ring_theory.valuation.valuation_subring ⟷ Mathlib.RingTheory.Valuation.ValuationSubring

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

@@ -772,8 +772,8 @@ def principalUnitGroup : Subgroup Kˣ
   hMul_mem' := by
     intro a b ha hb
     refine' lt_of_le_of_lt _ (max_lt hb ha)
-    rw [← one_mul (A.valuation (b - 1)), ← A.valuation.map_one_add_of_lt ha, add_sub_cancel'_right,
-      ← Valuation.map_mul, mul_sub_one, ← sub_add_sub_cancel]
+    rw [← one_mul (A.valuation (b - 1)), ← A.valuation.map_one_add_of_lt ha, add_sub_cancel, ←
+      Valuation.map_mul, mul_sub_one, ← sub_add_sub_cancel]
     exact A.valuation.map_add _ _
   one_mem' := by simp
   inv_mem' := by
@@ -782,14 +782,14 @@ def principalUnitGroup : Subgroup Kˣ
     conv =>
       lhs
       rw [← mul_one (A.valuation _), ← A.valuation.map_one_add_of_lt ha]
-    rwa [add_sub_cancel'_right, ← Valuation.map_mul, sub_mul, Units.inv_mul, ← neg_sub, one_mul,
+    rwa [add_sub_cancel, ← Valuation.map_mul, sub_mul, Units.inv_mul, ← neg_sub, one_mul,
       Valuation.map_neg]
 #align valuation_subring.principal_unit_group ValuationSubring.principalUnitGroup
 -/
 
 #print ValuationSubring.principal_units_le_units /-
 theorem principal_units_le_units : A.principalUnitGroup ≤ A.unitGroup := fun a h => by
-  simpa only [add_sub_cancel'_right] using A.valuation.map_one_add_of_lt h
+  simpa only [add_sub_cancel] using A.valuation.map_one_add_of_lt h
 #align valuation_subring.principal_units_le_units ValuationSubring.principal_units_le_units
 -/
 
@@ -810,8 +810,8 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
     by_cases h_2 : x⁻¹ + 1 = 0
     · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
       simpa only [h_2] using B.neg_mem _ B.one_mem
-    · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ← add_sub_cancel x⁻¹, ←
-        Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx ⊢
+    · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ←
+        add_sub_cancel_right x⁻¹, ← Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx ⊢
       simpa only [hx] using @h (Units.mk0 (x⁻¹ + 1) h_2)
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx

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

@@ -151,7 +151,7 @@ instance : ValuationRing A
     by_cases (a : K) = 0; · use 0; right; ext; simp [h]
     cases' A.mem_or_inv_mem (a / b) with hh hh
     · use⟨a / b, hh⟩; right; ext; field_simp; ring
-    · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh 
+    · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh
       use⟨b / a, hh⟩; left; ext; field_simp; ring
 
 instance : Algebra A K :=
@@ -246,7 +246,7 @@ theorem valuation_unit (a : Aˣ) : A.Valuation a = 1 := by
 theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.Valuation a = 1 :=
   ⟨fun h => A.valuation_unit h.Unit, fun h =>
     by
-    have ha : (a : K) ≠ 0 := by intro c; rw [c, A.valuation.map_zero] at h ; exact zero_ne_one h
+    have ha : (a : K) ≠ 0 := by intro c; rw [c, A.valuation.map_zero] at h; exact zero_ne_one h
     have ha' : (a : K)⁻¹ ∈ A := by rw [← valuation_le_one_iff, map_inv₀, h, inv_one]
     apply isUnit_of_mul_eq_one a ⟨a⁻¹, ha'⟩; ext; field_simp⟩
 #align valuation_subring.valuation_eq_one_iff ValuationSubring.valuation_eq_one_iff
@@ -423,7 +423,7 @@ theorem ofPrime_idealOfLE (R S : ValuationSubring K) (h : R ≤ S) :
   · rintro ⟨a, r, hr, rfl⟩; apply mul_mem; · exact h a.2
     · rw [← valuation_le_one_iff, map_inv₀, ← inv_one, inv_le_inv₀]
       · exact not_lt.1 ((not_iff_not.2 <| valuation_lt_one_iff S _).1 hr)
-      · intro hh; erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh 
+      · intro hh; erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh
         apply hr; rw [hh]; apply Ideal.zero_mem (R.ideal_of_le S h)
       · exact one_ne_zero
   · intro hx; by_cases hr : x ∈ R; · exact R.le_of_prime _ hr
@@ -449,8 +449,8 @@ theorem idealOfLE_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
     idealOfLE A S hS ≤ idealOfLE A R hR := fun x hx =>
   (valuation_lt_one_iff R _).2
     (by
-      by_contra c; push_neg at c ; replace c := monotone_map_of_le R S h c
-      rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c 
+      by_contra c; push_neg at c; replace c := monotone_map_of_le R S h c
+      rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
 #align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLE_le_of_le
 -/
@@ -475,7 +475,7 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
     map_rel_iff' := fun P Q =>
       ⟨fun h => by
         have := ideal_of_le_le_of_le A _ _ _ _ h
-        iterate 2 erw [ideal_of_le_of_prime] at this 
+        iterate 2 erw [ideal_of_le_of_prime] at this
         exact this, fun h => by apply of_prime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 -/
@@ -612,7 +612,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
   by
   constructor
   · intro h x hx
-    rw [← A.valuation_le_one_iff x, le_iff_lt_or_eq] at hx 
+    rw [← A.valuation_le_one_iff x, le_iff_lt_or_eq] at hx
     by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : 1 + x = 0
     · simp only [← add_eq_zero_iff_neg_eq.1 h_2, neg_mem _ _ (one_mem _)]
@@ -624,7 +624,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
     · have := h (show Units.mk0 x h_1 ∈ A.unit_group from hx)
       refine' SetLike.coe_mem (B.unit_group_mul_equiv ⟨_, this⟩ : B)
   · rintro h x (hx : A.valuation x = 1)
-    apply_fun A.map_of_le B h at hx 
+    apply_fun A.map_of_le B h at hx
     simpa using hx
 #align valuation_subring.unit_group_le_unit_group ValuationSubring.unitGroup_le_unitGroup
 -/
@@ -808,7 +808,7 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
   · intro h x hx
     by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : x⁻¹ + 1 = 0
-    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2 
+    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
       simpa only [h_2] using B.neg_mem _ B.one_mem
     · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ← add_sub_cancel x⁻¹, ←
         Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx ⊢

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Junyan Xu, Jack McKoen
 -/
-import Mathbin.RingTheory.Valuation.ValuationRing
-import Mathbin.RingTheory.Localization.AsSubring
-import Mathbin.RingTheory.Subring.Pointwise
-import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
+import RingTheory.Valuation.ValuationRing
+import RingTheory.Localization.AsSubring
+import RingTheory.Subring.Pointwise
+import AlgebraicGeometry.PrimeSpectrum.Basic
 
 #align_import ring_theory.valuation.valuation_subring from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
 

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

@@ -88,7 +88,7 @@ theorem add_mem (x y : K) : x ∈ A → y ∈ A → x + y ∈ A :=
 
 #print ValuationSubring.mul_mem /-
 theorem mul_mem (x y : K) : x ∈ A → y ∈ A → x * y ∈ A :=
-  A.toSubring.mul_mem
+  A.toSubring.hMul_mem
 #align valuation_subring.mul_mem ValuationSubring.mul_mem
 -/
 
@@ -109,7 +109,7 @@ instance : SubringClass (ValuationSubring K) K
   zero_mem := zero_mem
   add_mem := add_mem
   one_mem := one_mem
-  mul_mem := mul_mem
+  hMul_mem := mul_mem
   neg_mem := neg_mem
 
 #print ValuationSubring.toSubring_injective /-
@@ -666,7 +666,7 @@ section nonunits
 def nonunits : Subsemigroup K
     where
   carrier := {x | A.Valuation x < 1}
-  mul_mem' a b ha hb := (mul_lt_mul₀ ha hb).trans_eq <| mul_one _
+  hMul_mem' a b ha hb := (mul_lt_mul₀ ha hb).trans_eq <| mul_one _
 #align valuation_subring.nonunits ValuationSubring.nonunits
 -/
 
@@ -769,7 +769,7 @@ section PrincipalUnitGroup
 def principalUnitGroup : Subgroup Kˣ
     where
   carrier := {x | A.Valuation (x - 1) < 1}
-  mul_mem' := by
+  hMul_mem' := by
     intro a b ha hb
     refine' lt_of_le_of_lt _ (max_lt hb ha)
     rw [← one_mul (A.valuation (b - 1)), ← A.valuation.map_one_add_of_lt ha, add_sub_cancel'_right,

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

@@ -150,9 +150,9 @@ instance : ValuationRing A
     by_cases (b : K) = 0; · use 0; left; ext; simp [h]
     by_cases (a : K) = 0; · use 0; right; ext; simp [h]
     cases' A.mem_or_inv_mem (a / b) with hh hh
-    · use ⟨a / b, hh⟩; right; ext; field_simp; ring
+    · use⟨a / b, hh⟩; right; ext; field_simp; ring
     · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh 
-      use ⟨b / a, hh⟩; left; ext; field_simp; ring
+      use⟨b / a, hh⟩; left; ext; field_simp; ring
 
 instance : Algebra A K :=
   show Algebra A.toSubring K by infer_instance
@@ -169,9 +169,9 @@ instance : IsFractionRing A K
   map_units := fun ⟨y, hy⟩ =>
     (Units.mk0 (y : K) fun c => nonZeroDivisors.ne_zero hy <| Subtype.ext c).IsUnit
   surj z := by
-    by_cases z = 0; · use (0, 1); simp [h]
+    by_cases z = 0; · use(0, 1); simp [h]
     cases' A.mem_or_inv_mem z with hh hh
-    · use (⟨z, hh⟩, 1); simp
+    · use(⟨z, hh⟩, 1); simp
     · refine' ⟨⟨1, ⟨⟨_, hh⟩, _⟩⟩, mul_inv_cancel h⟩
       exact mem_nonZeroDivisors_iff_ne_zero.2 fun c => h (inv_eq_zero.mp (congr_arg coe c))
   eq_iff_exists a b :=

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Junyan Xu, Jack McKoen
-
-! This file was ported from Lean 3 source module ring_theory.valuation.valuation_subring
-! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Valuation.ValuationRing
 import Mathbin.RingTheory.Localization.AsSubring
 import Mathbin.RingTheory.Subring.Pointwise
 import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 
+#align_import ring_theory.valuation.valuation_subring from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
+
 /-!
 
 # Valuation subrings of a field

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

@@ -971,21 +971,21 @@ open scoped Pointwise
 
 variable {G : Type _} [Group G] [MulSemiringAction G K]
 
-#print ValuationSubring.pointwiseHasSmul /-
+#print ValuationSubring.pointwiseHasSMul /-
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale. -/
-def pointwiseHasSmul : SMul G (ValuationSubring K)
+def pointwiseHasSMul : SMul G (ValuationSubring K)
     where smul g
     S :=-- TODO: if we add `valuation_subring.map` at a later date, we should use it here
     { g • S.toSubring with
       mem_or_inv_mem' := fun x =>
         (mem_or_inv_mem S (g⁻¹ • x)).imp Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr fun h =>
           Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr <| by rwa [smul_inv''] }
-#align valuation_subring.pointwise_has_smul ValuationSubring.pointwiseHasSmul
+#align valuation_subring.pointwise_has_smul ValuationSubring.pointwiseHasSMul
 -/
 
-scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSmul
+scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSMul
 
 open scoped Pointwise
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Junyan Xu, Jack McKoen
 
 ! This file was ported from Lean 3 source module ring_theory.valuation.valuation_subring
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 
 # Valuation subrings of a field
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Projects
 
 The order structure on `valuation_subring K`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -30,11 +30,13 @@ noncomputable section
 
 variable (K : Type _) [Field K]
 
+#print ValuationSubring /-
 /-- A valuation subring of a field `K` is a subring `A` such that for every `x : K`,
 either `x ∈ A` or `x⁻¹ ∈ A`. -/
 structure ValuationSubring extends Subring K where
   mem_or_inv_mem' : ∀ x : K, x ∈ carrier ∨ x⁻¹ ∈ carrier
 #align valuation_subring ValuationSubring
+-/
 
 namespace ValuationSubring
 
@@ -45,44 +47,62 @@ instance : SetLike (ValuationSubring K) K
   coe A := A.toSubring
   coe_injective' := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ _; congr
 
+#print ValuationSubring.mem_carrier /-
 @[simp]
 theorem mem_carrier (x : K) : x ∈ A.carrier ↔ x ∈ A :=
   Iff.refl _
 #align valuation_subring.mem_carrier ValuationSubring.mem_carrier
+-/
 
+#print ValuationSubring.mem_toSubring /-
 @[simp]
 theorem mem_toSubring (x : K) : x ∈ A.toSubring ↔ x ∈ A :=
   Iff.refl _
 #align valuation_subring.mem_to_subring ValuationSubring.mem_toSubring
+-/
 
+#print ValuationSubring.ext /-
 @[ext]
 theorem ext (A B : ValuationSubring K) (h : ∀ x, x ∈ A ↔ x ∈ B) : A = B :=
   SetLike.ext h
 #align valuation_subring.ext ValuationSubring.ext
+-/
 
+#print ValuationSubring.zero_mem /-
 theorem zero_mem : (0 : K) ∈ A :=
   A.toSubring.zero_mem
 #align valuation_subring.zero_mem ValuationSubring.zero_mem
+-/
 
+#print ValuationSubring.one_mem /-
 theorem one_mem : (1 : K) ∈ A :=
   A.toSubring.one_mem
 #align valuation_subring.one_mem ValuationSubring.one_mem
+-/
 
+#print ValuationSubring.add_mem /-
 theorem add_mem (x y : K) : x ∈ A → y ∈ A → x + y ∈ A :=
   A.toSubring.add_mem
 #align valuation_subring.add_mem ValuationSubring.add_mem
+-/
 
+#print ValuationSubring.mul_mem /-
 theorem mul_mem (x y : K) : x ∈ A → y ∈ A → x * y ∈ A :=
   A.toSubring.mul_mem
 #align valuation_subring.mul_mem ValuationSubring.mul_mem
+-/
 
+#print ValuationSubring.neg_mem /-
 theorem neg_mem (x : K) : x ∈ A → -x ∈ A :=
   A.toSubring.neg_mem
 #align valuation_subring.neg_mem ValuationSubring.neg_mem
+-/
 
+#print ValuationSubring.mem_or_inv_mem /-
 theorem mem_or_inv_mem (x : K) : x ∈ A ∨ x⁻¹ ∈ A :=
   A.mem_or_inv_mem' _
 #align valuation_subring.mem_or_inv_mem ValuationSubring.mem_or_inv_mem
+-/
 
 instance : SubringClass (ValuationSubring K) K
     where
@@ -92,9 +112,11 @@ instance : SubringClass (ValuationSubring K) K
   mul_mem := mul_mem
   neg_mem := neg_mem
 
+#print ValuationSubring.toSubring_injective /-
 theorem toSubring_injective : Function.Injective (toSubring : ValuationSubring K → Subring K) :=
   fun x y h => by cases x; cases y; congr
 #align valuation_subring.to_subring_injective ValuationSubring.toSubring_injective
+-/
 
 instance : CommRing A :=
   show CommRing A.toSubring by infer_instance
@@ -105,12 +127,16 @@ instance : IsDomain A :=
 instance : Top (ValuationSubring K) :=
   Top.mk <| { (⊤ : Subring K) with mem_or_inv_mem' := fun x => Or.inl trivial }
 
+#print ValuationSubring.mem_top /-
 theorem mem_top (x : K) : x ∈ (⊤ : ValuationSubring K) :=
   trivial
 #align valuation_subring.mem_top ValuationSubring.mem_top
+-/
 
+#print ValuationSubring.le_top /-
 theorem le_top : A ≤ ⊤ := fun a ha => mem_top _
 #align valuation_subring.le_top ValuationSubring.le_top
+-/
 
 instance : OrderTop (ValuationSubring K) where
   top := ⊤
@@ -131,10 +157,12 @@ instance : ValuationRing A
 instance : Algebra A K :=
   show Algebra A.toSubring K by infer_instance
 
+#print ValuationSubring.algebraMap_apply /-
 @[simp]
 theorem algebraMap_apply (a : A) : algebraMap A K a = a :=
   rfl
 #align valuation_subring.algebra_map_apply ValuationSubring.algebraMap_apply
+-/
 
 instance : IsFractionRing A K
     where
@@ -150,50 +178,71 @@ instance : IsFractionRing A K
     ⟨fun h => ⟨1, by ext; simpa using h⟩, fun ⟨c, h⟩ =>
       congr_arg coe ((mul_eq_mul_left_iff.1 h).resolve_right (nonZeroDivisors.ne_zero c.2))⟩
 
+#print ValuationSubring.ValueGroup /-
 /-- The value group of the valuation associated to `A`. Note: it is actually a group with zero. -/
 def ValueGroup :=
   ValuationRing.ValueGroup A K
 deriving LinearOrderedCommGroupWithZero
 #align valuation_subring.value_group ValuationSubring.ValueGroup
+-/
 
+#print ValuationSubring.valuation /-
 /-- Any valuation subring of `K` induces a natural valuation on `K`. -/
 def valuation : Valuation K A.ValueGroup :=
   ValuationRing.valuation A K
 #align valuation_subring.valuation ValuationSubring.valuation
+-/
 
+#print ValuationSubring.inhabitedValueGroup /-
 instance inhabitedValueGroup : Inhabited A.ValueGroup :=
   ⟨A.Valuation 0⟩
 #align valuation_subring.inhabited_value_group ValuationSubring.inhabitedValueGroup
+-/
 
+#print ValuationSubring.valuation_le_one /-
 theorem valuation_le_one (a : A) : A.Valuation a ≤ 1 :=
   (ValuationRing.mem_integer_iff A K _).2 ⟨a, rfl⟩
 #align valuation_subring.valuation_le_one ValuationSubring.valuation_le_one
+-/
 
+#print ValuationSubring.mem_of_valuation_le_one /-
 theorem mem_of_valuation_le_one (x : K) (h : A.Valuation x ≤ 1) : x ∈ A :=
   let ⟨a, ha⟩ := (ValuationRing.mem_integer_iff A K x).1 h
   ha ▸ a.2
 #align valuation_subring.mem_of_valuation_le_one ValuationSubring.mem_of_valuation_le_one
+-/
 
+#print ValuationSubring.valuation_le_one_iff /-
 theorem valuation_le_one_iff (x : K) : A.Valuation x ≤ 1 ↔ x ∈ A :=
   ⟨mem_of_valuation_le_one _ _, fun ha => A.valuation_le_one ⟨x, ha⟩⟩
 #align valuation_subring.valuation_le_one_iff ValuationSubring.valuation_le_one_iff
+-/
 
+#print ValuationSubring.valuation_eq_iff /-
 theorem valuation_eq_iff (x y : K) : A.Valuation x = A.Valuation y ↔ ∃ a : Aˣ, (a : K) * y = x :=
   Quotient.eq''
 #align valuation_subring.valuation_eq_iff ValuationSubring.valuation_eq_iff
+-/
 
+#print ValuationSubring.valuation_le_iff /-
 theorem valuation_le_iff (x y : K) : A.Valuation x ≤ A.Valuation y ↔ ∃ a : A, (a : K) * y = x :=
   Iff.rfl
 #align valuation_subring.valuation_le_iff ValuationSubring.valuation_le_iff
+-/
 
+#print ValuationSubring.valuation_surjective /-
 theorem valuation_surjective : Function.Surjective A.Valuation :=
   surjective_quot_mk _
 #align valuation_subring.valuation_surjective ValuationSubring.valuation_surjective
+-/
 
+#print ValuationSubring.valuation_unit /-
 theorem valuation_unit (a : Aˣ) : A.Valuation a = 1 := by
   rw [← A.valuation.map_one, valuation_eq_iff]; use a; simp
 #align valuation_subring.valuation_unit ValuationSubring.valuation_unit
+-/
 
+#print ValuationSubring.valuation_eq_one_iff /-
 theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.Valuation a = 1 :=
   ⟨fun h => A.valuation_unit h.Unit, fun h =>
     by
@@ -201,34 +250,45 @@ theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.Valuation a = 1 :=
     have ha' : (a : K)⁻¹ ∈ A := by rw [← valuation_le_one_iff, map_inv₀, h, inv_one]
     apply isUnit_of_mul_eq_one a ⟨a⁻¹, ha'⟩; ext; field_simp⟩
 #align valuation_subring.valuation_eq_one_iff ValuationSubring.valuation_eq_one_iff
+-/
 
+#print ValuationSubring.valuation_lt_one_or_eq_one /-
 theorem valuation_lt_one_or_eq_one (a : A) : A.Valuation a < 1 ∨ A.Valuation a = 1 :=
   lt_or_eq_of_le (A.valuation_le_one a)
 #align valuation_subring.valuation_lt_one_or_eq_one ValuationSubring.valuation_lt_one_or_eq_one
+-/
 
+#print ValuationSubring.valuation_lt_one_iff /-
 theorem valuation_lt_one_iff (a : A) : a ∈ LocalRing.maximalIdeal A ↔ A.Valuation a < 1 :=
   by
   rw [LocalRing.mem_maximalIdeal]
   dsimp [nonunits]; rw [valuation_eq_one_iff]
   exact (A.valuation_le_one a).lt_iff_ne.symm
 #align valuation_subring.valuation_lt_one_iff ValuationSubring.valuation_lt_one_iff
+-/
 
+#print ValuationSubring.ofSubring /-
 /-- A subring `R` of `K` such that for all `x : K` either `x ∈ R` or `x⁻¹ ∈ R` is
   a valuation subring of `K`. -/
 def ofSubring (R : Subring K) (hR : ∀ x : K, x ∈ R ∨ x⁻¹ ∈ R) : ValuationSubring K :=
   { R with mem_or_inv_mem' := hR }
 #align valuation_subring.of_subring ValuationSubring.ofSubring
+-/
 
+#print ValuationSubring.mem_ofSubring /-
 @[simp]
 theorem mem_ofSubring (R : Subring K) (hR : ∀ x : K, x ∈ R ∨ x⁻¹ ∈ R) (x : K) :
     x ∈ ofSubring R hR ↔ x ∈ R :=
   Iff.refl _
 #align valuation_subring.mem_of_subring ValuationSubring.mem_ofSubring
+-/
 
+#print ValuationSubring.ofLE /-
 /-- An overring of a valuation ring is a valuation ring. -/
-def ofLe (R : ValuationSubring K) (S : Subring K) (h : R.toSubring ≤ S) : ValuationSubring K :=
+def ofLE (R : ValuationSubring K) (S : Subring K) (h : R.toSubring ≤ S) : ValuationSubring K :=
   { S with mem_or_inv_mem' := fun x => (R.mem_or_inv_mem x).imp (@h x) (@h _) }
-#align valuation_subring.of_le ValuationSubring.ofLe
+#align valuation_subring.of_le ValuationSubring.ofLE
+-/
 
 section Order
 
@@ -238,96 +298,127 @@ instance : SemilatticeSup (ValuationSubring K) :=
       PartialOrder
         (ValuationSubring
           K)) with
-    sup := fun R S => ofLe R (R.toSubring ⊔ S.toSubring) <| le_sup_left
+    sup := fun R S => ofLE R (R.toSubring ⊔ S.toSubring) <| le_sup_left
     le_sup_left := fun R S x hx => (le_sup_left : R.toSubring ≤ R.toSubring ⊔ S.toSubring) hx
     le_sup_right := fun R S x hx => (le_sup_right : S.toSubring ≤ R.toSubring ⊔ S.toSubring) hx
     sup_le := fun R S T hR hT x hx => (sup_le hR hT : R.toSubring ⊔ S.toSubring ≤ T.toSubring) hx }
 
+#print ValuationSubring.inclusion /-
 /-- The ring homomorphism induced by the partial order. -/
 def inclusion (R S : ValuationSubring K) (h : R ≤ S) : R →+* S :=
   Subring.inclusion h
 #align valuation_subring.inclusion ValuationSubring.inclusion
+-/
 
+#print ValuationSubring.subtype /-
 /-- The canonical ring homomorphism from a valuation ring to its field of fractions. -/
 def subtype (R : ValuationSubring K) : R →+* K :=
   Subring.subtype R.toSubring
 #align valuation_subring.subtype ValuationSubring.subtype
+-/
 
+#print ValuationSubring.mapOfLE /-
 /-- The canonical map on value groups induced by a coarsening of valuation rings. -/
-def mapOfLe (R S : ValuationSubring K) (h : R ≤ S) : R.ValueGroup →*₀ S.ValueGroup
+def mapOfLE (R S : ValuationSubring K) (h : R ≤ S) : R.ValueGroup →*₀ S.ValueGroup
     where
   toFun := Quotient.map' id fun x y ⟨u, hu⟩ => ⟨Units.map (R.inclusion S h).toMonoidHom u, hu⟩
   map_zero' := rfl
   map_one' := rfl
   map_mul' := by rintro ⟨⟩ ⟨⟩; rfl
-#align valuation_subring.map_of_le ValuationSubring.mapOfLe
+#align valuation_subring.map_of_le ValuationSubring.mapOfLE
+-/
 
+#print ValuationSubring.monotone_mapOfLE /-
 @[mono]
-theorem monotone_mapOfLe (R S : ValuationSubring K) (h : R ≤ S) : Monotone (R.mapOfLe S h) := by
+theorem monotone_mapOfLE (R S : ValuationSubring K) (h : R ≤ S) : Monotone (R.mapOfLE S h) := by
   rintro ⟨⟩ ⟨⟩ ⟨a, ha⟩; exact ⟨R.inclusion S h a, ha⟩
-#align valuation_subring.monotone_map_of_le ValuationSubring.monotone_mapOfLe
+#align valuation_subring.monotone_map_of_le ValuationSubring.monotone_mapOfLE
+-/
 
+#print ValuationSubring.mapOfLE_comp_valuation /-
 @[simp]
-theorem mapOfLe_comp_valuation (R S : ValuationSubring K) (h : R ≤ S) :
-    R.mapOfLe S h ∘ R.Valuation = S.Valuation := by ext; rfl
-#align valuation_subring.map_of_le_comp_valuation ValuationSubring.mapOfLe_comp_valuation
+theorem mapOfLE_comp_valuation (R S : ValuationSubring K) (h : R ≤ S) :
+    R.mapOfLE S h ∘ R.Valuation = S.Valuation := by ext; rfl
+#align valuation_subring.map_of_le_comp_valuation ValuationSubring.mapOfLE_comp_valuation
+-/
 
+#print ValuationSubring.mapOfLE_valuation_apply /-
 @[simp]
-theorem mapOfLe_valuation_apply (R S : ValuationSubring K) (h : R ≤ S) (x : K) :
-    R.mapOfLe S h (R.Valuation x) = S.Valuation x :=
+theorem mapOfLE_valuation_apply (R S : ValuationSubring K) (h : R ≤ S) (x : K) :
+    R.mapOfLE S h (R.Valuation x) = S.Valuation x :=
   rfl
-#align valuation_subring.map_of_le_valuation_apply ValuationSubring.mapOfLe_valuation_apply
+#align valuation_subring.map_of_le_valuation_apply ValuationSubring.mapOfLE_valuation_apply
+-/
 
+#print ValuationSubring.idealOfLE /-
 /-- The ideal corresponding to a coarsening of a valuation ring. -/
-def idealOfLe (R S : ValuationSubring K) (h : R ≤ S) : Ideal R :=
+def idealOfLE (R S : ValuationSubring K) (h : R ≤ S) : Ideal R :=
   (LocalRing.maximalIdeal S).comap (R.inclusion S h)
-#align valuation_subring.ideal_of_le ValuationSubring.idealOfLe
+#align valuation_subring.ideal_of_le ValuationSubring.idealOfLE
+-/
 
-instance prime_idealOfLe (R S : ValuationSubring K) (h : R ≤ S) : (idealOfLe R S h).IsPrime :=
+#print ValuationSubring.prime_idealOfLE /-
+instance prime_idealOfLE (R S : ValuationSubring K) (h : R ≤ S) : (idealOfLE R S h).IsPrime :=
   (LocalRing.maximalIdeal S).comap_isPrime _
-#align valuation_subring.prime_ideal_of_le ValuationSubring.prime_idealOfLe
+#align valuation_subring.prime_ideal_of_le ValuationSubring.prime_idealOfLE
+-/
 
+#print ValuationSubring.ofPrime /-
 /-- The coarsening of a valuation ring associated to a prime ideal. -/
 def ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] : ValuationSubring K :=
-  ofLe A (Localization.subalgebra.ofField K _ P.primeCompl_le_nonZeroDivisors).toSubring fun a ha =>
+  ofLE A (Localization.subalgebra.ofField K _ P.primeCompl_le_nonZeroDivisors).toSubring fun a ha =>
     Subalgebra.algebraMap_mem _ (⟨a, ha⟩ : A)
 #align valuation_subring.of_prime ValuationSubring.ofPrime
+-/
 
+#print ValuationSubring.ofPrimeAlgebra /-
 instance ofPrimeAlgebra (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
     Algebra A (A.of_prime P) :=
   Subalgebra.algebra _
 #align valuation_subring.of_prime_algebra ValuationSubring.ofPrimeAlgebra
+-/
 
+#print ValuationSubring.ofPrime_scalar_tower /-
 instance ofPrime_scalar_tower (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
     IsScalarTower A (A.of_prime P) K :=
   IsScalarTower.subalgebra' A K K _
 #align valuation_subring.of_prime_scalar_tower ValuationSubring.ofPrime_scalar_tower
+-/
 
+#print ValuationSubring.ofPrime_localization /-
 instance ofPrime_localization (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
     IsLocalization.AtPrime (A.of_prime P) P := by
   apply
     Localization.subalgebra.isLocalization_ofField K P.prime_compl
       P.prime_compl_le_non_zero_divisors
 #align valuation_subring.of_prime_localization ValuationSubring.ofPrime_localization
+-/
 
+#print ValuationSubring.le_ofPrime /-
 theorem le_ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] : A ≤ ofPrime A P :=
   fun a ha => Subalgebra.algebraMap_mem _ (⟨a, ha⟩ : A)
 #align valuation_subring.le_of_prime ValuationSubring.le_ofPrime
+-/
 
+#print ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl /-
 theorem ofPrime_valuation_eq_one_iff_mem_primeCompl (A : ValuationSubring K) (P : Ideal A)
     [P.IsPrime] (x : A) : (ofPrime A P).Valuation x = 1 ↔ x ∈ P.primeCompl := by
   rw [← IsLocalization.AtPrime.isUnit_to_map_iff (A.of_prime P) P x, valuation_eq_one_iff]; rfl
 #align valuation_subring.of_prime_valuation_eq_one_iff_mem_prime_compl ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl
+-/
 
+#print ValuationSubring.idealOfLE_ofPrime /-
 @[simp]
-theorem idealOfLe_ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
-    idealOfLe A (ofPrime A P) (le_ofPrime A P) = P := by ext;
+theorem idealOfLE_ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
+    idealOfLE A (ofPrime A P) (le_ofPrime A P) = P := by ext;
   apply IsLocalization.AtPrime.to_map_mem_maximal_iff
-#align valuation_subring.ideal_of_le_of_prime ValuationSubring.idealOfLe_ofPrime
+#align valuation_subring.ideal_of_le_of_prime ValuationSubring.idealOfLE_ofPrime
+-/
 
+#print ValuationSubring.ofPrime_idealOfLE /-
 @[simp]
-theorem ofPrime_idealOfLe (R S : ValuationSubring K) (h : R ≤ S) :
-    ofPrime R (idealOfLe R S h) = S := by
+theorem ofPrime_idealOfLE (R S : ValuationSubring K) (h : R ≤ S) :
+    ofPrime R (idealOfLE R S h) = S := by
   ext x; constructor
   · rintro ⟨a, r, hr, rfl⟩; apply mul_mem; · exact h a.2
     · rw [← valuation_le_one_iff, map_inv₀, ← inv_one, inv_le_inv₀]
@@ -344,31 +435,39 @@ theorem ofPrime_idealOfLe (R S : ValuationSubring K) (h : R ≤ S) :
         apply isUnit_of_mul_eq_one _ (⟨x, hx⟩ : S)
         ext; field_simp
       · field_simp
-#align valuation_subring.of_prime_ideal_of_le ValuationSubring.ofPrime_idealOfLe
+#align valuation_subring.of_prime_ideal_of_le ValuationSubring.ofPrime_idealOfLE
+-/
 
+#print ValuationSubring.ofPrime_le_of_le /-
 theorem ofPrime_le_of_le (P Q : Ideal A) [P.IsPrime] [Q.IsPrime] (h : P ≤ Q) :
     ofPrime A Q ≤ ofPrime A P := fun x ⟨a, s, hs, he⟩ => ⟨a, s, fun c => hs (h c), he⟩
 #align valuation_subring.of_prime_le_of_le ValuationSubring.ofPrime_le_of_le
+-/
 
-theorem idealOfLe_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤ S) (h : R ≤ S) :
-    idealOfLe A S hS ≤ idealOfLe A R hR := fun x hx =>
+#print ValuationSubring.idealOfLE_le_of_le /-
+theorem idealOfLE_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤ S) (h : R ≤ S) :
+    idealOfLE A S hS ≤ idealOfLE A R hR := fun x hx =>
   (valuation_lt_one_iff R _).2
     (by
       by_contra c; push_neg at c ; replace c := monotone_map_of_le R S h c
       rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c 
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
-#align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLe_le_of_le
+#align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLE_le_of_le
+-/
 
+#print ValuationSubring.primeSpectrumEquiv /-
 /-- The equivalence between coarsenings of a valuation ring and its prime ideals.-/
 @[simps]
 def primeSpectrumEquiv : PrimeSpectrum A ≃ {S | A ≤ S}
     where
   toFun P := ⟨ofPrime A P.asIdeal, le_ofPrime _ _⟩
-  invFun S := ⟨idealOfLe _ S S.2, inferInstance⟩
+  invFun S := ⟨idealOfLE _ S S.2, inferInstance⟩
   left_inv P := by ext1; simp
   right_inv S := by ext1; simp
 #align valuation_subring.prime_spectrum_equiv ValuationSubring.primeSpectrumEquiv
+-/
 
+#print ValuationSubring.primeSpectrumOrderEquiv /-
 /-- An ordered variant of `prime_spectrum_equiv`. -/
 @[simps]
 def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
@@ -379,7 +478,9 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
         iterate 2 erw [ideal_of_le_of_prime] at this 
         exact this, fun h => by apply of_prime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
+-/
 
+#print ValuationSubring.linearOrderOverring /-
 instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
   {
     (inferInstance :
@@ -390,6 +491,7 @@ instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
       (prime_spectrum_order_equiv A).symm.toRelEmbedding.IsTotal.Total
     decidableLe := inferInstance }
 #align valuation_subring.linear_order_overring ValuationSubring.linearOrderOverring
+-/
 
 end Order
 
@@ -401,6 +503,7 @@ variable {K} {Γ Γ₁ Γ₂ : Type _} [LinearOrderedCommGroupWithZero Γ]
   [LinearOrderedCommGroupWithZero Γ₁] [LinearOrderedCommGroupWithZero Γ₂] (v : Valuation K Γ)
   (v₁ : Valuation K Γ₁) (v₂ : Valuation K Γ₂)
 
+#print Valuation.valuationSubring /-
 /-- The valuation subring associated to a valuation. -/
 def valuationSubring : ValuationSubring K :=
   { v.integer with
@@ -414,12 +517,16 @@ def valuationSubring : ValuationSubring K :=
         · intro c; simpa [c] using h
         · exact one_ne_zero }
 #align valuation.valuation_subring Valuation.valuationSubring
+-/
 
+#print Valuation.mem_valuationSubring_iff /-
 @[simp]
 theorem mem_valuationSubring_iff (x : K) : x ∈ v.ValuationSubring ↔ v x ≤ 1 :=
   Iff.refl _
 #align valuation.mem_valuation_subring_iff Valuation.mem_valuationSubring_iff
+-/
 
+#print Valuation.isEquiv_iff_valuationSubring /-
 theorem isEquiv_iff_valuationSubring : v₁.IsEquiv v₂ ↔ v₁.ValuationSubring = v₂.ValuationSubring :=
   by
   constructor
@@ -429,7 +536,9 @@ theorem isEquiv_iff_valuationSubring : v₁.IsEquiv v₂ ↔ v₁.ValuationSubri
     have : x ∈ v₁.valuation_subring ↔ x ∈ v₂.valuation_subring := by rw [h]
     simpa using this
 #align valuation.is_equiv_iff_valuation_subring Valuation.isEquiv_iff_valuationSubring
+-/
 
+#print Valuation.isEquiv_valuation_valuationSubring /-
 theorem isEquiv_valuation_valuationSubring : v.IsEquiv v.ValuationSubring.Valuation :=
   by
   rw [is_equiv_iff_val_le_one]
@@ -437,6 +546,7 @@ theorem isEquiv_valuation_valuationSubring : v.IsEquiv v.ValuationSubring.Valuat
   rw [ValuationSubring.valuation_le_one_iff]
   rfl
 #align valuation.is_equiv_valuation_valuation_subring Valuation.isEquiv_valuation_valuationSubring
+-/
 
 end Valuation
 
@@ -444,23 +554,30 @@ namespace ValuationSubring
 
 variable {K} (A : ValuationSubring K)
 
+#print ValuationSubring.valuationSubring_valuation /-
 @[simp]
 theorem valuationSubring_valuation : A.Valuation.ValuationSubring = A := by ext;
   rw [← A.valuation_le_one_iff]; rfl
 #align valuation_subring.valuation_subring_valuation ValuationSubring.valuationSubring_valuation
+-/
 
 section UnitGroup
 
+#print ValuationSubring.unitGroup /-
 /-- The unit group of a valuation subring, as a subgroup of `Kˣ`. -/
 def unitGroup : Subgroup Kˣ :=
   (A.Valuation.toMonoidWithZeroHom.toMonoidHom.comp (Units.coeHom K)).ker
 #align valuation_subring.unit_group ValuationSubring.unitGroup
+-/
 
+#print ValuationSubring.mem_unitGroup_iff /-
 @[simp]
 theorem mem_unitGroup_iff (x : Kˣ) : x ∈ A.unitGroup ↔ A.Valuation x = 1 :=
   Iff.rfl
 #align valuation_subring.mem_unit_group_iff ValuationSubring.mem_unitGroup_iff
+-/
 
+#print ValuationSubring.unitGroupMulEquiv /-
 /-- For a valuation subring `A`, `A.unit_group` agrees with the units of `A`. -/
 def unitGroupMulEquiv : A.unitGroup ≃* Aˣ
     where
@@ -474,17 +591,23 @@ def unitGroupMulEquiv : A.unitGroup ≃* Aˣ
   right_inv a := by ext; rfl
   map_mul' a b := by ext; rfl
 #align valuation_subring.unit_group_mul_equiv ValuationSubring.unitGroupMulEquiv
+-/
 
+#print ValuationSubring.coe_unitGroupMulEquiv_apply /-
 @[simp]
 theorem coe_unitGroupMulEquiv_apply (a : A.unitGroup) : (A.unitGroupMulEquiv a : K) = a :=
   rfl
 #align valuation_subring.coe_unit_group_mul_equiv_apply ValuationSubring.coe_unitGroupMulEquiv_apply
+-/
 
+#print ValuationSubring.coe_unitGroupMulEquiv_symm_apply /-
 @[simp]
 theorem coe_unitGroupMulEquiv_symm_apply (a : Aˣ) : (A.unitGroupMulEquiv.symm a : K) = a :=
   rfl
 #align valuation_subring.coe_unit_group_mul_equiv_symm_apply ValuationSubring.coe_unitGroupMulEquiv_symm_apply
+-/
 
+#print ValuationSubring.unitGroup_le_unitGroup /-
 theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.unitGroup ↔ A ≤ B :=
   by
   constructor
@@ -504,15 +627,21 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
     apply_fun A.map_of_le B h at hx 
     simpa using hx
 #align valuation_subring.unit_group_le_unit_group ValuationSubring.unitGroup_le_unitGroup
+-/
 
+#print ValuationSubring.unitGroup_injective /-
 theorem unitGroup_injective : Function.Injective (unitGroup : ValuationSubring K → Subgroup _) :=
   fun A B h => by simpa only [le_antisymm_iff, unit_group_le_unit_group] using h
 #align valuation_subring.unit_group_injective ValuationSubring.unitGroup_injective
+-/
 
+#print ValuationSubring.eq_iff_unitGroup /-
 theorem eq_iff_unitGroup {A B : ValuationSubring K} : A = B ↔ A.unitGroup = B.unitGroup :=
   unitGroup_injective.eq_iff.symm
 #align valuation_subring.eq_iff_unit_group ValuationSubring.eq_iff_unitGroup
+-/
 
+#print ValuationSubring.unitGroupOrderEmbedding /-
 /-- The map on valuation subrings to their unit groups is an order embedding. -/
 def unitGroupOrderEmbedding : ValuationSubring K ↪o Subgroup Kˣ
     where
@@ -520,26 +649,34 @@ def unitGroupOrderEmbedding : ValuationSubring K ↪o Subgroup Kˣ
   inj' := unitGroup_injective
   map_rel_iff' A B := unitGroup_le_unitGroup
 #align valuation_subring.unit_group_order_embedding ValuationSubring.unitGroupOrderEmbedding
+-/
 
+#print ValuationSubring.unitGroup_strictMono /-
 theorem unitGroup_strictMono : StrictMono (unitGroup : ValuationSubring K → Subgroup _) :=
   unitGroupOrderEmbedding.StrictMono
 #align valuation_subring.unit_group_strict_mono ValuationSubring.unitGroup_strictMono
+-/
 
 end UnitGroup
 
 section nonunits
 
+#print ValuationSubring.nonunits /-
 /-- The nonunits of a valuation subring of `K`, as a subsemigroup of `K`-/
 def nonunits : Subsemigroup K
     where
   carrier := {x | A.Valuation x < 1}
   mul_mem' a b ha hb := (mul_lt_mul₀ ha hb).trans_eq <| mul_one _
 #align valuation_subring.nonunits ValuationSubring.nonunits
+-/
 
+#print ValuationSubring.mem_nonunits_iff /-
 theorem mem_nonunits_iff {x : K} : x ∈ A.nonunits ↔ A.Valuation x < 1 :=
   Iff.rfl
 #align valuation_subring.mem_nonunits_iff ValuationSubring.mem_nonunits_iff
+-/
 
+#print ValuationSubring.nonunits_le_nonunits /-
 theorem nonunits_le_nonunits {A B : ValuationSubring K} : B.nonunits ≤ A.nonunits ↔ A ≤ B :=
   by
   constructor
@@ -550,15 +687,21 @@ theorem nonunits_le_nonunits {A B : ValuationSubring K} : B.nonunits ≤ A.nonun
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
 #align valuation_subring.nonunits_le_nonunits ValuationSubring.nonunits_le_nonunits
+-/
 
+#print ValuationSubring.nonunits_injective /-
 theorem nonunits_injective : Function.Injective (nonunits : ValuationSubring K → Subsemigroup _) :=
   fun A B h => by simpa only [le_antisymm_iff, nonunits_le_nonunits] using h.symm
 #align valuation_subring.nonunits_injective ValuationSubring.nonunits_injective
+-/
 
+#print ValuationSubring.nonunits_inj /-
 theorem nonunits_inj {A B : ValuationSubring K} : A.nonunits = B.nonunits ↔ A = B :=
   nonunits_injective.eq_iff
 #align valuation_subring.nonunits_inj ValuationSubring.nonunits_inj
+-/
 
+#print ValuationSubring.nonunitsOrderEmbedding /-
 /-- The map on valuation subrings to their nonunits is a dual order embedding. -/
 def nonunitsOrderEmbedding : ValuationSubring K ↪o (Subsemigroup K)ᵒᵈ
     where
@@ -566,9 +709,11 @@ def nonunitsOrderEmbedding : ValuationSubring K ↪o (Subsemigroup K)ᵒᵈ
   inj' := nonunits_injective
   map_rel_iff' A B := nonunits_le_nonunits
 #align valuation_subring.nonunits_order_embedding ValuationSubring.nonunitsOrderEmbedding
+-/
 
 variable {A}
 
+#print ValuationSubring.coe_mem_nonunits_iff /-
 /-- The elements of `A.nonunits` are those of the maximal ideal of `A` after coercion to `K`.
 
 See also `mem_nonunits_iff_exists_mem_maximal_ideal`, which gets rid of the coercion to `K`,
@@ -577,15 +722,21 @@ at the expense of a more complicated right hand side.
 theorem coe_mem_nonunits_iff {a : A} : (a : K) ∈ A.nonunits ↔ a ∈ LocalRing.maximalIdeal A :=
   (valuation_lt_one_iff _ _).symm
 #align valuation_subring.coe_mem_nonunits_iff ValuationSubring.coe_mem_nonunits_iff
+-/
 
+#print ValuationSubring.nonunits_le /-
 theorem nonunits_le : A.nonunits ≤ A.toSubring.toSubmonoid.toSubsemigroup := fun a ha =>
   (A.valuation_le_one_iff _).mp (A.mem_nonunits_iff.mp ha).le
 #align valuation_subring.nonunits_le ValuationSubring.nonunits_le
+-/
 
+#print ValuationSubring.nonunits_subset /-
 theorem nonunits_subset : (A.nonunits : Set K) ⊆ A :=
   nonunits_le
 #align valuation_subring.nonunits_subset ValuationSubring.nonunits_subset
+-/
 
+#print ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal /-
 /-- The elements of `A.nonunits` are those of the maximal ideal of `A`.
 
 See also `coe_mem_nonunits_iff`, which has a simpler right hand side but requires the element
@@ -596,7 +747,9 @@ theorem mem_nonunits_iff_exists_mem_maximalIdeal {a : K} :
   ⟨fun h => ⟨nonunits_subset h, coe_mem_nonunits_iff.mp h⟩, fun ⟨ha, h⟩ =>
     coe_mem_nonunits_iff.mpr h⟩
 #align valuation_subring.mem_nonunits_iff_exists_mem_maximal_ideal ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal
+-/
 
+#print ValuationSubring.image_maximalIdeal /-
 /-- `A.nonunits` agrees with the maximal ideal of `A`, after taking its image in `K`. -/
 theorem image_maximalIdeal : (coe : A → K) '' LocalRing.maximalIdeal A = A.nonunits :=
   by
@@ -605,11 +758,13 @@ theorem image_maximalIdeal : (coe : A → K) '' LocalRing.maximalIdeal A = A.non
   erw [Subtype.exists]
   simp_rw [Subtype.coe_mk, exists_and_right, exists_eq_right]
 #align valuation_subring.image_maximal_ideal ValuationSubring.image_maximalIdeal
+-/
 
 end nonunits
 
 section PrincipalUnitGroup
 
+#print ValuationSubring.principalUnitGroup /-
 /-- The principal unit group of a valuation subring, as a subgroup of `Kˣ`. -/
 def principalUnitGroup : Subgroup Kˣ
     where
@@ -630,16 +785,22 @@ def principalUnitGroup : Subgroup Kˣ
     rwa [add_sub_cancel'_right, ← Valuation.map_mul, sub_mul, Units.inv_mul, ← neg_sub, one_mul,
       Valuation.map_neg]
 #align valuation_subring.principal_unit_group ValuationSubring.principalUnitGroup
+-/
 
+#print ValuationSubring.principal_units_le_units /-
 theorem principal_units_le_units : A.principalUnitGroup ≤ A.unitGroup := fun a h => by
   simpa only [add_sub_cancel'_right] using A.valuation.map_one_add_of_lt h
 #align valuation_subring.principal_units_le_units ValuationSubring.principal_units_le_units
+-/
 
+#print ValuationSubring.mem_principalUnitGroup_iff /-
 theorem mem_principalUnitGroup_iff (x : Kˣ) :
     x ∈ A.principalUnitGroup ↔ A.Valuation ((x : K) - 1) < 1 :=
   Iff.rfl
 #align valuation_subring.mem_principal_unit_group_iff ValuationSubring.mem_principalUnitGroup_iff
+-/
 
+#print ValuationSubring.principalUnitGroup_le_principalUnitGroup /-
 theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
     B.principalUnitGroup ≤ A.principalUnitGroup ↔ A ≤ B :=
   by
@@ -655,17 +816,23 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
 #align valuation_subring.principal_unit_group_le_principal_unit_group ValuationSubring.principalUnitGroup_le_principalUnitGroup
+-/
 
+#print ValuationSubring.principalUnitGroup_injective /-
 theorem principalUnitGroup_injective :
     Function.Injective (principalUnitGroup : ValuationSubring K → Subgroup _) := fun A B h => by
   simpa [le_antisymm_iff, principal_unit_group_le_principal_unit_group] using h.symm
 #align valuation_subring.principal_unit_group_injective ValuationSubring.principalUnitGroup_injective
+-/
 
+#print ValuationSubring.eq_iff_principalUnitGroup /-
 theorem eq_iff_principalUnitGroup {A B : ValuationSubring K} :
     A = B ↔ A.principalUnitGroup = B.principalUnitGroup :=
   principalUnitGroup_injective.eq_iff.symm
 #align valuation_subring.eq_iff_principal_unit_group ValuationSubring.eq_iff_principalUnitGroup
+-/
 
+#print ValuationSubring.principalUnitGroupOrderEmbedding /-
 /-- The map on valuation subrings to their principal unit groups is an order embedding. -/
 def principalUnitGroupOrderEmbedding : ValuationSubring K ↪o (Subgroup Kˣ)ᵒᵈ
     where
@@ -673,7 +840,9 @@ def principalUnitGroupOrderEmbedding : ValuationSubring K ↪o (Subgroup Kˣ)ᵒ
   inj' := principalUnitGroup_injective
   map_rel_iff' A B := principalUnitGroup_le_principalUnitGroup
 #align valuation_subring.principal_unit_group_order_embedding ValuationSubring.principalUnitGroupOrderEmbedding
+-/
 
+#print ValuationSubring.coe_mem_principalUnitGroup_iff /-
 theorem coe_mem_principalUnitGroup_iff {x : A.unitGroup} :
     (x : Kˣ) ∈ A.principalUnitGroup ↔
       A.unitGroupMulEquiv x ∈ (Units.map (LocalRing.residue A).toMonoidHom).ker :=
@@ -683,7 +852,9 @@ theorem coe_mem_principalUnitGroup_iff {x : A.unitGroup} :
   rw [← π.map_one, ← sub_eq_zero, ← π.map_sub, Ideal.Quotient.eq_zero_iff_mem, valuation_lt_one_iff]
   simpa
 #align valuation_subring.coe_mem_principal_unit_group_iff ValuationSubring.coe_mem_principalUnitGroup_iff
+-/
 
+#print ValuationSubring.principalUnitGroupEquiv /-
 /-- The principal unit group agrees with the kernel of the canonical map from
 the units of `A` to the units of the residue field of `A`. -/
 def principalUnitGroupEquiv :
@@ -699,43 +870,57 @@ def principalUnitGroupEquiv :
   right_inv x := by simp
   map_mul' x y := by rfl
 #align valuation_subring.principal_unit_group_equiv ValuationSubring.principalUnitGroupEquiv
+-/
 
+#print ValuationSubring.principalUnitGroupEquiv_apply /-
 @[simp]
 theorem principalUnitGroupEquiv_apply (a : A.principalUnitGroup) :
     (principalUnitGroupEquiv A a : K) = a :=
   rfl
 #align valuation_subring.principal_unit_group_equiv_apply ValuationSubring.principalUnitGroupEquiv_apply
+-/
 
+#print ValuationSubring.principalUnitGroup_symm_apply /-
 @[simp]
 theorem principalUnitGroup_symm_apply (a : (Units.map (LocalRing.residue A).toMonoidHom).ker) :
     (A.principalUnitGroupEquiv.symm a : K) = a :=
   rfl
 #align valuation_subring.principal_unit_group_symm_apply ValuationSubring.principalUnitGroup_symm_apply
+-/
 
+#print ValuationSubring.unitGroupToResidueFieldUnits /-
 /-- The canonical map from the unit group of `A` to the units of the residue field of `A`. -/
 def unitGroupToResidueFieldUnits : A.unitGroup →* (LocalRing.ResidueField A)ˣ :=
   MonoidHom.comp (Units.map <| (Ideal.Quotient.mk _).toMonoidHom) A.unitGroupMulEquiv.toMonoidHom
 #align valuation_subring.unit_group_to_residue_field_units ValuationSubring.unitGroupToResidueFieldUnits
+-/
 
+#print ValuationSubring.coe_unitGroupToResidueFieldUnits_apply /-
 @[simp]
 theorem coe_unitGroupToResidueFieldUnits_apply (x : A.unitGroup) :
     (A.unitGroupToResidueFieldUnits x : LocalRing.ResidueField A) =
       Ideal.Quotient.mk _ (A.unitGroupMulEquiv x : A) :=
   rfl
 #align valuation_subring.coe_unit_group_to_residue_field_units_apply ValuationSubring.coe_unitGroupToResidueFieldUnits_apply
+-/
 
+#print ValuationSubring.ker_unitGroupToResidueFieldUnits /-
 theorem ker_unitGroupToResidueFieldUnits :
     A.unitGroupToResidueFieldUnits.ker = A.principalUnitGroup.comap A.unitGroup.Subtype := by ext;
   simpa only [Subgroup.mem_comap, Subgroup.coeSubtype, coe_mem_principal_unit_group_iff]
 #align valuation_subring.ker_unit_group_to_residue_field_units ValuationSubring.ker_unitGroupToResidueFieldUnits
+-/
 
+#print ValuationSubring.surjective_unitGroupToResidueFieldUnits /-
 theorem surjective_unitGroupToResidueFieldUnits :
     Function.Surjective A.unitGroupToResidueFieldUnits :=
   (LocalRing.surjective_units_map_of_local_ringHom _ Ideal.Quotient.mk_surjective
         LocalRing.isLocalRingHom_residue).comp
     (MulEquiv.surjective _)
 #align valuation_subring.surjective_unit_group_to_residue_field_units ValuationSubring.surjective_unitGroupToResidueFieldUnits
+-/
 
+#print ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits /-
 /-- The quotient of the unit group of `A` by the principal unit group of `A` agrees with
 the units of the residue field of `A`. -/
 def unitsModPrincipalUnitsEquivResidueFieldUnits :
@@ -743,21 +928,25 @@ def unitsModPrincipalUnitsEquivResidueFieldUnits :
   (QuotientGroup.quotientMulEquivOfEq A.ker_unitGroupToResidueFieldUnits.symm).trans
     (QuotientGroup.quotientKerEquivOfSurjective _ A.surjective_unitGroupToResidueFieldUnits)
 #align valuation_subring.units_mod_principal_units_equiv_residue_field_units ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits
+-/
 
+#print ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk /-
 @[simp]
-theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotient_group_mk :
+theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk :
     A.unitsModPrincipalUnitsEquivResidueFieldUnits.toMonoidHom.comp (QuotientGroup.mk' _) =
       A.unitGroupToResidueFieldUnits :=
   rfl
-#align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotient_group_mk
+#align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk
+-/
 
+#print ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply /-
 @[simp]
-theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotient_group_mk_apply
-    (x : A.unitGroup) :
+theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply (x : A.unitGroup) :
     A.unitsModPrincipalUnitsEquivResidueFieldUnits.toMonoidHom (QuotientGroup.mk x) =
       A.unitGroupToResidueFieldUnits x :=
   rfl
-#align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk_apply ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotient_group_mk_apply
+#align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk_apply ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply
+-/
 
 end PrincipalUnitGroup
 
@@ -779,6 +968,7 @@ open scoped Pointwise
 
 variable {G : Type _} [Group G] [MulSemiringAction G K]
 
+#print ValuationSubring.pointwiseHasSmul /-
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale. -/
@@ -790,22 +980,28 @@ def pointwiseHasSmul : SMul G (ValuationSubring K)
         (mem_or_inv_mem S (g⁻¹ • x)).imp Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr fun h =>
           Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr <| by rwa [smul_inv''] }
 #align valuation_subring.pointwise_has_smul ValuationSubring.pointwiseHasSmul
+-/
 
 scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSmul
 
 open scoped Pointwise
 
+#print ValuationSubring.coe_pointwise_smul /-
 @[simp]
 theorem coe_pointwise_smul (g : G) (S : ValuationSubring K) : ↑(g • S) = g • (S : Set K) :=
   rfl
 #align valuation_subring.coe_pointwise_smul ValuationSubring.coe_pointwise_smul
+-/
 
+#print ValuationSubring.pointwise_smul_toSubring /-
 @[simp]
 theorem pointwise_smul_toSubring (g : G) (S : ValuationSubring K) :
     (g • S).toSubring = g • S.toSubring :=
   rfl
 #align valuation_subring.pointwise_smul_to_subring ValuationSubring.pointwise_smul_toSubring
+-/
 
+#print ValuationSubring.pointwiseMulAction /-
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale.
@@ -814,54 +1010,73 @@ This is a stronger version of `valuation_subring.pointwise_has_smul`. -/
 def pointwiseMulAction : MulAction G (ValuationSubring K) :=
   toSubring_injective.MulAction toSubring pointwise_smul_toSubring
 #align valuation_subring.pointwise_mul_action ValuationSubring.pointwiseMulAction
+-/
 
 scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseMulAction
 
 open scoped Pointwise
 
+#print ValuationSubring.smul_mem_pointwise_smul /-
 theorem smul_mem_pointwise_smul (g : G) (x : K) (S : ValuationSubring K) : x ∈ S → g • x ∈ g • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ g • (S : Set K))
 #align valuation_subring.smul_mem_pointwise_smul ValuationSubring.smul_mem_pointwise_smul
+-/
 
+#print ValuationSubring.mem_smul_pointwise_iff_exists /-
 theorem mem_smul_pointwise_iff_exists (g : G) (x : K) (S : ValuationSubring K) :
     x ∈ g • S ↔ ∃ s : K, s ∈ S ∧ g • s = x :=
   (Set.mem_smul_set : x ∈ g • (S : Set K) ↔ _)
 #align valuation_subring.mem_smul_pointwise_iff_exists ValuationSubring.mem_smul_pointwise_iff_exists
+-/
 
+#print ValuationSubring.pointwise_central_scalar /-
 instance pointwise_central_scalar [MulSemiringAction Gᵐᵒᵖ K] [IsCentralScalar G K] :
     IsCentralScalar G (ValuationSubring K) :=
   ⟨fun g S => toSubring_injective <| op_smul_eq_smul g S.to_subring⟩
 #align valuation_subring.pointwise_central_scalar ValuationSubring.pointwise_central_scalar
+-/
 
+#print ValuationSubring.smul_mem_pointwise_smul_iff /-
 @[simp]
 theorem smul_mem_pointwise_smul_iff {g : G} {S : ValuationSubring K} {x : K} :
     g • x ∈ g • S ↔ x ∈ S :=
   Set.smul_mem_smul_set_iff
 #align valuation_subring.smul_mem_pointwise_smul_iff ValuationSubring.smul_mem_pointwise_smul_iff
+-/
 
+#print ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem /-
 theorem mem_pointwise_smul_iff_inv_smul_mem {g : G} {S : ValuationSubring K} {x : K} :
     x ∈ g • S ↔ g⁻¹ • x ∈ S :=
   Set.mem_smul_set_iff_inv_smul_mem
 #align valuation_subring.mem_pointwise_smul_iff_inv_smul_mem ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem
+-/
 
+#print ValuationSubring.mem_inv_pointwise_smul_iff /-
 theorem mem_inv_pointwise_smul_iff {g : G} {S : ValuationSubring K} {x : K} :
     x ∈ g⁻¹ • S ↔ g • x ∈ S :=
   Set.mem_inv_smul_set_iff
 #align valuation_subring.mem_inv_pointwise_smul_iff ValuationSubring.mem_inv_pointwise_smul_iff
+-/
 
+#print ValuationSubring.pointwise_smul_le_pointwise_smul_iff /-
 @[simp]
 theorem pointwise_smul_le_pointwise_smul_iff {g : G} {S T : ValuationSubring K} :
     g • S ≤ g • T ↔ S ≤ T :=
   Set.set_smul_subset_set_smul_iff
 #align valuation_subring.pointwise_smul_le_pointwise_smul_iff ValuationSubring.pointwise_smul_le_pointwise_smul_iff
+-/
 
+#print ValuationSubring.pointwise_smul_subset_iff /-
 theorem pointwise_smul_subset_iff {g : G} {S T : ValuationSubring K} : g • S ≤ T ↔ S ≤ g⁻¹ • T :=
   Set.set_smul_subset_iff
 #align valuation_subring.pointwise_smul_subset_iff ValuationSubring.pointwise_smul_subset_iff
+-/
 
+#print ValuationSubring.subset_pointwise_smul_iff /-
 theorem subset_pointwise_smul_iff {g : G} {S T : ValuationSubring K} : S ≤ g • T ↔ g⁻¹ • S ≤ T :=
   Set.subset_set_smul_iff
 #align valuation_subring.subset_pointwise_smul_iff ValuationSubring.subset_pointwise_smul_iff
+-/
 
 end PointwiseActions
 
@@ -869,25 +1084,33 @@ section
 
 variable {L J : Type _} [Field L] [Field J]
 
+#print ValuationSubring.comap /-
 /-- The pullback of a valuation subring `A` along a ring homomorphism `K →+* L`. -/
 def comap (A : ValuationSubring L) (f : K →+* L) : ValuationSubring K :=
   { A.toSubring.comap f with mem_or_inv_mem' := fun k => by simp [ValuationSubring.mem_or_inv_mem] }
 #align valuation_subring.comap ValuationSubring.comap
+-/
 
+#print ValuationSubring.coe_comap /-
 @[simp]
 theorem coe_comap (A : ValuationSubring L) (f : K →+* L) : (A.comap f : Set K) = f ⁻¹' A :=
   rfl
 #align valuation_subring.coe_comap ValuationSubring.coe_comap
+-/
 
+#print ValuationSubring.mem_comap /-
 @[simp]
 theorem mem_comap {A : ValuationSubring L} {f : K →+* L} {x : K} : x ∈ A.comap f ↔ f x ∈ A :=
   Iff.rfl
 #align valuation_subring.mem_comap ValuationSubring.mem_comap
+-/
 
+#print ValuationSubring.comap_comap /-
 theorem comap_comap (A : ValuationSubring J) (g : L →+* J) (f : K →+* L) :
     (A.comap g).comap f = A.comap (g.comp f) :=
   rfl
 #align valuation_subring.comap_comap ValuationSubring.comap_comap
+-/
 
 end
 
@@ -897,10 +1120,12 @@ namespace Valuation
 
 variable {Γ : Type _} [LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ) (x : Kˣ)
 
+#print Valuation.mem_unitGroup_iff /-
 @[simp]
 theorem mem_unitGroup_iff : x ∈ v.ValuationSubring.unitGroup ↔ v x = 1 :=
   (Valuation.isEquiv_iff_val_eq_one _ _).mp (Valuation.isEquiv_valuation_valuationSubring _).symm
 #align valuation.mem_unit_group_iff Valuation.mem_unitGroup_iff
+-/
 
 end Valuation
 

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

@@ -354,14 +354,14 @@ theorem idealOfLe_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
     idealOfLe A S hS ≤ idealOfLe A R hR := fun x hx =>
   (valuation_lt_one_iff R _).2
     (by
-      by_contra c; push_neg  at c ; replace c := monotone_map_of_le R S h c
+      by_contra c; push_neg at c ; replace c := monotone_map_of_le R S h c
       rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c 
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
 #align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLe_le_of_le
 
 /-- The equivalence between coarsenings of a valuation ring and its prime ideals.-/
 @[simps]
-def primeSpectrumEquiv : PrimeSpectrum A ≃ { S | A ≤ S }
+def primeSpectrumEquiv : PrimeSpectrum A ≃ {S | A ≤ S}
     where
   toFun P := ⟨ofPrime A P.asIdeal, le_ofPrime _ _⟩
   invFun S := ⟨idealOfLe _ S S.2, inferInstance⟩
@@ -371,7 +371,7 @@ def primeSpectrumEquiv : PrimeSpectrum A ≃ { S | A ≤ S }
 
 /-- An ordered variant of `prime_spectrum_equiv`. -/
 @[simps]
-def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o { S | A ≤ S } :=
+def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
   { primeSpectrumEquiv A with
     map_rel_iff' := fun P Q =>
       ⟨fun h => by
@@ -380,7 +380,7 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o { S | A ≤ S } :=
         exact this, fun h => by apply of_prime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
-instance linearOrderOverring : LinearOrder { S | A ≤ S } :=
+instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
   {
     (inferInstance :
       PartialOrder
@@ -501,7 +501,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
     · have := h (show Units.mk0 x h_1 ∈ A.unit_group from hx)
       refine' SetLike.coe_mem (B.unit_group_mul_equiv ⟨_, this⟩ : B)
   · rintro h x (hx : A.valuation x = 1)
-    apply_fun A.map_of_le B h  at hx 
+    apply_fun A.map_of_le B h at hx 
     simpa using hx
 #align valuation_subring.unit_group_le_unit_group ValuationSubring.unitGroup_le_unitGroup
 
@@ -532,7 +532,7 @@ section nonunits
 /-- The nonunits of a valuation subring of `K`, as a subsemigroup of `K`-/
 def nonunits : Subsemigroup K
     where
-  carrier := { x | A.Valuation x < 1 }
+  carrier := {x | A.Valuation x < 1}
   mul_mem' a b ha hb := (mul_lt_mul₀ ha hb).trans_eq <| mul_one _
 #align valuation_subring.nonunits ValuationSubring.nonunits
 
@@ -613,7 +613,7 @@ section PrincipalUnitGroup
 /-- The principal unit group of a valuation subring, as a subgroup of `Kˣ`. -/
 def principalUnitGroup : Subgroup Kˣ
     where
-  carrier := { x | A.Valuation (x - 1) < 1 }
+  carrier := {x | A.Valuation (x - 1) < 1}
   mul_mem' := by
     intro a b ha hb
     refine' lt_of_le_of_lt _ (max_lt hb ha)

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

@@ -125,7 +125,7 @@ instance : ValuationRing A
     by_cases (a : K) = 0; · use 0; right; ext; simp [h]
     cases' A.mem_or_inv_mem (a / b) with hh hh
     · use ⟨a / b, hh⟩; right; ext; field_simp; ring
-    · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh
+    · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh 
       use ⟨b / a, hh⟩; left; ext; field_simp; ring
 
 instance : Algebra A K :=
@@ -152,7 +152,8 @@ instance : IsFractionRing A K
 
 /-- The value group of the valuation associated to `A`. Note: it is actually a group with zero. -/
 def ValueGroup :=
-  ValuationRing.ValueGroup A K deriving LinearOrderedCommGroupWithZero
+  ValuationRing.ValueGroup A K
+deriving LinearOrderedCommGroupWithZero
 #align valuation_subring.value_group ValuationSubring.ValueGroup
 
 /-- Any valuation subring of `K` induces a natural valuation on `K`. -/
@@ -196,7 +197,7 @@ theorem valuation_unit (a : Aˣ) : A.Valuation a = 1 := by
 theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.Valuation a = 1 :=
   ⟨fun h => A.valuation_unit h.Unit, fun h =>
     by
-    have ha : (a : K) ≠ 0 := by intro c; rw [c, A.valuation.map_zero] at h; exact zero_ne_one h
+    have ha : (a : K) ≠ 0 := by intro c; rw [c, A.valuation.map_zero] at h ; exact zero_ne_one h
     have ha' : (a : K)⁻¹ ∈ A := by rw [← valuation_le_one_iff, map_inv₀, h, inv_one]
     apply isUnit_of_mul_eq_one a ⟨a⁻¹, ha'⟩; ext; field_simp⟩
 #align valuation_subring.valuation_eq_one_iff ValuationSubring.valuation_eq_one_iff
@@ -331,7 +332,7 @@ theorem ofPrime_idealOfLe (R S : ValuationSubring K) (h : R ≤ S) :
   · rintro ⟨a, r, hr, rfl⟩; apply mul_mem; · exact h a.2
     · rw [← valuation_le_one_iff, map_inv₀, ← inv_one, inv_le_inv₀]
       · exact not_lt.1 ((not_iff_not.2 <| valuation_lt_one_iff S _).1 hr)
-      · intro hh; erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh
+      · intro hh; erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh 
         apply hr; rw [hh]; apply Ideal.zero_mem (R.ideal_of_le S h)
       · exact one_ne_zero
   · intro hx; by_cases hr : x ∈ R; · exact R.le_of_prime _ hr
@@ -353,8 +354,8 @@ theorem idealOfLe_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
     idealOfLe A S hS ≤ idealOfLe A R hR := fun x hx =>
   (valuation_lt_one_iff R _).2
     (by
-      by_contra c; push_neg  at c; replace c := monotone_map_of_le R S h c
-      rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c
+      by_contra c; push_neg  at c ; replace c := monotone_map_of_le R S h c
+      rw [(map_of_le _ _ _).map_one, map_of_le_valuation_apply] at c 
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
 #align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLe_le_of_le
 
@@ -375,7 +376,7 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o { S | A ≤ S } :=
     map_rel_iff' := fun P Q =>
       ⟨fun h => by
         have := ideal_of_le_le_of_le A _ _ _ _ h
-        iterate 2 erw [ideal_of_le_of_prime] at this
+        iterate 2 erw [ideal_of_le_of_prime] at this 
         exact this, fun h => by apply of_prime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
@@ -488,7 +489,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
   by
   constructor
   · intro h x hx
-    rw [← A.valuation_le_one_iff x, le_iff_lt_or_eq] at hx
+    rw [← A.valuation_le_one_iff x, le_iff_lt_or_eq] at hx 
     by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : 1 + x = 0
     · simp only [← add_eq_zero_iff_neg_eq.1 h_2, neg_mem _ _ (one_mem _)]
@@ -500,7 +501,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
     · have := h (show Units.mk0 x h_1 ∈ A.unit_group from hx)
       refine' SetLike.coe_mem (B.unit_group_mul_equiv ⟨_, this⟩ : B)
   · rintro h x (hx : A.valuation x = 1)
-    apply_fun A.map_of_le B h  at hx
+    apply_fun A.map_of_le B h  at hx 
     simpa using hx
 #align valuation_subring.unit_group_le_unit_group ValuationSubring.unitGroup_le_unitGroup
 
@@ -544,7 +545,7 @@ theorem nonunits_le_nonunits {A B : ValuationSubring K} : B.nonunits ≤ A.nonun
   constructor
   · intro h x hx
     by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
-    rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1] at hx⊢
+    rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1] at hx ⊢
     by_contra h_2; exact hx (h h_2)
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
@@ -646,10 +647,10 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
   · intro h x hx
     by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : x⁻¹ + 1 = 0
-    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
+    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2 
       simpa only [h_2] using B.neg_mem _ B.one_mem
     · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ← add_sub_cancel x⁻¹, ←
-        Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx⊢
+        Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx ⊢
       simpa only [hx] using @h (Units.mk0 (x⁻¹ + 1) h_2)
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx

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

@@ -24,7 +24,7 @@ The order structure on `valuation_subring K`.
 -/
 
 
-open Classical
+open scoped Classical
 
 noncomputable section
 
@@ -774,7 +774,7 @@ in sync.
 
 section PointwiseActions
 
-open Pointwise
+open scoped Pointwise
 
 variable {G : Type _} [Group G] [MulSemiringAction G K]
 
@@ -792,7 +792,7 @@ def pointwiseHasSmul : SMul G (ValuationSubring K)
 
 scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSmul
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem coe_pointwise_smul (g : G) (S : ValuationSubring K) : ↑(g • S) = g • (S : Set K) :=
@@ -816,7 +816,7 @@ def pointwiseMulAction : MulAction G (ValuationSubring K) :=
 
 scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseMulAction
 
-open Pointwise
+open scoped Pointwise
 
 theorem smul_mem_pointwise_smul (g : G) (x : K) (S : ValuationSubring K) : x ∈ S → g • x ∈ g • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ g • (S : Set K))

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

@@ -43,9 +43,7 @@ variable {K} (A : ValuationSubring K)
 instance : SetLike (ValuationSubring K) K
     where
   coe A := A.toSubring
-  coe_injective' := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ _
-    congr
+  coe_injective' := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ _; congr
 
 @[simp]
 theorem mem_carrier (x : K) : x ∈ A.carrier ↔ x ∈ A :=
@@ -95,10 +93,7 @@ instance : SubringClass (ValuationSubring K) K
   neg_mem := neg_mem
 
 theorem toSubring_injective : Function.Injective (toSubring : ValuationSubring K → Subring K) :=
-  fun x y h => by
-  cases x
-  cases y
-  congr
+  fun x y h => by cases x; cases y; congr
 #align valuation_subring.to_subring_injective ValuationSubring.toSubring_injective
 
 instance : CommRing A :=
@@ -126,28 +121,12 @@ instance : Inhabited (ValuationSubring K) :=
 
 instance : ValuationRing A
     where cond a b := by
-    by_cases (b : K) = 0;
-    · use 0
-      left
-      ext
-      simp [h]
-    by_cases (a : K) = 0;
-    · use 0
-      right
-      ext
-      simp [h]
+    by_cases (b : K) = 0; · use 0; left; ext; simp [h]
+    by_cases (a : K) = 0; · use 0; right; ext; simp [h]
     cases' A.mem_or_inv_mem (a / b) with hh hh
-    · use ⟨a / b, hh⟩
-      right
-      ext
-      field_simp
-      ring
+    · use ⟨a / b, hh⟩; right; ext; field_simp; ring
     · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh
-      use ⟨b / a, hh⟩
-      left
-      ext
-      field_simp
-      ring
+      use ⟨b / a, hh⟩; left; ext; field_simp; ring
 
 instance : Algebra A K :=
   show Algebra A.toSubring K by infer_instance
@@ -162,20 +141,13 @@ instance : IsFractionRing A K
   map_units := fun ⟨y, hy⟩ =>
     (Units.mk0 (y : K) fun c => nonZeroDivisors.ne_zero hy <| Subtype.ext c).IsUnit
   surj z := by
-    by_cases z = 0;
-    · use (0, 1)
-      simp [h]
+    by_cases z = 0; · use (0, 1); simp [h]
     cases' A.mem_or_inv_mem z with hh hh
-    · use (⟨z, hh⟩, 1)
-      simp
+    · use (⟨z, hh⟩, 1); simp
     · refine' ⟨⟨1, ⟨⟨_, hh⟩, _⟩⟩, mul_inv_cancel h⟩
       exact mem_nonZeroDivisors_iff_ne_zero.2 fun c => h (inv_eq_zero.mp (congr_arg coe c))
   eq_iff_exists a b :=
-    ⟨fun h =>
-      ⟨1, by
-        ext
-        simpa using h⟩,
-      fun ⟨c, h⟩ =>
+    ⟨fun h => ⟨1, by ext; simpa using h⟩, fun ⟨c, h⟩ =>
       congr_arg coe ((mul_eq_mul_left_iff.1 h).resolve_right (nonZeroDivisors.ne_zero c.2))⟩
 
 /-- The value group of the valuation associated to `A`. Note: it is actually a group with zero. -/
@@ -217,24 +189,16 @@ theorem valuation_surjective : Function.Surjective A.Valuation :=
   surjective_quot_mk _
 #align valuation_subring.valuation_surjective ValuationSubring.valuation_surjective
 
-theorem valuation_unit (a : Aˣ) : A.Valuation a = 1 :=
-  by
-  rw [← A.valuation.map_one, valuation_eq_iff]
-  use a
-  simp
+theorem valuation_unit (a : Aˣ) : A.Valuation a = 1 := by
+  rw [← A.valuation.map_one, valuation_eq_iff]; use a; simp
 #align valuation_subring.valuation_unit ValuationSubring.valuation_unit
 
 theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.Valuation a = 1 :=
   ⟨fun h => A.valuation_unit h.Unit, fun h =>
     by
-    have ha : (a : K) ≠ 0 := by
-      intro c
-      rw [c, A.valuation.map_zero] at h
-      exact zero_ne_one h
+    have ha : (a : K) ≠ 0 := by intro c; rw [c, A.valuation.map_zero] at h; exact zero_ne_one h
     have ha' : (a : K)⁻¹ ∈ A := by rw [← valuation_le_one_iff, map_inv₀, h, inv_one]
-    apply isUnit_of_mul_eq_one a ⟨a⁻¹, ha'⟩
-    ext
-    field_simp⟩
+    apply isUnit_of_mul_eq_one a ⟨a⁻¹, ha'⟩; ext; field_simp⟩
 #align valuation_subring.valuation_eq_one_iff ValuationSubring.valuation_eq_one_iff
 
 theorem valuation_lt_one_or_eq_one (a : A) : A.Valuation a < 1 ∨ A.Valuation a = 1 :=
@@ -294,24 +258,17 @@ def mapOfLe (R S : ValuationSubring K) (h : R ≤ S) : R.ValueGroup →*₀ S.Va
   toFun := Quotient.map' id fun x y ⟨u, hu⟩ => ⟨Units.map (R.inclusion S h).toMonoidHom u, hu⟩
   map_zero' := rfl
   map_one' := rfl
-  map_mul' := by
-    rintro ⟨⟩ ⟨⟩
-    rfl
+  map_mul' := by rintro ⟨⟩ ⟨⟩; rfl
 #align valuation_subring.map_of_le ValuationSubring.mapOfLe
 
 @[mono]
-theorem monotone_mapOfLe (R S : ValuationSubring K) (h : R ≤ S) : Monotone (R.mapOfLe S h) :=
-  by
-  rintro ⟨⟩ ⟨⟩ ⟨a, ha⟩
-  exact ⟨R.inclusion S h a, ha⟩
+theorem monotone_mapOfLe (R S : ValuationSubring K) (h : R ≤ S) : Monotone (R.mapOfLe S h) := by
+  rintro ⟨⟩ ⟨⟩ ⟨a, ha⟩; exact ⟨R.inclusion S h a, ha⟩
 #align valuation_subring.monotone_map_of_le ValuationSubring.monotone_mapOfLe
 
 @[simp]
 theorem mapOfLe_comp_valuation (R S : ValuationSubring K) (h : R ≤ S) :
-    R.mapOfLe S h ∘ R.Valuation = S.Valuation :=
-  by
-  ext
-  rfl
+    R.mapOfLe S h ∘ R.Valuation = S.Valuation := by ext; rfl
 #align valuation_subring.map_of_le_comp_valuation ValuationSubring.mapOfLe_comp_valuation
 
 @[simp]
@@ -363,9 +320,7 @@ theorem ofPrime_valuation_eq_one_iff_mem_primeCompl (A : ValuationSubring K) (P
 
 @[simp]
 theorem idealOfLe_ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
-    idealOfLe A (ofPrime A P) (le_ofPrime A P) = P :=
-  by
-  ext
+    idealOfLe A (ofPrime A P) (le_ofPrime A P) = P := by ext;
   apply IsLocalization.AtPrime.to_map_mem_maximal_iff
 #align valuation_subring.ideal_of_le_of_prime ValuationSubring.idealOfLe_ofPrime
 
@@ -373,33 +328,20 @@ theorem idealOfLe_ofPrime (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
 theorem ofPrime_idealOfLe (R S : ValuationSubring K) (h : R ≤ S) :
     ofPrime R (idealOfLe R S h) = S := by
   ext x; constructor
-  · rintro ⟨a, r, hr, rfl⟩
-    apply mul_mem
-    · exact h a.2
+  · rintro ⟨a, r, hr, rfl⟩; apply mul_mem; · exact h a.2
     · rw [← valuation_le_one_iff, map_inv₀, ← inv_one, inv_le_inv₀]
       · exact not_lt.1 ((not_iff_not.2 <| valuation_lt_one_iff S _).1 hr)
-      · intro hh
-        erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh
-        apply hr
-        rw [hh]
-        apply Ideal.zero_mem (R.ideal_of_le S h)
+      · intro hh; erw [Valuation.zero_iff, Subring.coe_eq_zero_iff] at hh
+        apply hr; rw [hh]; apply Ideal.zero_mem (R.ideal_of_le S h)
       · exact one_ne_zero
-  · intro hx
-    by_cases hr : x ∈ R
-    · exact R.le_of_prime _ hr
-    have : x ≠ 0 := fun h =>
-      hr
-        (by
-          rw [h]
-          exact R.zero_mem)
+  · intro hx; by_cases hr : x ∈ R; · exact R.le_of_prime _ hr
+    have : x ≠ 0 := fun h => hr (by rw [h]; exact R.zero_mem)
     replace hr := (R.mem_or_inv_mem x).resolve_left hr
-    · use 1, x⁻¹, hr
-      constructor
+    · use 1, x⁻¹, hr; constructor
       · change (⟨x⁻¹, h hr⟩ : S) ∉ nonunits S
         erw [mem_nonunits_iff, Classical.not_not]
         apply isUnit_of_mul_eq_one _ (⟨x, hx⟩ : S)
-        ext
-        field_simp
+        ext; field_simp
       · field_simp
 #align valuation_subring.of_prime_ideal_of_le ValuationSubring.ofPrime_idealOfLe
 
@@ -422,12 +364,8 @@ def primeSpectrumEquiv : PrimeSpectrum A ≃ { S | A ≤ S }
     where
   toFun P := ⟨ofPrime A P.asIdeal, le_ofPrime _ _⟩
   invFun S := ⟨idealOfLe _ S S.2, inferInstance⟩
-  left_inv P := by
-    ext1
-    simp
-  right_inv S := by
-    ext1
-    simp
+  left_inv P := by ext1; simp
+  right_inv S := by ext1; simp
 #align valuation_subring.prime_spectrum_equiv ValuationSubring.primeSpectrumEquiv
 
 /-- An ordered variant of `prime_spectrum_equiv`. -/
@@ -438,9 +376,7 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o { S | A ≤ S } :=
       ⟨fun h => by
         have := ideal_of_le_le_of_le A _ _ _ _ h
         iterate 2 erw [ideal_of_le_of_prime] at this
-        exact this, fun h => by
-        apply of_prime_le_of_le
-        exact h⟩ }
+        exact this, fun h => by apply of_prime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
 instance linearOrderOverring : LinearOrder { S | A ≤ S } :=
@@ -470,14 +406,11 @@ def valuationSubring : ValuationSubring K :=
     mem_or_inv_mem' := by
       intro x
       cases le_or_lt (v x) 1
-      · left
-        exact h
-      · right
-        change v x⁻¹ ≤ 1
+      · left; exact h
+      · right; change v x⁻¹ ≤ 1
         rw [map_inv₀ v, ← inv_one, inv_le_inv₀]
         · exact le_of_lt h
-        · intro c
-          simpa [c] using h
+        · intro c; simpa [c] using h
         · exact one_ne_zero }
 #align valuation.valuation_subring Valuation.valuationSubring
 
@@ -489,12 +422,8 @@ theorem mem_valuationSubring_iff (x : K) : x ∈ v.ValuationSubring ↔ v x ≤
 theorem isEquiv_iff_valuationSubring : v₁.IsEquiv v₂ ↔ v₁.ValuationSubring = v₂.ValuationSubring :=
   by
   constructor
-  · intro h
-    ext x
-    specialize h x 1
-    simpa using h
-  · intro h
-    apply is_equiv_of_val_le_one
+  · intro h; ext x; specialize h x 1; simpa using h
+  · intro h; apply is_equiv_of_val_le_one
     intro x
     have : x ∈ v₁.valuation_subring ↔ x ∈ v₂.valuation_subring := by rw [h]
     simpa using this
@@ -515,11 +444,8 @@ namespace ValuationSubring
 variable {K} (A : ValuationSubring K)
 
 @[simp]
-theorem valuationSubring_valuation : A.Valuation.ValuationSubring = A :=
-  by
-  ext
-  rw [← A.valuation_le_one_iff]
-  rfl
+theorem valuationSubring_valuation : A.Valuation.ValuationSubring = A := by ext;
+  rw [← A.valuation_le_one_iff]; rfl
 #align valuation_subring.valuation_subring_valuation ValuationSubring.valuationSubring_valuation
 
 section UnitGroup
@@ -543,15 +469,9 @@ def unitGroupMulEquiv : A.unitGroup ≃* Aˣ
       val_inv := Subtype.ext (Units.mul_inv x)
       inv_val := Subtype.ext (Units.inv_mul x) }
   invFun x := ⟨Units.map A.Subtype.toMonoidHom x, A.valuation_unit x⟩
-  left_inv a := by
-    ext
-    rfl
-  right_inv a := by
-    ext
-    rfl
-  map_mul' a b := by
-    ext
-    rfl
+  left_inv a := by ext; rfl
+  right_inv a := by ext; rfl
+  map_mul' a b := by ext; rfl
 #align valuation_subring.unit_group_mul_equiv ValuationSubring.unitGroupMulEquiv
 
 @[simp]
@@ -569,8 +489,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
   constructor
   · intro h x hx
     rw [← A.valuation_le_one_iff x, le_iff_lt_or_eq] at hx
-    by_cases h_1 : x = 0
-    · simp only [h_1, zero_mem]
+    by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : 1 + x = 0
     · simp only [← add_eq_zero_iff_neg_eq.1 h_2, neg_mem _ _ (one_mem _)]
     cases hx
@@ -624,14 +543,11 @@ theorem nonunits_le_nonunits {A B : ValuationSubring K} : B.nonunits ≤ A.nonun
   by
   constructor
   · intro h x hx
-    by_cases h_1 : x = 0
-    · simp only [h_1, zero_mem]
+    by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1] at hx⊢
-    by_contra h_2
-    exact hx (h h_2)
+    by_contra h_2; exact hx (h h_2)
   · intro h x hx
-    by_contra h_1
-    exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
+    by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
 #align valuation_subring.nonunits_le_nonunits ValuationSubring.nonunits_le_nonunits
 
 theorem nonunits_injective : Function.Injective (nonunits : ValuationSubring K → Subsemigroup _) :=
@@ -728,8 +644,7 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
   by
   constructor
   · intro h x hx
-    by_cases h_1 : x = 0
-    · simp only [h_1, zero_mem]
+    by_cases h_1 : x = 0; · simp only [h_1, zero_mem]
     by_cases h_2 : x⁻¹ + 1 = 0
     · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
       simpa only [h_2] using B.neg_mem _ B.one_mem
@@ -737,8 +652,7 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
         Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx⊢
       simpa only [hx] using @h (Units.mk0 (x⁻¹ + 1) h_2)
   · intro h x hx
-    by_contra h_1
-    exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
+    by_contra h_1; exact not_lt.2 (monotone_map_of_le _ _ h (not_lt.1 h_1)) hx
 #align valuation_subring.principal_unit_group_le_principal_unit_group ValuationSubring.principalUnitGroup_le_principalUnitGroup
 
 theorem principalUnitGroup_injective :
@@ -778,9 +692,7 @@ def principalUnitGroupEquiv :
     ⟨A.unitGroupMulEquiv ⟨_, A.principal_units_le_units x.2⟩,
       A.coe_mem_principalUnitGroup_iff.1 x.2⟩
   invFun x :=
-    ⟨A.unitGroupMulEquiv.symm x,
-      by
-      rw [A.coe_mem_principal_unit_group_iff]
+    ⟨A.unitGroupMulEquiv.symm x, by rw [A.coe_mem_principal_unit_group_iff];
       simpa using SetLike.coe_mem x⟩
   left_inv x := by simp
   right_inv x := by simp
@@ -812,9 +724,7 @@ theorem coe_unitGroupToResidueFieldUnits_apply (x : A.unitGroup) :
 #align valuation_subring.coe_unit_group_to_residue_field_units_apply ValuationSubring.coe_unitGroupToResidueFieldUnits_apply
 
 theorem ker_unitGroupToResidueFieldUnits :
-    A.unitGroupToResidueFieldUnits.ker = A.principalUnitGroup.comap A.unitGroup.Subtype :=
-  by
-  ext
+    A.unitGroupToResidueFieldUnits.ker = A.principalUnitGroup.comap A.unitGroup.Subtype := by ext;
   simpa only [Subgroup.mem_comap, Subgroup.coeSubtype, coe_mem_principal_unit_group_iff]
 #align valuation_subring.ker_unit_group_to_residue_field_units ValuationSubring.ker_unitGroupToResidueFieldUnits
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -988,7 +988,7 @@ variable {Γ : Type _} [LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ)
 
 @[simp]
 theorem mem_unitGroup_iff : x ∈ v.ValuationSubring.unitGroup ↔ v x = 1 :=
-  (Valuation.IsEquiv_iff_val_eq_one _ _).mp (Valuation.isEquiv_valuation_valuationSubring _).symm
+  (Valuation.isEquiv_iff_val_eq_one _ _).mp (Valuation.isEquiv_valuation_valuationSubring _).symm
 #align valuation.mem_unit_group_iff Valuation.mem_unitGroup_iff
 
 end Valuation

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -988,7 +988,7 @@ variable {Γ : Type _} [LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ)
 
 @[simp]
 theorem mem_unitGroup_iff : x ∈ v.ValuationSubring.unitGroup ↔ v x = 1 :=
-  (Valuation.isEquiv_iff_val_eq_one _ _).mp (Valuation.isEquiv_valuation_valuationSubring _).symm
+  (Valuation.IsEquiv_iff_val_eq_one _ _).mp (Valuation.isEquiv_valuation_valuationSubring _).symm
 #align valuation.mem_unit_group_iff Valuation.mem_unitGroup_iff
 
 end Valuation

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Junyan Xu, Jack McKoen
 
 ! This file was ported from Lean 3 source module ring_theory.valuation.valuation_subring
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -731,7 +731,7 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
     by_cases h_1 : x = 0
     · simp only [h_1, zero_mem]
     by_cases h_2 : x⁻¹ + 1 = 0
-    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_inv_eq, inv_neg, inv_one] at h_2
+    · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
       simpa only [h_2] using B.neg_mem _ B.one_mem
     · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ← add_sub_cancel x⁻¹, ←
         Units.val_mk0 h_2, ← mem_principal_unit_group_iff] at hx⊢

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

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

@@ -127,13 +127,11 @@ instance : ValuationRing A where
       right
       ext
       field_simp
-      ring
     · rw [show (a / b : K)⁻¹ = b / a by field_simp] at hh
       use ⟨b / a, hh⟩;
       left
       ext
       field_simp
-      ring
 
 instance : Algebra A K :=
   show Algebra A.toSubring K by infer_instance

A mix of various changes; generated with a script and manually tweaked.

@@ -826,7 +826,7 @@ theorem pointwise_smul_toSubring (g : G) (S : ValuationSubring K) :
 
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
-This is available as an instance in the `pointwise` locale.
+This is available as an instance in the `Pointwise` locale.
 
 This is a stronger version of `ValuationSubring.pointwiseSMul`. -/
 def pointwiseMulAction : MulAction G (ValuationSubring K) :=

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -375,7 +375,7 @@ theorem idealOfLE_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
 #align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLE_le_of_le
 
-/-- The equivalence between coarsenings of a valuation ring and its prime ideals.-/
+/-- The equivalence between coarsenings of a valuation ring and its prime ideals. -/
 @[simps]
 def primeSpectrumEquiv : PrimeSpectrum A ≃ {S // A ≤ S} where
   toFun P := ⟨ofPrime A P.asIdeal, le_ofPrime _ _⟩

Everywhere we have a smul_mem_pointwise_smul lemma, I've added this result.

@@ -841,6 +841,9 @@ theorem smul_mem_pointwise_smul (g : G) (x : K) (S : ValuationSubring K) : x ∈
   (Set.smul_mem_smul_set : _ → _ ∈ g • (S : Set K))
 #align valuation_subring.smul_mem_pointwise_smul ValuationSubring.smul_mem_pointwise_smul
 
+instance : CovariantClass G (ValuationSubring K) HSMul.hSMul LE.le :=
+  ⟨fun _ _ _ => Set.image_subset _⟩
+
 theorem mem_smul_pointwise_iff_exists (g : G) (x : K) (S : ValuationSubring K) :
     x ∈ g • S ↔ ∃ s : K, s ∈ S ∧ g • s = x :=
   (Set.mem_smul_set : x ∈ g • (S : Set K) ↔ _)

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 | |

@@ -631,7 +631,7 @@ def principalUnitGroup : Subgroup Kˣ where
     rw [Set.mem_setOf] at ha hb
     refine' lt_of_le_of_lt _ (max_lt hb ha)
     -- Porting note: `sub_add_sub_cancel` needed some help
-    rw [← one_mul (A.valuation (b - 1)), ← A.valuation.map_one_add_of_lt ha, add_sub_cancel'_right,
+    rw [← one_mul (A.valuation (b - 1)), ← A.valuation.map_one_add_of_lt ha, add_sub_cancel,
       ← Valuation.map_mul, mul_sub_one, ← sub_add_sub_cancel (↑(a * b) : K) _ 1]
     exact A.valuation.map_add _ _
   one_mem' := by simp
@@ -641,12 +641,12 @@ def principalUnitGroup : Subgroup Kˣ where
     conv =>
       lhs
       rw [← mul_one (A.valuation _), ← A.valuation.map_one_add_of_lt ha]
-    rwa [add_sub_cancel'_right, ← Valuation.map_mul, sub_mul, Units.inv_mul, ← neg_sub, one_mul,
+    rwa [add_sub_cancel, ← Valuation.map_mul, sub_mul, Units.inv_mul, ← neg_sub, one_mul,
       Valuation.map_neg]
 #align valuation_subring.principal_unit_group ValuationSubring.principalUnitGroup
 
 theorem principal_units_le_units : A.principalUnitGroup ≤ A.unitGroup := fun a h => by
-  simpa only [add_sub_cancel'_right] using A.valuation.map_one_add_of_lt h
+  simpa only [add_sub_cancel] using A.valuation.map_one_add_of_lt h
 #align valuation_subring.principal_units_le_units ValuationSubring.principal_units_le_units
 
 theorem mem_principalUnitGroup_iff (x : Kˣ) :
@@ -662,8 +662,8 @@ theorem principalUnitGroup_le_principalUnitGroup {A B : ValuationSubring K} :
     by_cases h_2 : x⁻¹ + 1 = 0
     · rw [add_eq_zero_iff_eq_neg, inv_eq_iff_eq_inv, inv_neg, inv_one] at h_2
       simpa only [h_2] using B.neg_mem _ B.one_mem
-    · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1, ← add_sub_cancel x⁻¹, ←
-        Units.val_mk0 h_2, ← mem_principalUnitGroup_iff] at hx ⊢
+    · rw [← valuation_le_one_iff, ← not_lt, Valuation.one_lt_val_iff _ h_1,
+        ← add_sub_cancel_right x⁻¹, ← Units.val_mk0 h_2, ← mem_principalUnitGroup_iff] at hx ⊢
       simpa only [hx] using @h (Units.mk0 (x⁻¹ + 1) h_2)
   · intro h x hx
     by_contra h_1; exact not_lt.2 (monotone_mapOfLE _ _ h (not_lt.1 h_1)) hx

Classifies by adding issue number #10959 porting notes claiming anything semantically equivalent to:

• "simp cannot prove this"
• "simp used to be able to close this goal"
• "simp can't handle this"
• "simp used to work here"

@@ -47,7 +47,7 @@ instance : SetLike (ValuationSubring K) K where
     replace h := SetLike.coe_injective' h
     congr
 
-@[simp, nolint simpNF] -- Porting note: simp cannot prove that
+@[simp, nolint simpNF] -- Porting note (#10959): simp cannot prove that
 theorem mem_carrier (x : K) : x ∈ A.carrier ↔ x ∈ A := Iff.refl _
 #align valuation_subring.mem_carrier ValuationSubring.mem_carrier
 

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

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

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

@@ -513,7 +513,7 @@ theorem unitGroup_le_unitGroup {A B : ValuationSubring K} : A.unitGroup ≤ B.un
         B.add_mem _ _ (show 1 + x ∈ B from SetLike.coe_mem (B.unitGroupMulEquiv ⟨_, this⟩ : B))
           (B.neg_mem _ B.one_mem)
     · have := h (show Units.mk0 x h_1 ∈ A.unitGroup from hx)
-      refine' SetLike.coe_mem (B.unitGroupMulEquiv ⟨_, this⟩ : B)
+      exact SetLike.coe_mem (B.unitGroupMulEquiv ⟨_, this⟩ : B)
   · rintro h x (hx : A.valuation x = 1)
     apply_fun A.mapOfLE B h at hx
     simpa using hx

Classifies by adding issue number (#10754) to porting notes claiming added instance.

@@ -307,7 +307,7 @@ instance ofPrimeAlgebra (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
 #align valuation_subring.of_prime_algebra ValuationSubring.ofPrimeAlgebra
 
 instance ofPrime_scalar_tower (A : ValuationSubring K) (P : Ideal A) [P.IsPrime] :
-    -- Porting note: added instance
+    -- porting note (#10754): added instance
     letI : SMul A (A.ofPrime P) := SMulZeroClass.toSMul
     IsScalarTower A (A.ofPrime P) K :=
   IsScalarTower.subalgebra' A K K

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>

@@ -205,8 +205,8 @@ theorem valuation_unit (a : Aˣ) : A.valuation a = 1 := by
 
 theorem valuation_eq_one_iff (a : A) : IsUnit a ↔ A.valuation a = 1 :=
   ⟨fun h => A.valuation_unit h.unit, fun h => by
-    have ha : (a : K) ≠ 0
-    · intro c
+    have ha : (a : K) ≠ 0 := by
+      intro c
       rw [c, A.valuation.map_zero] at h
       exact zero_ne_one h
     have ha' : (a : K)⁻¹ ∈ A := by rw [← valuation_le_one_iff, map_inv₀, h, inv_one]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -385,7 +385,7 @@ def primeSpectrumEquiv : PrimeSpectrum A ≃ {S // A ≤ S} where
 #align valuation_subring.prime_spectrum_equiv ValuationSubring.primeSpectrumEquiv
 
 /-- An ordered variant of `primeSpectrumEquiv`. -/
-@[simps]
+@[simps!]
 def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S // A ≤ S} :=
   { primeSpectrumEquiv A with
     map_rel_iff' :=

Part of #9411

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

@@ -762,7 +762,7 @@ def unitsModPrincipalUnitsEquivResidueFieldUnits :
     (QuotientGroup.quotientKerEquivOfSurjective _ A.surjective_unitGroupToResidueFieldUnits)
 #align valuation_subring.units_mod_principal_units_equiv_residue_field_units ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits
 
--- Porting note: Lean needs to be reminded of this instance
+/-- Porting note: Lean needs to be reminded of this instance -/
 local instance : MulOneClass ({ x // x ∈ unitGroup A } ⧸
   Subgroup.comap (Subgroup.subtype (unitGroup A)) (principalUnitGroup A)) := inferInstance
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -422,7 +422,7 @@ def valuationSubring : ValuationSubring K :=
   { v.integer with
     mem_or_inv_mem' := by
       intro x
-      cases' le_or_lt (v x) 1 with h h
+      rcases le_or_lt (v x) 1 with h | h
       · left; exact h
       · right; change v x⁻¹ ≤ 1
         rw [map_inv₀ v, ← inv_one, inv_le_inv₀]

I've also got a change to make this required, but I'd like to land this first.

@@ -113,12 +113,12 @@ instance : Inhabited (ValuationSubring K) :=
 
 instance : ValuationRing A where
   cond' a b := by
-    by_cases (b : K) = 0
+    by_cases h : (b : K) = 0
     · use 0
       left
       ext
       simp [h]
-    by_cases (a : K) = 0
+    by_cases h : (a : K) = 0
     · use 0; right
       ext
       simp [h]
@@ -149,7 +149,7 @@ instance : IsFractionRing A K where
   map_units' := fun ⟨y, hy⟩ =>
     (Units.mk0 (y : K) fun c => nonZeroDivisors.ne_zero hy <| Subtype.ext c).isUnit
   surj' z := by
-    by_cases z = 0; · use (0, 1); simp [h]
+    by_cases h : z = 0; · use (0, 1); simp [h]
     cases' A.mem_or_inv_mem z with hh hh
     · use (⟨z, hh⟩, 1); simp
     · refine ⟨⟨1, ⟨⟨_, hh⟩, ?_⟩⟩, mul_inv_cancel h⟩

The other direction is a consequence of IsLocalization.map_units.

Also do the same for LocalizationMap and IsLocalizedModule.

This means we have one less fact to prove when constructing an IsLocalization (etc.) instance (thus many proofs are golfed), but once we construct it we still have access to the eq_iff_exists lemmas (without the prime) so the API doesn't get less powerful.

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

@@ -154,9 +154,7 @@ instance : IsFractionRing A K where
     · use (⟨z, hh⟩, 1); simp
     · refine ⟨⟨1, ⟨⟨_, hh⟩, ?_⟩⟩, mul_inv_cancel h⟩
       exact mem_nonZeroDivisors_iff_ne_zero.2 fun c => h (inv_eq_zero.mp (congr_arg Subtype.val c))
-  eq_iff_exists' {a b} :=
-    ⟨fun h => ⟨1, by ext; simpa using h⟩, fun ⟨c, h⟩ =>
-      congr_arg Subtype.val ((mul_eq_mul_left_iff.1 h).resolve_right (nonZeroDivisors.ne_zero c.2))⟩
+  exists_of_eq {a b} h := ⟨1, by ext; simpa using h⟩
 
 /-- The value group of the valuation associated to `A`. Note: it is actually a group with zero. -/
 def ValueGroup :=

Currently the file uses {S | A ≤ S} for primeSpectrumEquiv and other declarations. This changes those to {S // A ≤ S} which makes the simpNF happier about the generated simp lemmas.

@@ -379,7 +379,7 @@ theorem idealOfLE_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
 
 /-- The equivalence between coarsenings of a valuation ring and its prime ideals.-/
 @[simps]
-def primeSpectrumEquiv : PrimeSpectrum A ≃ {S | A ≤ S} where
+def primeSpectrumEquiv : PrimeSpectrum A ≃ {S // A ≤ S} where
   toFun P := ⟨ofPrime A P.asIdeal, le_ofPrime _ _⟩
   invFun S := ⟨idealOfLE _ S S.2, inferInstance⟩
   left_inv P := by ext1; simp
@@ -388,7 +388,7 @@ def primeSpectrumEquiv : PrimeSpectrum A ≃ {S | A ≤ S} where
 
 /-- An ordered variant of `primeSpectrumEquiv`. -/
 @[simps]
-def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
+def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S // A ≤ S} :=
   { primeSpectrumEquiv A with
     map_rel_iff' :=
       ⟨fun h => by
@@ -400,13 +400,7 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
       fun h => by apply ofPrime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
--- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] ValuationSubring.primeSpectrumEquiv_symm_apply_asIdeal
-  ValuationSubring.primeSpectrumEquiv_apply_coe
-  ValuationSubring.primeSpectrumOrderEquiv_apply
-  ValuationSubring.primeSpectrumOrderEquiv_symm_apply
-
-instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
+instance linearOrderOverring : LinearOrder {S // A ≤ S} :=
   { (inferInstance : PartialOrder _) with
     le_total :=
       let i : IsTotal (PrimeSpectrum A) (· ≤ ·) := ⟨fun ⟨x, _⟩ ⟨y, _⟩ => LE.isTotal.total x y⟩

This reverts commit f3695eb2.

@@ -400,6 +400,12 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
       fun h => by apply ofPrime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
+-- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ValuationSubring.primeSpectrumEquiv_symm_apply_asIdeal
+  ValuationSubring.primeSpectrumEquiv_apply_coe
+  ValuationSubring.primeSpectrumOrderEquiv_apply
+  ValuationSubring.primeSpectrumOrderEquiv_symm_apply
+
 instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
   { (inferInstance : PartialOrder _) with
     le_total :=
@@ -712,13 +718,15 @@ def principalUnitGroupEquiv :
   map_mul' x y := rfl
 #align valuation_subring.principal_unit_group_equiv ValuationSubring.principalUnitGroupEquiv
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem principalUnitGroupEquiv_apply (a : A.principalUnitGroup) :
     (((principalUnitGroupEquiv A a : Aˣ) : A) : K) = (a : Kˣ) :=
   rfl
 #align valuation_subring.principal_unit_group_equiv_apply ValuationSubring.principalUnitGroupEquiv_apply
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem principalUnitGroup_symm_apply (a : (Units.map (LocalRing.residue A).toMonoidHom).ker) :
     ((A.principalUnitGroupEquiv.symm a : Kˣ) : K) = ((a : Aˣ) : A) :=
   rfl
@@ -772,7 +780,8 @@ theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk :
       A.unitGroupToResidueFieldUnits := rfl
 #align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply
     (x : A.unitGroup) :
     A.unitsModPrincipalUnitsEquivResidueFieldUnits.toMonoidHom (QuotientGroup.mk x) =

This reverts commit 26eb2b0a.

@@ -400,12 +400,6 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
       fun h => by apply ofPrime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
--- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] ValuationSubring.primeSpectrumEquiv_symm_apply_asIdeal
-  ValuationSubring.primeSpectrumEquiv_apply_coe
-  ValuationSubring.primeSpectrumOrderEquiv_apply
-  ValuationSubring.primeSpectrumOrderEquiv_symm_apply
-
 instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
   { (inferInstance : PartialOrder _) with
     le_total :=
@@ -718,15 +712,13 @@ def principalUnitGroupEquiv :
   map_mul' x y := rfl
 #align valuation_subring.principal_unit_group_equiv ValuationSubring.principalUnitGroupEquiv
 
--- This was always a bad simp lemma, but the linter only noticed after lean4#2644
-@[simp, nolint simpNF]
+@[simp]
 theorem principalUnitGroupEquiv_apply (a : A.principalUnitGroup) :
     (((principalUnitGroupEquiv A a : Aˣ) : A) : K) = (a : Kˣ) :=
   rfl
 #align valuation_subring.principal_unit_group_equiv_apply ValuationSubring.principalUnitGroupEquiv_apply
 
--- This was always a bad simp lemma, but the linter only noticed after lean4#2644
-@[simp, nolint simpNF]
+@[simp]
 theorem principalUnitGroup_symm_apply (a : (Units.map (LocalRing.residue A).toMonoidHom).ker) :
     ((A.principalUnitGroupEquiv.symm a : Kˣ) : K) = ((a : Aˣ) : A) :=
   rfl
@@ -780,8 +772,7 @@ theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk :
       A.unitGroupToResidueFieldUnits := rfl
 #align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk
 
--- This was always a bad simp lemma, but the linter only noticed after lean4#2644
-@[simp, nolint simpNF]
+@[simp]
 theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply
     (x : A.unitGroup) :
     A.unitsModPrincipalUnitsEquivResidueFieldUnits.toMonoidHom (QuotientGroup.mk x) =

This includes all the changes from #7606.

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

@@ -400,6 +400,12 @@ def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
       fun h => by apply ofPrime_le_of_le; exact h⟩ }
 #align valuation_subring.prime_spectrum_order_equiv ValuationSubring.primeSpectrumOrderEquiv
 
+-- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] ValuationSubring.primeSpectrumEquiv_symm_apply_asIdeal
+  ValuationSubring.primeSpectrumEquiv_apply_coe
+  ValuationSubring.primeSpectrumOrderEquiv_apply
+  ValuationSubring.primeSpectrumOrderEquiv_symm_apply
+
 instance linearOrderOverring : LinearOrder {S | A ≤ S} :=
   { (inferInstance : PartialOrder _) with
     le_total :=
@@ -712,13 +718,15 @@ def principalUnitGroupEquiv :
   map_mul' x y := rfl
 #align valuation_subring.principal_unit_group_equiv ValuationSubring.principalUnitGroupEquiv
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem principalUnitGroupEquiv_apply (a : A.principalUnitGroup) :
     (((principalUnitGroupEquiv A a : Aˣ) : A) : K) = (a : Kˣ) :=
   rfl
 #align valuation_subring.principal_unit_group_equiv_apply ValuationSubring.principalUnitGroupEquiv_apply
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem principalUnitGroup_symm_apply (a : (Units.map (LocalRing.residue A).toMonoidHom).ker) :
     ((A.principalUnitGroupEquiv.symm a : Kˣ) : K) = ((a : Aˣ) : A) :=
   rfl
@@ -772,7 +780,8 @@ theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk :
       A.unitGroupToResidueFieldUnits := rfl
 #align valuation_subring.units_mod_principal_units_equiv_residue_field_units_comp_quotient_group_mk ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk
 
-@[simp]
+-- This was always a bad simp lemma, but the linter only noticed after lean4#2644
+@[simp, nolint simpNF]
 theorem unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply
     (x : A.unitGroup) :
     A.unitsModPrincipalUnitsEquivResidueFieldUnits.toMonoidHom (QuotientGroup.mk x) =

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

@@ -709,7 +709,7 @@ def principalUnitGroupEquiv :
       rw [A.coe_mem_principalUnitGroup_iff]; simpa using SetLike.coe_mem x⟩
   left_inv x := by simp
   right_inv x := by simp
-  map_mul' x y := by rfl
+  map_mul' x y := rfl
 #align valuation_subring.principal_unit_group_equiv ValuationSubring.principalUnitGroupEquiv
 
 @[simp]

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

@@ -615,7 +615,7 @@ theorem image_maximalIdeal : ((↑) : A → K) '' LocalRing.maximalIdeal A = A.n
   ext a
   simp only [Set.mem_image, SetLike.mem_coe, mem_nonunits_iff_exists_mem_maximalIdeal]
   erw [Subtype.exists]
-  simp_rw [Subtype.coe_mk, exists_and_right, exists_eq_right]
+  simp_rw [exists_and_right, exists_eq_right]
   -- Porting note: added
   simp
 #align valuation_subring.image_maximal_ideal ValuationSubring.image_maximalIdeal

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

This has nice performance benefits.

@@ -415,7 +415,7 @@ end ValuationSubring
 namespace Valuation
 
 variable {K}
-variable {Γ Γ₁ Γ₂ : Type _} [LinearOrderedCommGroupWithZero Γ]
+variable {Γ Γ₁ Γ₂ : Type*} [LinearOrderedCommGroupWithZero Γ]
   [LinearOrderedCommGroupWithZero Γ₁] [LinearOrderedCommGroupWithZero Γ₂] (v : Valuation K Γ)
   (v₁ : Valuation K Γ₁) (v₂ : Valuation K Γ₂)
 
@@ -797,7 +797,7 @@ section PointwiseActions
 
 open scoped Pointwise
 
-variable {G : Type _} [Group G] [MulSemiringAction G K]
+variable {G : Type*} [Group G] [MulSemiringAction G K]
 
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
@@ -880,7 +880,7 @@ end PointwiseActions
 
 section
 
-variable {L J : Type _} [Field L] [Field J]
+variable {L J : Type*} [Field L] [Field J]
 
 /-- The pullback of a valuation subring `A` along a ring homomorphism `K →+* L`. -/
 def comap (A : ValuationSubring L) (f : K →+* L) : ValuationSubring K :=
@@ -906,7 +906,7 @@ end ValuationSubring
 
 namespace Valuation
 
-variable {Γ : Type _} [LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ) (x : Kˣ)
+variable {Γ : Type*} [LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ) (x : Kˣ)
 
 -- @[simp] -- Porting note: not in simpNF
 theorem mem_unitGroup_iff : x ∈ v.valuationSubring.unitGroup ↔ v x = 1 :=

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz, Junyan Xu, Jack McKoen
-
-! This file was ported from Lean 3 source module ring_theory.valuation.valuation_subring
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Valuation.ValuationRing
 import Mathlib.RingTheory.Localization.AsSubring
 import Mathlib.RingTheory.Subring.Pointwise
 import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
 
+#align_import ring_theory.valuation.valuation_subring from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 
 # Valuation subrings of a field

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -375,7 +375,7 @@ theorem idealOfLE_le_of_le (R S : ValuationSubring K) (hR : A ≤ R) (hS : A ≤
     idealOfLE A S hS ≤ idealOfLE A R hR := fun x hx =>
   (valuation_lt_one_iff R _).2
     (by
-      by_contra c; push_neg at c ; replace c := monotone_mapOfLE R S h c
+      by_contra c; push_neg at c; replace c := monotone_mapOfLE R S h c
       rw [(mapOfLE _ _ _).map_one, mapOfLE_valuation_apply] at c
       apply not_le_of_lt ((valuation_lt_one_iff S _).1 hx) c)
 #align valuation_subring.ideal_of_le_le_of_le ValuationSubring.idealOfLE_le_of_le

@@ -389,7 +389,7 @@ def primeSpectrumEquiv : PrimeSpectrum A ≃ {S | A ≤ S} where
   right_inv S := by ext1; simp
 #align valuation_subring.prime_spectrum_equiv ValuationSubring.primeSpectrumEquiv
 
-/-- An ordered variant of `prime_spectrum_equiv`. -/
+/-- An ordered variant of `primeSpectrumEquiv`. -/
 @[simps]
 def primeSpectrumOrderEquiv : (PrimeSpectrum A)ᵒᵈ ≃o {S | A ≤ S} :=
   { primeSpectrumEquiv A with
@@ -480,7 +480,7 @@ def unitGroup : Subgroup Kˣ :=
 theorem mem_unitGroup_iff (x : Kˣ) : x ∈ A.unitGroup ↔ A.valuation x = 1 := Iff.rfl
 #align valuation_subring.mem_unit_group_iff ValuationSubring.mem_unitGroup_iff
 
-/-- For a valuation subring `A`, `A.unit_group` agrees with the units of `A`. -/
+/-- For a valuation subring `A`, `A.unitGroup` agrees with the units of `A`. -/
 def unitGroupMulEquiv : A.unitGroup ≃* Aˣ where
   toFun x :=
     { val := ⟨(x : Kˣ), mem_of_valuation_le_one A _ x.prop.le⟩
@@ -587,7 +587,7 @@ variable {A}
 
 /-- The elements of `A.nonunits` are those of the maximal ideal of `A` after coercion to `K`.
 
-See also `mem_nonunits_iff_exists_mem_maximal_ideal`, which gets rid of the coercion to `K`,
+See also `mem_nonunits_iff_exists_mem_maximalIdeal`, which gets rid of the coercion to `K`,
 at the expense of a more complicated right hand side.
  -/
 theorem coe_mem_nonunits_iff {a : A} : (a : K) ∈ A.nonunits ↔ a ∈ LocalRing.maximalIdeal A :=
@@ -805,16 +805,15 @@ variable {G : Type _} [Group G] [MulSemiringAction G K]
 /-- The action on a valuation subring corresponding to applying the action to every element.
 
 This is available as an instance in the `Pointwise` locale. -/
-def pointwiseHasSmul : SMul G (ValuationSubring K)
-    where smul g
-    S :=-- TODO: if we add `ValuationSubring.map` at a later date, we should use it here
+def pointwiseHasSMul : SMul G (ValuationSubring K) where
+  smul g S :=-- TODO: if we add `ValuationSubring.map` at a later date, we should use it here
     { g • S.toSubring with
       mem_or_inv_mem' := fun x =>
         (mem_or_inv_mem S (g⁻¹ • x)).imp Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr fun h =>
           Subring.mem_pointwise_smul_iff_inv_smul_mem.mpr <| by rwa [smul_inv''] }
-#align valuation_subring.pointwise_has_smul ValuationSubring.pointwiseHasSmul
+#align valuation_subring.pointwise_has_smul ValuationSubring.pointwiseHasSMul
 
-scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSmul
+scoped[Pointwise] attribute [instance] ValuationSubring.pointwiseHasSMul
 
 open scoped Pointwise
 

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Xavier-François Roblot <46200072+xroblot@users.noreply.github.com>