   by apply Quotient.map'_mk''
 #align ideal.quotient_to_quotient_range_pow_quot_succ_aux_mk Ideal.quotientToQuotientRangePowQuotSuccAux_mk
 
@@ -520,7 +520,7 @@ noncomputable def quotientToQuotientRangePowQuotSucc {i : ℕ} {a : S} (a_mem :
   map_add' := by
     intro x y; refine' Quotient.inductionOn' x fun x => Quotient.inductionOn' y fun y => _
     simp only [Submodule.Quotient.mk''_eq_mk, ← Submodule.Quotient.mk_add,
-      quotientToQuotientRangePowQuotSuccAux_mk, add_mul]
+      quotientToQuotientRangePowQuotSuccAux_mk, mul_add]
     exact congr_arg Submodule.Quotient.mk rfl
   map_smul' := by
     intro x y; refine' Quotient.inductionOn' x fun x => Quotient.inductionOn' y fun y => _
@@ -530,11 +530,12 @@ noncomputable def quotientToQuotientRangePowQuotSucc {i : ℕ} {a : S} (a_mem :
     ext
     simp only [mul_assoc, _root_.map_mul, Quotient.mk_eq_mk, Submodule.coe_smul_of_tower,
       Algebra.smul_def, Quotient.algebraMap_quotient_pow_ramificationIdx]
+    ring
 #align ideal.quotient_to_quotient_range_pow_quot_succ Ideal.quotientToQuotientRangePowQuotSucc
 
 theorem quotientToQuotientRangePowQuotSucc_mk {i : ℕ} {a : S} (a_mem : a ∈ P ^ i) (x : S) :
     quotientToQuotientRangePowQuotSucc f p P a_mem (Submodule.Quotient.mk x) =
-      Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_left _ x a_mem)⟩ :=
+      Submodule.Quotient.mk ⟨_, Ideal.mem_map_of_mem _ (Ideal.mul_mem_right x _ a_mem)⟩ :=
   quotientToQuotientRangePowQuotSuccAux_mk f p P a_mem x
 #align ideal.quotient_to_quotient_range_pow_quot_succ_mk Ideal.quotientToQuotientRangePowQuotSucc_mk
 
@@ -551,10 +552,10 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDedekindDomain S] [P.IsP
       rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
         sup_eq_left.mpr Pe_le_Pi1] at hz
       rw [powQuotSuccInclusion_apply_coe, Subtype.coe_mk, Submodule.Quotient.quot_mk_eq_mk,
-        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← sub_mul] at h
+        Ideal.Quotient.mk_eq_mk, ← map_sub, Ideal.Quotient.eq, ← mul_sub] at h
       exact
-        (Ideal.IsPrime.mul_mem_pow _
-              ((Submodule.sub_mem_iff_right _ hz).mp (Pe_le_Pi1 h))).resolve_right
+        (Ideal.IsPrime.mem_pow_mul _
+              ((Submodule.sub_mem_iff_right _ hz).mp (Pe_le_Pi1 h))).resolve_left
           a_not_mem
 #align ideal.quotient_to_quotient_range_pow_quot_succ_injective Ideal.quotientToQuotientRangePowQuotSucc_injective
 
@@ -575,7 +576,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDedekindDomain S]
       Submodule.coe_sub]
     refine ⟨⟨_, Ideal.mem_map_of_mem _ (Submodule.neg_mem _ hz)⟩, ?_⟩
     rw [powQuotSuccInclusion_apply_coe, Subtype.coe_mk, Ideal.Quotient.mk_eq_mk, map_add,
-      mul_comm y a, sub_add_cancel_left, map_neg]
+      sub_add_cancel_left, map_neg]
   letI := Classical.decEq (Ideal S)
   rw [sup_eq_prod_inf_factors _ (pow_ne_zero _ hP0), normalizedFactors_pow,
     normalizedFactors_irreducible ((Ideal.prime_iff_isPrime hP0).mpr hP).irreducible, normalize_eq,
@@ -626,7 +627,7 @@ theorem rank_pow_quot [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P 
       = (e - i) • Module.rank (R ⧸ p) (S ⧸ P)
   refine @Nat.decreasingInduction' Q i e (fun j lt_e _le_j ih => ?_) hi ?_
   · dsimp only [Q]
-    rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul, Nat.sub_succ, ← Nat.succ_eq_add_one,
+    rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul', Nat.sub_succ, ← Nat.succ_eq_add_one,
       Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt lt_e)]
     assumption
   · dsimp only [Q]

Probably because in mathlib4 the definition IsDedekindDomain extends Domain, and this was not the case in mathlib3, there are unused hypothesis of the form

variable [IsDomain R] [IsDedekindDomain R]

and this PR removes the first one, that can be inferred by the second, both in variable declarations and in theorem/definition assumptions. A regex search has been performed on the library to search for all occurrences and none is left.

@@ -138,7 +138,7 @@ theorem le_comap_of_ramificationIdx_ne_zero (h : ramificationIdx f p P ≠ 0) :
 
 namespace IsDedekindDomain
 
-variable [IsDomain S] [IsDedekindDomain S]
+variable [IsDedekindDomain S]
 
 theorem ramificationIdx_eq_normalizedFactors_count (hp0 : map f p ≠ ⊥) (hP : P.IsPrime)
     (hP0 : P ≠ ⊥) : ramificationIdx f p P = (normalizedFactors (map f p)).count P := by
@@ -241,7 +241,7 @@ The statement we prove is actually slightly more general:
  * it suffices that the inclusion `algebraMap R S : R → S` is nontrivial
  * the function `f' : V'' → V'` doesn't need to be injective
 -/
-theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedekindDomain R]
+theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDedekindDomain R]
     (hRS : RingHom.ker (algebraMap R S) ≠ ⊤) (f : V'' →ₗ[R] V) (hf : Function.Injective f)
     (f' : V'' →ₗ[R] V') {ι : Type*} {b : ι → V''} (hb' : LinearIndependent S (f' ∘ b)) :
     LinearIndependent K (f ∘ b) := by
@@ -388,7 +388,7 @@ variable (K L)
 
 /-- If `p` is a maximal ideal of `R`, and `S` is the integral closure of `R` in `L`,
 then the dimension `[S/pS : R/p]` is equal to `[Frac(S) : Frac(R)]`. -/
-theorem finrank_quotient_map [IsDomain R] [IsDomain S] [IsDedekindDomain R] [Algebra K L]
+theorem finrank_quotient_map [IsDomain S] [IsDedekindDomain R] [Algebra K L]
     [Algebra R L] [IsScalarTower R K L] [IsScalarTower R S L] [IsIntegralClosure S R L]
     [hp : p.IsMaximal] [IsNoetherian R S] :
     finrank (R ⧸ p) (S ⧸ map (algebraMap R S) p) = finrank K L := by
@@ -538,7 +538,7 @@ theorem quotientToQuotientRangePowQuotSucc_mk {i : ℕ} {a : S} (a_mem : a ∈ P
   quotientToQuotientRangePowQuotSuccAux_mk f p P a_mem x
 #align ideal.quotient_to_quotient_range_pow_quot_succ_mk Ideal.quotientToQuotientRangePowQuotSucc_mk
 
-theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDomain S] [P.IsPrime]
+theorem quotientToQuotientRangePowQuotSucc_injective [IsDedekindDomain S] [P.IsPrime]
     {i : ℕ} (hi : i < e) {a : S} (a_mem : a ∈ P ^ i) (a_not_mem : a ∉ P ^ (i + 1)) :
     Function.Injective (quotientToQuotientRangePowQuotSucc f p P a_mem) := fun x =>
   Quotient.inductionOn' x fun x y =>
@@ -558,7 +558,7 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
           a_not_mem
 #align ideal.quotient_to_quotient_range_pow_quot_succ_injective Ideal.quotientToQuotientRangePowQuotSucc_injective
 
-theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDomain S]
+theorem quotientToQuotientRangePowQuotSucc_surjective [IsDedekindDomain S]
     (hP0 : P ≠ ⊥) [hP : P.IsPrime] {i : ℕ} (hi : i < e) {a : S} (a_mem : a ∈ P ^ i)
     (a_not_mem : a ∉ P ^ (i + 1)) :
     Function.Surjective (quotientToQuotientRangePowQuotSucc f p P a_mem) := by
@@ -590,7 +590,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
 
 /-- Quotienting `P^i / P^e` by its subspace `P^(i+1) ⧸ P^e` is
 `R ⧸ p`-linearly isomorphic to `S ⧸ P`. -/
-noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekindDomain S]
+noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDedekindDomain S]
     [P.IsPrime] (hP : P ≠ ⊥) {i : ℕ} (hi : i < e) :
     ((P ^ i).map (Ideal.Quotient.mk (P ^ e)) ⧸ LinearMap.range (powQuotSuccInclusion f p P i))
       ≃ₗ[R ⧸ p] S ⧸ P := by
@@ -605,7 +605,7 @@ noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekin
 
 /-- Since the inclusion `(P^(i + 1) / P^e) ⊂ (P^i / P^e)` has a kernel isomorphic to `P / S`,
 `[P^i / P^e : R / p] = [P^(i+1) / P^e : R / p] + [P / S : R / p]` -/
-theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
+theorem rank_pow_quot_aux [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
     {i : ℕ} (hi : i < e) :
     Module.rank (R ⧸ p) (Ideal.map (Ideal.Quotient.mk (P ^ e)) (P ^ i)) =
       Module.rank (R ⧸ p) (S ⧸ P) +
@@ -616,7 +616,7 @@ theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsP
   exact (rank_quotient_add_rank (LinearMap.range (powQuotSuccInclusion f p P i))).symm
 #align ideal.rank_pow_quot_aux Ideal.rank_pow_quot_aux
 
-theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
+theorem rank_pow_quot [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime] (hP0 : P ≠ ⊥)
     (i : ℕ) (hi : i ≤ e) :
     Module.rank (R ⧸ p) (Ideal.map (Ideal.Quotient.mk (P ^ e)) (P ^ i)) =
       (e - i) • Module.rank (R ⧸ p) (S ⧸ P) := by
@@ -636,7 +636,7 @@ theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime
 
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]` is equal to `e * [S/P : R/p]`. -/
-theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime]
+theorem rank_prime_pow_ramificationIdx [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime]
     (hP0 : P ≠ ⊥) (he : e ≠ 0) :
     Module.rank (R ⧸ p) (S ⧸ P ^ e) =
       e •
@@ -651,7 +651,7 @@ theorem rank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] [p.IsMa
 
 /-- If `p` is a maximal ideal of `R`, `S` extends `R` and `P^e` lies over `p`,
 then the dimension `[S/(P^e) : R/p]`, as a natural number, is equal to `e * [S/P : R/p]`. -/
-theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0 : P ≠ ⊥)
+theorem finrank_prime_pow_ramificationIdx [IsDedekindDomain S] (hP0 : P ≠ ⊥)
     [p.IsMaximal] [P.IsPrime] (he : e ≠ 0) :
     finrank (R ⧸ p) (S ⧸ P ^ e) =
       e *
@@ -681,7 +681,7 @@ open scoped Classical
 /-! ## Properties of the factors of `p.map (algebraMap R S)` -/
 
 
-variable [IsDomain S] [IsDedekindDomain S] [Algebra R S]
+variable [IsDedekindDomain S] [Algebra R S]
 
 theorem Factors.ne_bot (P : (factors (map (algebraMap R S) p)).toFinset) : (P : Ideal S) ≠ ⊥ :=
   (prime_of_factor _ (Multiset.mem_toFinset.mp P.2)).ne_zero
@@ -800,9 +800,9 @@ for `P` ranging over the primes lying over `p`, `∑ P, e P * f P = [Frac(S) : F
 here `S` is a finite `R`-module (and thus `Frac(S) : Frac(R)` is a finite extension) and `p`
 is maximal.
 -/
-theorem sum_ramification_inertia (K L : Type*) [Field K] [Field L] [IsDomain R]
-    [IsDedekindDomain R] [Algebra R K] [IsFractionRing R K] [Algebra S L] [IsFractionRing S L]
-    [Algebra K L] [Algebra R L] [IsScalarTower R S L] [IsScalarTower R K L] [IsNoetherian R S]
+theorem sum_ramification_inertia (K L : Type*) [Field K] [Field L] [IsDedekindDomain R]
+    [Algebra R K] [IsFractionRing R K] [Algebra S L] [IsFractionRing S L] [Algebra K L]
+    [Algebra R L] [IsScalarTower R S L] [IsScalarTower R K L] [IsNoetherian R S]
     [IsIntegralClosure S R L] [p.IsMaximal] (hp0 : p ≠ ⊥) :
     (∑ P in (factors (map (algebraMap R S) p)).toFinset,
         ramificationIdx (algebraMap R S) p P * inertiaDeg (algebraMap R S) p P) =

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 | |

@@ -575,7 +575,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
       Submodule.coe_sub]
     refine ⟨⟨_, Ideal.mem_map_of_mem _ (Submodule.neg_mem _ hz)⟩, ?_⟩
     rw [powQuotSuccInclusion_apply_coe, Subtype.coe_mk, Ideal.Quotient.mk_eq_mk, map_add,
-      mul_comm y a, sub_add_cancel', map_neg]
+      mul_comm y a, sub_add_cancel_left, map_neg]
   letI := Classical.decEq (Ideal S)
   rw [sup_eq_prod_inf_factors _ (pow_ne_zero _ hP0), normalizedFactors_pow,
     normalizedFactors_irreducible ((Ideal.prime_iff_isPrime hP0).mpr hP).irreducible, normalize_eq,

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)

@@ -45,9 +45,7 @@ namespace Ideal
 universe u v
 
 variable {R : Type u} [CommRing R]
-
 variable {S : Type v} [CommRing S] (f : R →+* S)
-
 variable (p : Ideal R) (P : Ideal S)
 
 open FiniteDimensional
@@ -227,19 +225,12 @@ open scoped BigOperators
 open scoped nonZeroDivisors
 
 variable [Algebra R S]
-
 variable {K : Type*} [Field K] [Algebra R K] [hRK : IsFractionRing R K]
-
 variable {L : Type*} [Field L] [Algebra S L] [IsFractionRing S L]
-
 variable {V V' V'' : Type*}
-
 variable [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
-
 variable [AddCommGroup V'] [Module R V'] [Module S V'] [IsScalarTower R S V']
-
 variable [AddCommGroup V''] [Module R V'']
-
 variable (K)
 
 /-- Let `V` be a vector space over `K = Frac(R)`, `S / R` a ring extension

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -332,7 +332,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   let B := A.adjugate
   have A_smul : ∀ i, ∑ j, A i j • a j = 0 := by
     intros
-    simp [Matrix.sub_apply, Matrix.of_apply, ne_eq, Matrix.one_apply, sub_smul,
+    simp [A, Matrix.sub_apply, Matrix.of_apply, ne_eq, Matrix.one_apply, sub_smul,
       Finset.sum_sub_distrib, hA', sub_self]
   -- since `span S {det A} / M = 0`.
   have d_smul : ∀ i, A.det • a i = 0 := by
@@ -341,7 +341,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
       A.det • a i = ∑ j, (B * A) i j • a j := ?_
       _ = ∑ k, B i k • ∑ j, A k j • a j := ?_
       _ = 0 := Finset.sum_eq_zero fun k _ => ?_
-    · simp only [Matrix.adjugate_mul, Matrix.smul_apply, Matrix.one_apply, smul_eq_mul, ite_true,
+    · simp only [B, Matrix.adjugate_mul, Matrix.smul_apply, Matrix.one_apply, smul_eq_mul, ite_true,
         mul_ite, mul_one, mul_zero, ite_smul, zero_smul, Finset.sum_ite_eq, Finset.mem_univ]
     · simp only [Matrix.mul_apply, Finset.smul_sum, Finset.sum_smul, smul_smul]
       rw [Finset.sum_comm]
@@ -634,11 +634,11 @@ theorem rank_pow_quot [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsPrime
     fun i => Module.rank (R ⧸ p) { x // x ∈ map (Quotient.mk (P ^ e)) (P ^ i) }
       = (e - i) • Module.rank (R ⧸ p) (S ⧸ P)
   refine @Nat.decreasingInduction' Q i e (fun j lt_e _le_j ih => ?_) hi ?_
-  · dsimp only
+  · dsimp only [Q]
     rw [rank_pow_quot_aux f p P _ lt_e, ih, ← succ_nsmul, Nat.sub_succ, ← Nat.succ_eq_add_one,
       Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt lt_e)]
     assumption
-  · dsimp only
+  · dsimp only [Q]
     rw [Nat.sub_self, zero_nsmul, map_quotient_self]
     exact rank_bot (R ⧸ p) (S ⧸ P ^ e)
 #align ideal.rank_pow_quot Ideal.rank_pow_quot

Remove unnecessary "rw"s.

@@ -370,7 +370,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
     haveI := Ideal.Quotient.nontrivial hp
     calc
       Ideal.Quotient.mk p A.det = Matrix.det ((Ideal.Quotient.mk p).mapMatrix A) := by
-        rw [RingHom.map_det, RingHom.mapMatrix_apply]
+        rw [RingHom.map_det]
       _ = Matrix.det ((Ideal.Quotient.mk p).mapMatrix (Matrix.of A' - 1)) := rfl
       _ = Matrix.det fun i j =>
           (Ideal.Quotient.mk p) (A' i j) - (1 : Matrix (Fin n) (Fin n) (R ⧸ p)) i j := ?_

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>

@@ -575,8 +575,8 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
   have Pe_le_Pi : P ^ e ≤ P ^ i := Ideal.pow_le_pow_right hi.le
   rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
     sup_eq_left.mpr Pe_le_Pi] at hx
-  suffices hx' : x ∈ Ideal.span {a} ⊔ P ^ (i + 1)
-  · obtain ⟨y', hy', z, hz, rfl⟩ := Submodule.mem_sup.mp hx'
+  suffices hx' : x ∈ Ideal.span {a} ⊔ P ^ (i + 1) by
+    obtain ⟨y', hy', z, hz, rfl⟩ := Submodule.mem_sup.mp hx'
     obtain ⟨y, rfl⟩ := Ideal.mem_span_singleton.mp hy'
     refine ⟨Submodule.Quotient.mk y, ?_⟩
     simp only [Submodule.Quotient.quot_mk_eq_mk, quotientToQuotientRangePowQuotSucc_mk,

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -366,7 +366,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   -- Because `det A ≠ 0`, we have `span L {det A} = ⊤`.
   · rw [eq_comm, Submodule.restrictScalars_eq_top_iff, Ideal.span_singleton_eq_top]
     refine IsUnit.mk0 _ ((map_ne_zero_iff (algebraMap R L) hRL).mpr ?_)
-    refine @ne_zero_of_map _ _ _ _ _ _ (Ideal.Quotient.mk p) _ ?_
+    refine ne_zero_of_map (f := Ideal.Quotient.mk p) ?_
     haveI := Ideal.Quotient.nontrivial hp
     calc
       Ideal.Quotient.mk p A.det = Matrix.det ((Ideal.Quotient.mk p).mapMatrix A) := by

Rename lemmas to enable new-style dot notation or drop repeating FiniteDimensional.finiteDimensional_*. Restore old names as deprecated aliases.

@@ -748,7 +748,7 @@ theorem Factors.inertiaDeg_ne_zero [IsNoetherian R S] [p.IsMaximal]
 instance Factors.finiteDimensional_quotient_pow [IsNoetherian R S] [p.IsMaximal]
     (P : (factors (map (algebraMap R S) p)).toFinset) :
     FiniteDimensional (R ⧸ p) (S ⧸ (P : Ideal S) ^ ramificationIdx (algebraMap R S) p P) := by
-  refine FiniteDimensional.finiteDimensional_of_finrank ?_
+  refine .of_finrank_pos ?_
   rw [pos_iff_ne_zero, Factors.finrank_pow_ramificationIdx]
   exact mul_ne_zero (Factors.ramificationIdx_ne_zero p P) (Factors.inertiaDeg_ne_zero p P)
 #align ideal.factors.finite_dimensional_quotient_pow Ideal.Factors.finiteDimensional_quotient_pow

The files Mathlib.LinearAlgebra.FreeModule.Rank, Mathlib.LinearAlgebra.FreeModule.Finite.Rank, Mathlib.LinearAlgebra.Dimension and Mathlib.LinearAlgebra.Finrank were reorganized into a folder Mathlib.LinearAlgebra.Dimension, containing the following files

• Basic.lean: Contains the definition of Module.rank.
• Finrank.lean: Contains the definition of FiniteDimensional.finrank.
• StrongRankCondition.lean: Contains results about rank and finrank over rings satisfying strong rank condition
• Free.lean: Contains results about rank and finrank of free modules
• Finite.lean: Contains conditions or consequences for rank to be finite or zero
• Constructions.lean: Contains the calculation of the rank of various constructions.
• DivisionRing.lean: Contains results about rank and finrank of spaces over division rings.
• LinearMap.lean: Contains results about LinearMap.rank

API changes: IsNoetherian.rank_lt_aleph0 and FiniteDimensional.rank_lt_aleph0 are replaced with rank_lt_aleph0. Module.Free.finite_basis was renamed to Module.Finite.finite_basis. FiniteDimensional.finrank_eq_rank was renamed to finrank_eq_rank. rank_eq_cardinal_basis and rank_eq_cardinal_basis' were removed in favour of Basis.mk_eq_mk and Basis.mk_eq_mk''.

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

@@ -3,7 +3,6 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathlib.LinearAlgebra.FreeModule.Finite.Rank
 import Mathlib.RingTheory.DedekindDomain.Ideal
 
 #align_import number_theory.ramification_inertia from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"

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.

@@ -88,7 +88,7 @@ theorem ramificationIdx_spec {n : ℕ} (hle : map f p ≤ P ^ n) (hgt : ¬map f
   have : Q n := by
     intro k hk
     refine le_of_not_lt fun hnk => ?_
-    exact hgt (hk.trans (Ideal.pow_le_pow hnk))
+    exact hgt (hk.trans (Ideal.pow_le_pow_right hnk))
   rw [ramificationIdx_eq_find ⟨n, this⟩]
   refine le_antisymm (Nat.find_min' _ this) (le_of_not_gt fun h : Nat.find _ < n => ?_)
   obtain this' := Nat.find_spec ⟨n, this⟩
@@ -101,7 +101,7 @@ theorem ramificationIdx_lt {n : ℕ} (hgt : ¬map f p ≤ P ^ n) : ramificationI
   · rw [Nat.lt_succ_iff]
     have : ∀ k, map f p ≤ P ^ k → k ≤ n := by
       refine fun k hk => le_of_not_lt fun hnk => ?_
-      exact hgt (hk.trans (Ideal.pow_le_pow hnk))
+      exact hgt (hk.trans (Ideal.pow_le_pow_right hnk))
     rw [ramificationIdx_eq_find ⟨n, this⟩]
     exact Nat.find_min' ⟨n, this⟩ this
 #align ideal.ramification_idx_lt Ideal.ramificationIdx_lt
@@ -486,7 +486,7 @@ theorem Quotient.algebraMap_quotient_of_ramificationIdx_neZero (x : R) :
 def powQuotSuccInclusion (i : ℕ) :
     Ideal.map (Ideal.Quotient.mk (P ^ e)) (P ^ (i + 1)) →ₗ[R ⧸ p]
     Ideal.map (Ideal.Quotient.mk (P ^ e)) (P ^ i) where
-  toFun x := ⟨x, Ideal.map_mono (Ideal.pow_le_pow i.le_succ) x.2⟩
+  toFun x := ⟨x, Ideal.map_mono (Ideal.pow_le_pow_right i.le_succ) x.2⟩
   map_add' _ _ := rfl
   map_smul' _ _ := rfl
 #align ideal.pow_quot_succ_inclusion Ideal.powQuotSuccInclusion
@@ -553,7 +553,7 @@ theorem quotientToQuotientRangePowQuotSucc_injective [IsDomain S] [IsDedekindDom
     Function.Injective (quotientToQuotientRangePowQuotSucc f p P a_mem) := fun x =>
   Quotient.inductionOn' x fun x y =>
     Quotient.inductionOn' y fun y h => by
-      have Pe_le_Pi1 : P ^ e ≤ P ^ (i + 1) := Ideal.pow_le_pow hi
+      have Pe_le_Pi1 : P ^ e ≤ P ^ (i + 1) := Ideal.pow_le_pow_right hi
       simp only [Submodule.Quotient.mk''_eq_mk, quotientToQuotientRangePowQuotSucc_mk,
         Submodule.Quotient.eq, LinearMap.mem_range, Subtype.ext_iff, Subtype.coe_mk,
         Submodule.coe_sub] at h ⊢
@@ -573,7 +573,7 @@ theorem quotientToQuotientRangePowQuotSucc_surjective [IsDomain S] [IsDedekindDo
     (a_not_mem : a ∉ P ^ (i + 1)) :
     Function.Surjective (quotientToQuotientRangePowQuotSucc f p P a_mem) := by
   rintro ⟨⟨⟨x⟩, hx⟩⟩
-  have Pe_le_Pi : P ^ e ≤ P ^ i := Ideal.pow_le_pow hi.le
+  have Pe_le_Pi : P ^ e ≤ P ^ i := Ideal.pow_le_pow_right hi.le
   rw [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.mk_eq_mk, Ideal.mem_quotient_iff_mem_sup,
     sup_eq_left.mpr Pe_le_Pi] at hx
   suffices hx' : x ∈ Ideal.span {a} ⊔ P ^ (i + 1)
@@ -606,7 +606,7 @@ noncomputable def quotientRangePowQuotSuccInclusionEquiv [IsDomain S] [IsDedekin
       ≃ₗ[R ⧸ p] S ⧸ P := by
   choose a a_mem a_not_mem using
     SetLike.exists_of_lt
-      (Ideal.strictAnti_pow P hP (Ideal.IsPrime.ne_top inferInstance) (le_refl i.succ))
+      (Ideal.pow_right_strictAnti P hP (Ideal.IsPrime.ne_top inferInstance) (le_refl i.succ))
   refine' (LinearEquiv.ofBijective _ ⟨_, _⟩).symm
   · exact quotientToQuotientRangePowQuotSucc f p P a_mem
   · exact quotientToQuotientRangePowQuotSucc_injective f p P hi a_mem a_not_mem

Two simple lemmas, smul_ite_zero, and ite_smul_zero. Also delete Finset.sum_univ_ite since it is now provable by simp thanks to these.

Rename and turn around the following to match the direction that simp goes in:

• ite_mul_zero_left → ite_zero_mul
• ite_mul_zero_right → mul_ite_zero
• ite_and_mul_zero → ite_zero_mul_ite_zero

@@ -333,8 +333,8 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   let B := A.adjugate
   have A_smul : ∀ i, ∑ j, A i j • a j = 0 := by
     intros
-    simp only [Matrix.sub_apply, Matrix.of_apply, ne_eq, Matrix.one_apply, sub_smul,
-      Finset.sum_sub_distrib, hA', Finset.sum_univ_ite, sub_self]
+    simp [Matrix.sub_apply, Matrix.of_apply, ne_eq, Matrix.one_apply, sub_smul,
+      Finset.sum_sub_distrib, hA', sub_self]
   -- since `span S {det A} / M = 0`.
   have d_smul : ∀ i, A.det • a i = 0 := by
     intro i

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>

@@ -391,7 +391,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
     haveI : NoZeroSMulDivisors R L := NoZeroSMulDivisors.of_algebraMap_injective hRL
     rw [← IsFractionRing.isAlgebraic_iff' R S]
     intro x
-    exact IsIntegral.isAlgebraic _ (isIntegral_of_noetherian inferInstance _)
+    exact (isIntegral_of_noetherian inferInstance _).isAlgebraic
 #align ideal.finrank_quotient_map.span_eq_top Ideal.FinrankQuotientMap.span_eq_top
 
 variable (K L)

Also _root_.map_smul when in the neighbourhood.

@@ -275,12 +275,12 @@ theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedek
     exact hgI _ (hg' j hjs)
   refine ⟨fun i => algebraMap R S (g' i), ?_, j, hjs, hgI⟩
   have eq : f (∑ i in s, g' i • b i) = 0 := by
-    rw [LinearMap.map_sum, ← smul_zero a, ← eq, Finset.smul_sum]
+    rw [map_sum, ← smul_zero a, ← eq, Finset.smul_sum]
     refine Finset.sum_congr rfl ?_
     intro i hi
     rw [LinearMap.map_smul, ← IsScalarTower.algebraMap_smul K, hg' i hi, ← smul_assoc,
       smul_eq_mul, Function.comp_apply]
-  simp only [IsScalarTower.algebraMap_smul, ← LinearMap.map_smul, ← LinearMap.map_sum,
+  simp only [IsScalarTower.algebraMap_smul, ← map_smul, ← map_sum,
     (f.map_eq_zero_iff hf).mp eq, LinearMap.map_zero, (· ∘ ·)]
 #align ideal.finrank_quotient_map.linear_independent_of_nontrivial Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial
 

@@ -454,7 +454,7 @@ local notation "e" => ramificationIdx f p P
 /-- `R / p` has a canonical map to `S / (P ^ e)`, where `e` is the ramification index
 of `P` over `p`. -/
 noncomputable instance Quotient.algebraQuotientPowRamificationIdx : Algebra (R ⧸ p) (S ⧸ P ^ e) :=
-  Quotient.algebraQuotientOfLeComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)
+  Quotient.algebraQuotientOfLEComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)
 #align ideal.quotient.algebra_quotient_pow_ramification_idx Ideal.Quotient.algebraQuotientPowRamificationIdx
 
 @[simp]
@@ -469,7 +469,7 @@ variable [hfp : NeZero (ramificationIdx f p P)]
 This can't be an instance since the map `f : R → S` is generally not inferrable.
 -/
 def Quotient.algebraQuotientOfRamificationIdxNeZero : Algebra (R ⧸ p) (S ⧸ P) :=
-  Quotient.algebraQuotientOfLeComap (le_comap_of_ramificationIdx_ne_zero hfp.out)
+  Quotient.algebraQuotientOfLEComap (le_comap_of_ramificationIdx_ne_zero hfp.out)
 #align ideal.quotient.algebra_quotient_of_ramification_idx_ne_zero Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero
 
 set_option synthInstance.checkSynthOrder false -- Porting note: this is okay by the remark below

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

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

@@ -679,7 +679,7 @@ theorem finrank_prime_pow_ramificationIdx [IsDomain S] [IsDedekindDomain S] (hP0
     rw [finrank_eq_rank', Nat.cast_mul, finrank_eq_rank', hdim, nsmul_eq_mul]
   have hPe := mt (finiteDimensional_iff_of_rank_eq_nsmul he hdim).mp hP
   simp only [finrank_of_infinite_dimensional hP, finrank_of_infinite_dimensional hPe,
-    MulZeroClass.mul_zero]
+    mul_zero]
 #align ideal.finrank_prime_pow_ramification_idx Ideal.finrank_prime_pow_ramificationIdx
 
 end FactLeComap

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -339,7 +339,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   have d_smul : ∀ i, A.det • a i = 0 := by
     intro i
     calc
-      A.det • a i = ∑ j, (B ⬝ A) i j • a j := ?_
+      A.det • a i = ∑ j, (B * A) i j • a j := ?_
       _ = ∑ k, B i k • ∑ j, A k j • a j := ?_
       _ = 0 := Finset.sum_eq_zero fun k _ => ?_
     · simp only [Matrix.adjugate_mul, Matrix.smul_apply, Matrix.one_apply, smul_eq_mul, ite_true,

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

This has nice performance benefits.

@@ -229,11 +229,11 @@ open scoped nonZeroDivisors
 
 variable [Algebra R S]
 
-variable {K : Type _} [Field K] [Algebra R K] [hRK : IsFractionRing R K]
+variable {K : Type*} [Field K] [Algebra R K] [hRK : IsFractionRing R K]
 
-variable {L : Type _} [Field L] [Algebra S L] [IsFractionRing S L]
+variable {L : Type*} [Field L] [Algebra S L] [IsFractionRing S L]
 
-variable {V V' V'' : Type _}
+variable {V V' V'' : Type*}
 
 variable [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
@@ -253,7 +253,7 @@ The statement we prove is actually slightly more general:
 -/
 theorem FinrankQuotientMap.linearIndependent_of_nontrivial [IsDomain R] [IsDedekindDomain R]
     (hRS : RingHom.ker (algebraMap R S) ≠ ⊤) (f : V'' →ₗ[R] V) (hf : Function.Injective f)
-    (f' : V'' →ₗ[R] V') {ι : Type _} {b : ι → V''} (hb' : LinearIndependent S (f' ∘ b)) :
+    (f' : V'' →ₗ[R] V') {ι : Type*} {b : ι → V''} (hb' : LinearIndependent S (f' ∘ b)) :
     LinearIndependent K (f ∘ b) := by
   contrapose! hb' with hb
   -- Informally, if we have a nontrivial linear dependence with coefficients `g` in `K`,
@@ -810,7 +810,7 @@ for `P` ranging over the primes lying over `p`, `∑ P, e P * f P = [Frac(S) : F
 here `S` is a finite `R`-module (and thus `Frac(S) : Frac(R)` is a finite extension) and `p`
 is maximal.
 -/
-theorem sum_ramification_inertia (K L : Type _) [Field K] [Field L] [IsDomain R]
+theorem sum_ramification_inertia (K L : Type*) [Field K] [Field L] [IsDomain R]
     [IsDedekindDomain R] [Algebra R K] [IsFractionRing R K] [Algebra S L] [IsFractionRing S L]
     [Algebra K L] [Algebra R L] [IsScalarTower R S L] [IsScalarTower R K L] [IsNoetherian R S]
     [IsIntegralClosure S R L] [p.IsMaximal] (hp0 : p ≠ ⊥) :

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

@@ -621,7 +621,7 @@ theorem rank_pow_quot_aux [IsDomain S] [IsDedekindDomain S] [p.IsMaximal] [P.IsP
       Module.rank (R ⧸ p) (S ⧸ P) +
         Module.rank (R ⧸ p) (Ideal.map (Ideal.Quotient.mk (P ^ e)) (P ^ (i + 1))) := by
   letI : Field (R ⧸ p) := Ideal.Quotient.field _
-  rw [rank_eq_of_injective _ (powQuotSuccInclusion_injective f p P i),
+  rw [← rank_range_of_injective _ (powQuotSuccInclusion_injective f p P i),
     (quotientRangePowQuotSuccInclusionEquiv f p P hP0 hi).symm.rank_eq]
   exact (rank_quotient_add_rank (LinearMap.range (powQuotSuccInclusion f p P i))).symm
 #align ideal.rank_pow_quot_aux Ideal.rank_pow_quot_aux

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.ramification_inertia
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.FreeModule.Finite.Rank
 import Mathlib.RingTheory.DedekindDomain.Ideal
 
+#align_import number_theory.ramification_inertia from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
+
 /-!
 # Ramification index and inertia degree
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -87,7 +87,7 @@ theorem ramificationIdx_eq_zero (h : ∀ n : ℕ, ∃ k, map f p ≤ P ^ k ∧ n
 
 theorem ramificationIdx_spec {n : ℕ} (hle : map f p ≤ P ^ n) (hgt : ¬map f p ≤ P ^ (n + 1)) :
     ramificationIdx f p P = n := by
-  let Q : ℕ → Prop := fun m =>  ∀ k : ℕ, map f p ≤ P ^ k → k ≤ m
+  let Q : ℕ → Prop := fun m => ∀ k : ℕ, map f p ≤ P ^ k → k ≤ m
   have : Q n := by
     intro k hk
     refine le_of_not_lt fun hnk => ?_
@@ -219,7 +219,7 @@ theorem inertiaDeg_algebraMap [Algebra R S] [Algebra (R ⧸ p) (S ⧸ P)]
   refine' Algebra.algebra_ext _ _ fun x' => Quotient.inductionOn' x' fun x => _
   change Ideal.Quotient.lift p _ _ (Ideal.Quotient.mk p x) = algebraMap _ _ (Ideal.Quotient.mk p x)
   rw [Ideal.Quotient.lift_mk, ← Ideal.Quotient.algebraMap_eq P, ← IsScalarTower.algebraMap_eq,
-    ← Ideal.Quotient.algebraMap_eq,  ← IsScalarTower.algebraMap_apply]
+    ← Ideal.Quotient.algebraMap_eq, ← IsScalarTower.algebraMap_apply]
 #align ideal.inertia_deg_algebra_map Ideal.inertiaDeg_algebraMap
 
 end DecEq

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -322,7 +322,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
         rw [Submodule.map_smul'', Submodule.map_top, M.range_mkQ]
       _ = ⊤ := by rw [Ideal.smul_top_eq_map, (Submodule.map_mkQ_eq_top M _).mpr hb']
   -- we can write the elements of `a` as `p`-linear combinations of other elements of `a`.
-  have exists_sum : ∀ x : S ⧸ M, ∃ a' : Fin n → R, (∀ i, a' i ∈ p) ∧ (∑ i, a' i • a i) = x := by
+  have exists_sum : ∀ x : S ⧸ M, ∃ a' : Fin n → R, (∀ i, a' i ∈ p) ∧ ∑ i, a' i • a i = x := by
     intro x
     obtain ⟨a'', ha'', hx⟩ := (Submodule.mem_ideal_smul_span_iff_exists_sum p a x).1
       (by { rw [ha, smul_top_eq]; exact Submodule.mem_top } :
@@ -334,7 +334,7 @@ theorem FinrankQuotientMap.span_eq_top [IsDomain R] [IsDomain S] [Algebra K L] [
   -- This gives us a(n invertible) matrix `A` such that `det A ∈ (M = span R b)`,
   let A : Matrix (Fin n) (Fin n) R := Matrix.of A' - 1
   let B := A.adjugate
-  have A_smul : ∀ i, (∑ j, A i j • a j) = 0 := by
+  have A_smul : ∀ i, ∑ j, A i j • a j = 0 := by
     intros
     simp only [Matrix.sub_apply, Matrix.of_apply, ne_eq, Matrix.one_apply, sub_smul,
       Finset.sum_sub_distrib, hA', Finset.sum_univ_ite, sub_self]